Constellation Pisces on the coordinate plane. Astronomy on the coordinate plane

Great philosopher, a mathematician and physicist who lived in the 17th century, said: “Respect for others gives reason to respect oneself,” “I think, therefore I exist,” “It’s not enough to have a good mind, the main thing is to use it correctly.” So today you and I will create, respecting each other, comprehending our actions, and applying theoretical and practical knowledge in practice. And the topic of the lesson is “Astrology on the coordinate plane.”

And true.

N equality.

T theorem.

4.Very bad rating. E unit.

R radius.

R difference.

7. The point lying on the OX axis is called - A bscissa.

INTERRA And-interesting, n-new, etc.).

Then the guys pronounce it, and I write down the epithets on the “map” created during the lesson, and they write it on their star. Conclusion: “Here she is - the new star of Interra in our sky, and may she illuminate your path of knowledge, ideas, fantasies, discoveries today, tomorrow and always!”

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"Astrology on the coordinate plane"

ASTROLOGY ON THE COORDINATE PLANE

Plotnikova Svetlana Vladimirovna, mathematics teacher of the Municipal Educational Institution of the Novosibirsk District of the Novosibirsk Region “Gusinobrodskaya Secondary School No. 18”

Subject (focus): mathematics.

Children's age: 8-9 grade.

Location: cabinet.

The purpose of this event:

updating knowledge on the topic “ Coordinate plane» and the acquisition of new ones for active inclusion in project activities;

Recall the construction of points and figures on a coordinate plane according to given coordinates, learn to determine the coordinates of points (at the level of educational activities).

Develop the ability to make decisions both independently and in a team.

Be able to navigate the information space.

The great philosopher, mathematician, physicist, who lived in the 17th century, said: “Respect for others gives reason to respect oneself,” “I think, therefore I exist,” “It is not enough to have a good mind, the main thing is to use it correctly.” So today you and I will create, respecting each other, comprehending our actions, and applying theoretical and practical knowledge in practice. And the topic of the lesson is “Astrology on the coordinate plane.”

Guys, today we will talk a little about astrology, the study of the influence of celestial bodies on earthly objects, including humans, although some consider it a pseudoscience. However, throughout the world, astrology, along with genetics and sociology, are an equivalent source from which pedagogy draws the necessary knowledge.

On a cloudless, moonless night, a majestic picture of the starry sky opens up. At first glance, it seems that it is impossible to understand the scattering of stars. But knowing the starry sky is interesting and useful. It has long attracted people. Thousands of years ago, people mentally connected the brightest stars into various figures (constellations) and named them after characters from myths and legends, animals and objects. Different peoples had their own myths and legends about the constellations, their own names, and the number of constellations varied among different peoples.

Today we will try to transfer constellations from the starry sky to the coordinate plane, and also “discover” a new star, which recently lit up in our sky.

Guys, now, in order to repeat the material on the topic “Coordinate Plane,” we will answer the questions of the quiz.

And now I propose to try to transfer the constellations from the starry sky to the coordinate plane. On your desks there are pieces of paper with the image of a coordinate plane, next to them are the coordinates of the points. After constructing the points at the specified coordinates, you need to connect them with segments in the sequence indicated below. The constructed image will be a model of the constellations discussed earlier. Each group must depict 4 constellation models. I wish you success!

After the models are depicted, let's put them on our "universe" (sheets of whatman paper on the board) in the following order: Aries-Taurus-Gemini-Cancer-Leo-Virgo-Libra-Scorpio-Sagittarius-Capricorn-Aquarius-Pisces. The number written in the right corner indicates the serial number of your sign in the arrangement of constellations. I attach constellations to the “Universe”. Guys, each of you has a star, call it by your name, sign it, attach it near your constellation on the map of the universe. The guys attach their constellations to the map.

And now each of you will open the X-Star, which I talked about at the beginning of the lesson. To do this, you must plot the specified points with coordinates in the coordinate system, and then connect them in the specified sequence. I do the construction on the board. Our star has a name that you and I can guess by answering the questions.

Point with coordinates…. the letter with which the word begins is assigned.

1. The expression can be false or And true.

2. An expression with a variable of the form 3x-5≤0. N equality.

3. Statement to be proven. T theorem.

4.Very bad rating. E unit.

5. A segment connecting the center of a circle to any point on the circle. R radius.

6. Subtraction can be called differently - R difference.

7. The point lying on the OX axis is called - A bscissa.

Tell me, guys, what is the name of our star - INTERRA. And now, guys, I give you a few minutes so that you give our star some characteristic, distinctive properties and qualities inherent only to it. The letters that make up the name of our star will help you with this. The guys in groups come up with (for example, And-interesting, n-new, etc.).

Then the guys pronounce it, and I write down the epithets on the “map” created during the lesson, and they write it on their star. Conclusion: “Here she is, the new star of Interra in our sky, and may she illuminate your path of knowledge, ideas, fantasies, discoveries today, tomorrow and always!”

Municipal budgetary educational institution

Isaevskaya basic secondary school

Zodiac signs on

coordinate plane

Completed by: 6th grade students

Banko Tatyana Sergeevna

Vorobyov Sergey Stanislavovich

Head: Shevakov Andrey Ivanovich

mathematic teacher

Kh. Isaev

2016

Brief summary

This work contains two main aspects of the study: theoretical and practical. First side research work is to identify the basic concepts: the history of the origin of the coordinate plane, who and how represented the coordinate plane, what is the significance of the coordinate plane and the signs of the zodiac.

The second part is to construct 12 zodiac signs in the coordinate plane.

Results of a survey among classmates. Who was born, under what zodiac sign.

1. Introduction.

We live in a huge world full of mysteries and wonders. Throughout its history, humanity has tried to unravel them, strived for new knowledge and discoveries....

Since childhood, everyone loves to look at the stars in the sky. We always liked watching the starry sky. But then we had no idea that in addition to their beautiful location in the sky, you can learn about the zodiac constellations unique, interesting myths and legends, theories of origin and much more about the signs of the Zodiac. We decided to explore the signs of the Zodiac using the coordinate plane, because I really love mathematics.

Many people know about the zodiac constellations, but not everyone can find them. This work is aimed at constructing the signs of the Zodiac on the coordinate plane.

Purpose: consideration of the signs of the Zodiac through the theory of the coordinate plane.

Tasks:

1) Get acquainted with the history of the origin of coordinates.

2) Study the zodiac constellations.

3) Construct an image of the constellation on the coordinate plane.

4) Conduct astrological research on school students.

Content

1. Introduction………………………………………...........……………………

2. History of the origin of coordinates……………………………………….

4. The starry sky and the legend of the 12 signs of the Zodiac…………………………

5. Twelve constellations.................................................... ...............................

6. Zodiac signs in coordinates…………………...……………….

7. Astrological research of schoolchildren…………….......………..

8. Interesting facts about the elements……………………………………..

9. List of references……………………………………………………...……………….

10. Conclusion……………………………………………………………….…………….

2. History of the origin of coordinates.

200 years BC, the Greek scientist Hipparchus introduced geographical coordinates. He suggested drawing on geographical map parallels and meridians and indicate latitude and longitude with numbers. Using these two numbers, you can accurately determine the position of an island, village, mountain or well in the desert and plot them on a map or globe.

Eastern longitude and northern latitude are indicated by numbers with a plus sign, and western longitude and southern latitude by numbers with a minus sign. Thus, a pair of signed numbers uniquely identifies a point on the globe.

The writer Jules Verne has some novels based on situations related to geographical coordinates. These are the novels "The Amazing Adventures of Uncle Antifer" and "The Children of Captain Grant."

For a long time Only geography - "land description" - used this wonderful invention, and only in the 14th century the French mathematician Nicolas Orsem (1323-1382) tried to apply it to "land measurement" - geometry. He proposed to cover the plane with a rectangular grid and call latitude and longitude what we now call abscissa and ordinate.

Based on this successful innovation, the coordinate method arose, linking geometry with algebra. The main credit for the creation of this method belongs to the great French mathematician Rene Descartes (1596 - 1650). In his honor, such a coordinate system is called Cartesian, denoting the location of any point on the plane by the distances from this point to the “zero latitude” - the abscissa axis and the “zero meridian” - the ordinate axis. According to the tradition introduced by Descartes, the “latitude” of a point is denoted by the letter x, "longitude" - the letter "y".

We need to select a certain plane and introduce a Cartesian coordinate system on it, and compare to our point the coordinates of its projection onto this plane and the distance from it to the plane, taken with a plus sign for one half of the space and with a minus sign for the other; this way we get a Cartesian coordinate system.

4.Starry sky and the legend of the 12 signs of the Zodiac.

Astrology is the science of the influence of stars, constellations and planets on humans and the Earth. Among the 88 constellations that decorate the night sky, a special place is occupied by those among which the Sun passes its annual path. Twelve constellations on the path of the Sun: Aries, Taurus, Gemini, Cancer, Leo, Virgo, Libra, Scorpio, Sagittarius, Capricorn, Aquarius, Pisces. The sun passes through every sign of the Zodiac, but according to legend Ancient Greece, The Sun moves through 13 signs. The thirteenth is Ophiuchus, but according to ancient traditions it is not classified as a zodiac constellation.

Most of the names belong to animals, so these constellations received the names of the zodiac (from the Greek zodiakos - “animal circle”).

In fact, of course, the Earth moves around its star, but it seems to us that it is the Sun that changes its location. The ancient astronomers thought so too, giving names to the zodiacal constellations.

They noticed that the Sun always walks across the sky one way and every month “visits” the signs of the Zodiac: in January - Capricorn, in February - Aquarius, in March - Pisces... It has long been believed that the sign of the Zodiac, that is, The month of a person’s birth determines his character, influences his behavior and predetermines his fate. Each zodiac sign has its own legend about its origin, here are a few of them:

Lion - a huge lion settled not far from Nemea. Horror gripped the people when they heard his roar. The people did not leave their homes, hunger set in, and illness began.

The valiant Hercules decided to kill Nemean Lion. Hercules wandered for a long time along the slopes of the mountains. The sun began to set. And then a terrifying roar reached the hero. In several jumps, Hercules reached the lion's den - a huge cave with two exits. When a giant beast emerged from the cave with a roar, Hercules showered it with arrows, but none of them even wounded the monster. Then Hercules threw away his bow and attacked the lion with a club. With a powerful blow to the head, the hero stunned the beast, grabbed him by the neck with his powerful hands and strangled him.

Having shouldered a huge carcass, Hercules went to Nemea. There he made a sacrifice to Zeus and established the Nemean Games in memory of this feat. And he began to wear lion skin instead of a cloak.

Cancer - when Hercules went to fight the hydra, a huge Cancer crawled out of the reeds to meet him and grabbed Hercules by the leg. The angry Hercules crushed him, thereby inadvertently eliminating another enemy.

Capricorn - when the day of the winter solstice arrived, the hour had come for the great Zeus to be born. Rhea, the goddess, wrapped a stone in swaddling clothes and handed it to her formidable husband. The evil husband did not notice the substitution and swallowed it. The goddess hid the newborn Zeus in a deep cave on the island of Crete, leaving him in the care of the forest nymphs. And the goat Amalthea fed him with her milk. The years flew by. Zeus grew up and matured. Rebelling against his father, he freed his divine brothers and sisters, becoming the leader between them. Zeus did not forget his nurse, the goat Amalthea, placing her in the sky - this is the constellation CAPRICORN.

Virgo - seeing human greed and malice, the gods decided to leave this vicious world. Virgin Astraea, goddess of justice, daughter of the almighty Zeus and the goddess of justice Themis, the latter left the earth. Astraea was transported to the sky and turned into the constellation VIRGO.

Libra - when Astraea was transported to the sky and turned into the constellation VIRGO. In her hands she holds SCALES - a symbol of justice, harmony and equality.

Aquarius - in memory of the Great Flood, Zeus lit the constellation AQUARIUS in the sky. The Greeks called it Hydrochos, the Romans called it Acuarius, and the Arabs called it Sakib - alma. All this means the same thing: a person pouring water.

Pisces - once upon a time, the goddess of love and beauty Aphrodite and her son Eros walked along the bank of a river, near which the wild Typhon, who had escaped from the dungeon, hid. Suddenly the ferocious Typhon attacked them. Horrified by his wild appearance, the immortals rushed into the water, turned into sparkling fish and swam away from the vile monster. This is how Aphrodite and her son Eros were saved, and the constellation FISH shone in the sky in honor of this.

Scorpio - Hera placed Scorpio in heaven because he killed the evil hunter Orion, who decided to exterminate all animals on earth.

In order to navigate the star maze, people combined the brightest stars into geometric figures, or constellations, they gave them the names of heroes, gods and animals. With the help of the teacher, I built constellations according to the proposed coordinates.

Constellation Ursa Major

(-1 0 ; 5 ), (- 6 ;5), (- 4 ; 4 ), (-1 ; 3 )
(- 1 ; 1 ), (4 ;0), (6 ; 3 ), (-1 ; 3 )

Constellation “Taurus”

1. (11;-1), (10;1), (6;1), (3;-1), (5;-3)
(3;-1), (6;1), (3;2), (2;3), (-2;6), (-8;8)

2. (3;2), (0;2), (-10;5).

Constellation "Sagittarius"

1. (-4;-6), (-8;-6), (-4;-8), (-8;-6), (-9;1), (-5;2), (-2;2), (0;0) , (3;1) , (6;2), (7;-1), (9;-1), (12;0).

2. (9;4), (6;2), (7;-1), (6;-4), (7;-6)

3. (3;1), (1;2), (-1;1), (1;2), (-1;5), (-4;8), (-1;5) , (0;6).

Constellation “Virgo”

1. (-8;-3), (-5;-3), (-4;-5), (2;-5), (3;-2), (6;0), (9;1), (13;3), (14;6), (11;7).

2. (2;-5), (1;1), (-2;2), (-9;2).

3. (1;1), (5;3), (4;8), (5;3), (6;0).

Constellation “Libra”

(-4;5), (-3;3), (1;5)
(4;9), (8;5), (6;0), (4;9)
(6;0), (0;-3).

Constellation “Leo”

(10;6), (9;4), (7;4), (5;5), (2;4), (2;2),
(4;-1), (8;-2), (4;-1), (-5;0), (-7;-3), (-7;-5), (-7;-3), (-5;0), (-9;0), (-5;2), (2;2).

Constellation “ Cancer ”

(- 2 ; 8 ), (- 1 ; 1 ), ( -2 ; -2 ), ( -7 ;- 7 ), ( -2 ;- 2 ) ,
( 6 ; 8).

Constellation “Aquarius”

1. (-7;-7), (-4;-3), (-4;1), (-7;2), (-1;7)
(0;5), (3;7), (1;1), (2;-3).

2. (3;7) (7;3) (13;1).

Constellation "Gemini"

1. (3 ;-2), (-3;1), (-7;3), (-7;5), (-4;7),

(0;6), (6;3), (10;2), (12;2), (10;2),

(7;-2), (5;-4), (7;-2), (2;-1), (-3;1).

Constellation "Pisces"

(10;-7), (12;-6), (14;-8), (12;-9), (10;-9), (10;-7), (6;-6), (0;-6) , (-7;-7) , (-11;-9), (-7;-8), (-11;-9), (-4;6), (-5;8), (-4;10).

Constellation "Scorpio"

(-7;1), (-7;-1) , (-5;-3), (-3;-3), (-1;-2), (0;0) , (1;2), (4;5) , (5;5), (9;6), (8;8), (8;12), (7;9).

Constellation “Aries”

(-7;-2), (-3;0), (0;6), (10;2)
(13;0), (13;-1)

Constellation "Capricorn"

(7;7), (6;5), (1;-2), (-6;0), (-9;3),

(2;3), (6;5).

Constellation Ursa Major (Slide 5)

CONSTELLATION OF ARIES.

The constellation Aries was highly revered in ancient times. Supreme God In Egypt, Amon-Ra was depicted with a ram's head, and the road to his temple was an alley of sphinxes with ram's heads. It was believed that the constellation Aries was named after Aries with the Golden Fleece, after which the Argonauts sailed. By the way, there are a number of constellations in the sky that reflect the Argo Ship. The alpha (brightest) star of this constellation is called Gamal (Arabic for “adult ram”)

CONSTELLATION TAURUS . (Slide 7)

Among the ancient peoples, the most important constellation was Taurus, since New Year began in the spring. In the zodiac, Taurus is the most ancient constellation, since cattle breeding played a huge role in the life of ancient peoples, and the bull (Taurus) was associated with the constellation where the Sun seemed to conquer winter and herald the arrival of spring and summer. In general, many ancient peoples revered this animal and considered it sacred. IN Ancient Egypt there was the sacred bull Apis, who was worshiped during his lifetime and whose mummy was solemnly buried in a magnificent tomb. Every 25 years Apis was replaced with a new one. In Greece, the bull was also held in high esteem. In Crete the bull was called Minotaur. The heroes of Hellas Hercules, Theseus, Jason pacified the bulls.

WHERE ARE THE TWINS IN SKY FROM? (Slide 8)

In this constellation, two bright stars are very close to each other. They received their name in honor of the Argonauts Dioscuri - Castor and Pollux - twins, sons of Zeus, the most powerful of the Olympian gods. Castor was famous as a skilled charioteer, and Pollux as an unsurpassed fist fighter. They took part in the Argonauts' campaign and the Calydonian hunt. But one day the Dioscuri did not share the spoils with their cousins, the giants Idas and Lynceus. In the battle with them, the brothers were severely wounded. And when Castor died, the immortal Pollux did not want to part with his brother and asked Zeus not to separate them. The Dioscuri brothers were considered in ancient times to be the patrons of sailors caught in a storm.

CONSTELLATION CANCER. (Slide 9)

The constellation Cancer is one of the most inconspicuous zodiac constellations. His story is very interesting. Cancer moves tail first. About two thousand years ago there was a point in the constellation Cancer summer solstice(i.e. the longest daylight hours). The sun, having reached its maximum distance at this time, began to “back away” to the north. The length of the day gradually decreased. According to classical ancient mythology a huge sea Cancer attacked Hercules while he was fighting the Hydra. The hero crushed him, but the goddess Hera, who hated Hercules, placed Cancer in heaven. The Louvre houses the famous Egyptian circle of the zodiac, in which the constellation Cancer is located above all others.

CONSTELLATION LEO. (Slide 10)

About 4.5 thousand years ago, the summer solstice point was located in this constellation, and the Sun was in this constellation during the hottest time of the year. Therefore, among many peoples, it was the Lion that became the symbol of fire. The Assyrians called this constellation “the great fire,” and the Chaldeans associated the fierce lion with the no less fierce heat that occurred every summer. They believed that the Sun received additional strength and warmth by being among the stars of Leo. In Egypt, this constellation was also associated with the summer period: flocks of lions, escaping the heat, migrated from the desert to the Nile valley, which was flooding at that time. Therefore, the Egyptians placed images in the form of a lion's head with an open mouth on the gates of irrigation canals that directed water to the fields.

VIRGO. (Slide 11)

The constellation Virgo, located next to Leo, this constellation was sometimes represented by the fairy-tale sphinx - a mythical creature with the body of a lion and the head of a woman. Often in early myths, the Virgin was identified with Rhea, the mother of the god Zeus. There is information that in this constellation ancient observers saw Astraea, the daughter of Themis and the god Zeus - the goddess of justice, a symbol of purity and innocence, who left the Earth due to the crimes of people. The Virgin is usually depicted with the rod of Mercury and an ear of corn, which indicates the connection of this star with human agricultural activities. It is possible that her appearance in the sky coincided with the beginning of some agricultural work.

SCALES -

THE ONLY “NON-LIVING” CONSTELLATION. (Slide 12)

Over two thousand years ago in this constellation there was a point autumn equinox. The equality of day and night could be one of the reasons why the zodiac constellation received the name “Libra”. Scales - a symbol of balance - could simply remind ancient farmers of the need to weigh the harvest. One of the myths explains the appearance of the zodiac constellation Libra as a reminder to people of the need to strictly observe the laws. On behalf of Zeus and Themis, their daughter Astraea regularly “inspected” the Earth (armed with scales and blindfolded, in order to judge everything objectively and mercilessly punish deceivers, liars and everyone who dared to commit all kinds of unjust acts). So Zeus decided that his daughter’s Libra should be placed in heaven.

CONSTELLATION SCORPIO. (Slide 13)

Not only because of its external similarity, this constellation was assigned the role of a poisonous creature. The sun entered this area of the sky in late autumn, when all nature seemed to be dying, to be reborn again, like the god Dionysus, in early spring next year. The sun was considered to have been “stinged” by some poisonous creature (by the way, in this area of the sky there is also the constellation Snake!), “as a result of which it was sick” all winter, remaining weak and pale. It was he, the heavenly Scorpio, who most frightened the unfortunate Phaeton, the son of the god Helios, who decided to ride across the sky on his fiery chariot, without listening to his father’s warnings. According to many astronomers, the sign of Scorpio is the most sinister - a symbol of death. It seemed especially scary when the planet of disasters - Saturn - appeared in it. Scorpio is a constellation where new stars often flare up.

WHO IS THE STAR SAGITTARIUS AIMING AT? (Slide 14)

Even Scorpio himself is afraid of the evil Sagittarius, at whom he aims with a bow. Sometimes you can find an image of Sagittarius in the form of a centaur with two faces: one facing backward, the other forward. In this way he resembles the Roman god Janus. The first month of the year, January, is associated with the name Janus. And the Sun is in Sagittarius in winter. Thus, the constellation seems to symbolize the end of the old and the beginning of the new year, with one of its faces looking into the past, and the other into the future. In the direction of the constellation Sagittarius is the center of our Galaxy.

CONSTELLATION CAPRICORN. (Slide 15)

Capricorn - mythical creature with the body of a goat and the tail of a fish. According to the most widespread ancient Greek legend, the goat-footed god Pan, son of Hermes, patron of shepherds, was frightened by the hundred-headed giant Typhon and threw himself into the water in horror. From then on he became a water god and grew a fish tail. Transformed into a constellation by the god Zeus, Capricorn became the ruler of the waters and the harbinger of storms. It was believed that he sent abundant rains to the earth. Many ancient peoples revered the goat as a sacred animal, and services were held in honor of the goat. People dressed in sacred clothes made of goat skins and brought a gift to the gods - a sacrificial goat. It is with such customs and with this constellation that the idea of a “scapegoat” is associated. First, a sacrifice was made to God, and then another goat was brought to the high priest, on which he laid his hands and thereby, as it were, transferred to him all the sins of the people. And after that the goat was released into the desert.

WHERE DOES AQUARIUS POUR WATER? (Slide 16)

Associated with the constellation Aquarius is the myth of Noah and his family - the only people who escaped from global flood in the ark. The name of the constellation leads to the “homeland of the Flood” in the valley of the Tigris and Euphrates rivers. In some letters ancient people- Sumerians - these two rivers are depicted flowing from the vessel of Aquarius. In Egypt, the constellation Aquarius was observed in the sky on the days of the highest water level in the Nile River. It was believed that the god of water was throwing a huge ladle into the Nile. It is possible that the legend about one of the labors of Hercules is connected with the constellation Aquarius - the cleaning of the Augean stables (for which the hero needed to dam three rivers).

FISH CLOSING THE RING OF THE ZODIAC CONSTELLATIONS. (Slide 17)

The very arrangement of the stars in the sky suggests the idea of two fish tied together with a ribbon or rope. The origin of the name of the constellation Pisces is very ancient. The Sun entered this constellation at the time of rich fishing. The goddess of fertility was depicted as a woman with a fish tail, which, as legend has it, appeared when she and her son, frightened by a monster, threw themselves into the water.

SIGNS AND CONSTELLATIONS OF THE ZODIAC

Background stars located in the ecliptic plane are united into the so-called zodiacal constellations.

(Slide 18)

Each constellation corresponds to a zodiac sign

There are 12 zodiac constellations in total. These are Aries, Taurus, Gemini, Cancer, Leo, Virgo, Libra, Scorpio, Sagittarius, Capricorn, Aquarius, Pisces.

These names arose in ancient times. The word “zodiac” itself (in Greekzodiakos) comes from the word "zoon“-“animal”, since most constellations have been given the names of various animals by popular fantasy.

Zodiac
(1961 Valishin Yu.I.)

Looking at the zodiac belt,
We will see Cancer in January,
And in February we will notice Leo.
His keeper was
In cold March, the evil Virgin,
Leo's neighbor in the sky on the left.
Having bought myself a scale in April,
They wanted to live in peace
But in March the terrible Scorpio
They were robbed of peace and sleep.
The beautiful Sagittarius killed him,
Father June's son is unhappy,
In July, brother Capricorn
The dream of Leo and Virgo saved
And in August for many days
Uncle Aquarius has arrived.
From Pisces to the ear he is in September
Cooked and ate in the yard,
Roasted Aries in October
Taurus stabbed to death in November
And in December, in the end,
A pair of Geminis was born.

2.5.1. Constellation Aries.

The beginning of the zodiac is considered to beAries constellation , here 2 thousand years ago the point of the vernal equinox was located. Over the past time, it has shifted greatly and is now located in the constellation Pisces; it is still designated by the sign of the constellation Aries. When the sun is at this point and moves from the Southern hemisphere of the celestial sphere to the Northern, astronomical spring begins.

It is most convenient to observe the constellation in the fall, when the sun is far from it.

Constellation Taurus.

Taurus - one of the most beautiful winter constellations. In November - December it is observed almost all night. 125 stars are visible to the naked eye. The brightest - Aldebaran - is red-orange in color (its temperature is about 3500°). Near Aldebaran it is easy to see the placer, not very bright stars forming a triangle (Taurus muzzle).
2.5.3. Constellation Gemini.Twins - the northernmost of the zodiac constellations. Observed in winter. Its brightest stars are Castor and Pollux. This was the name of the twin brothers who went with Jason on a campaign for the Golden Fleece. The brighter Pollux is orange in color. Upon closer inspection, this star turns out to be a system of four stars.

2.5.4. Constellation Cancer.

The constellation Cancer is best observed in the spring. The Roman scientist Pliny the Elder wrote about him: “In the sign of Cancer there are two small stars called Donkeys, and among them is a small cloud called the Manger.” A “foggy star” (Manger) is really visible between them.

2.5.5. Constellation Leo.

Zodiac constellation Leo best seen during the spring months. It’s easy to find: A clear trapezoid of four bright stars forms the torso of Leo, and a curved chain of weaker stars forms the head and mane of the king of beasts. Regulus is the main star of the constellation, which has 2 satellites, one of them is a star very similar to the Sun. Regulus is a white hot, rather large star, it is almost 3 times larger than the Sun, and in terms of the amount of emitted light energy it exceeds it 140 times.

2.5.6. Virgo constellation.

The ancient Greeks called this constellation Parthenos, which in Greek means "Virgo". The heavenly maiden is often depicted with a sheaf of ears of grain in her hands, and the name of her main star, Spica, is translated from Greek as “ear of grain.” The constellation was known in ancient times and was usually associated with the beginning of the harvest.

2.5.7. Constellation Libra.

Small constellation Libra appeared on star maps relatively recently. The name of the constellation is due to the fact that in ancient times it was the location of the autumnal equinox. The ancient Roman poet Virgil wrote: “When Libra equalizes the hours of day and night and divides equally light and darkness in the world, then, farmer, take your working oxen to the field.”
2.5.8. Constellation Scorpio.

Scorpion - constellation of the southern sky. The most prominent star is Antares. This is a double star, a red giant, quite bright. Antares can compete with Mars in brilliance and color. But it is not difficult to distinguish the luminaries. Mars shines evenly, and Antares, like all stars, flickers.

2.5.9. Constellation Sagittarius.Sagittarius constellation located near the Milky Way. Ancient Greek myths tell about the wise centaur Chiron, who created the first model of the celestial sphere, and left one place for himself. But another centaur, the cunning and cunning Krotos, took this place by deception, becoming the constellation Sagittarius. Zeus nevertheless placed Chiron in the sky, turning it into the constellation Centaur. And the evil Sagittarius behaves belligerently even in the sky, aiming his bow at Scorpio.

2.5.10. Constellation Capricorn.

This mythical creature with the body of a goat and the tail of a fish gave its name to one of the constellations of the zodiac. An ancient Greek legend tells how the goat-footed god Pan, the patron of shepherds, met the hundred-headed giant Typhon and threw himself into the water in horror. After this, Pan grew a fish tail, and he also became a water god. The stars of the constellation are not very interesting. It is curious that the star Algedi Capricorn is double. Physically, these 2 luminaries are not connected; they are moving away from each other in different directions. These stars are called optical binaries.

2.5.11. Constellation Aquarius.

In this zodiac constellation different peoples I saw a man pouring water. The name of the constellation most likely came from Mesopotamia. IN constellation Aquarius About 90 stars can be seen with the naked eye. One of the largest planetary nebulae is located here.

2.5.12. Constellation Pisces.

"Water" Pisces constellation - the last in the circle of the zodiac. It is visible in the sky in autumn, and the Sun comes into it at the end of winter. Main star Pisces – Alrisha, translated means “lace”. Through binoculars it is visible as a bluish star, and a telescope allows you to see a satellite of the same color.

7. Astrological research of students of the Isaev school.

Elements of students of the Isaevskaya school.

8. Interesting facts about the elements.

Element of Fire. The characteristics of this element are warmth and dryness, which are accompanied by metaphysical energy, life and its power. There are 3 signs in the Zodiac that have these qualities, the so-called. fire trine (triangle): Aries, Leo, Sagittarius. The Fire trine is considered a creative trine. Principle: action, activity, energy.

Fire is the main controlling force of instinct, spirit, thought and mind, forcing us to move forward, believe, hope, and defend our convictions. The main driving force of Fire is ambition. Fire gives zeal, impatience, carelessness, self-confidence, temper, impetuosity, courage, courage, belligerence. It supports life in the human body, is responsible for temperature control and stimulates metabolism.

People in whose horoscopes the trine of the Fire element is highlighted have a choleric temperament. These people will never go unnoticed; they will achieve recognition from others, especially in an environment that is close to them in spirit and ideologically connected with them. These people have a creative spirit and unshakable will, inexhaustible “Martian energy” and extraordinary penetrating power. The Fire element gives organizational talent, a thirst for activity and enterprise. Fire knows the power of self-esteem.

Element of Earth. The characteristics of this element are cold and dryness, metaphysical matter, strength and density. In the Zodiac, this element is represented by the earth's trine (triangle): Taurus, Virgo, Capricorn. The Earth trine is considered a materialistic trine. Principle: stability.

The earth creates forms, laws, gives concreteness, stability, stability. The earth structures, analyzes, classifies, creates the foundation. She is characterized by such qualities as inertia, confidence, practicality, reliability, patience, rigor. In the body, the Earth gives inhibition, petrification through contraction and compression, and slows down the metabolic process.

People whose horoscopes express the element of Earth have a melancholic temperament. These are people of sober reason and prudence, very practical and businesslike. The goal of their life is always real and achievable, and the path to this goal is outlined already in their young years. If they deviate from their goal, it is very slightly and then more due to internal reasons than external ones. People of this trine achieve success thanks to such excellent character traits as perseverance, perseverance, endurance, endurance, determination, and steadfastness. They do not have such imagination and a bright, lively imagination as the signs of the Water trine, they do not have utopian ideas like the signs of Fire, but they persistently pursue their goal and always achieve it. They choose the path of least external resistance, and when obstacles arise, they mobilize their strength and energy to overcome everything that prevents them from achieving their intended goal.

Element of Air. Features of this element are warmth and humidity, flexibility, divisibility, adaptability. In the Zodiac, these qualities correspond to the air trine (triangle): Gemini, Libra and Aquarius. The trine of Air is considered the trine of ideas and intellectuality. Principle: exchange, contact.

Air determines contacts and relationships. The element of Air endows a person with such qualities as mobility, activity, liveliness, changeability, flexibility, agility, receptivity, omnipresence, limitlessness, curiosity. The air is independent, free.

People whose horoscopes express the element of Air have a sanguine temperament. Such people can make an impression. They are quick in decisions and deeds, easily and quickly grasp any information, then pass it all on to other people, processed in their own way. They instantly adapt to any changes and changes in life. They are characterized by spiritual flexibility, mental lability, mental mobility, they are tireless as long as they are passionate about something. The monotony tires them.

Element of Water. Features of this element are cold and humidity, metaphysical sensitivity, feeling, perception. There are 3 signs of this quality in the Zodiac - a water trine (triangle): Cancer, Scorpio, Pisces. The Water trine is considered the trine of feelings and sensations. Principle: internal constancy despite external variability. Water is emotions, inner peace, preservation, memory. She is plastic, changeable, secretive. Gives such qualities as uncertainty, daydreaming, imaginative thinking, gentleness of manifestation. It slows down metabolism in the body, controls fluids and the work of endocrine glands.

People whose horoscopes express the element of Water have a phlegmatic temperament. These people have great sensitivity, are very receptive and impressionable, thinking, living more inner life than external. People of the Water trine are usually contemplative, they think about both their own good and the good of their loved ones, however, at times they can be indifferent, lethargic, and lazy, with the exception of people of the Scorpio sign. Their external manifestation of feelings is not as pronounced as that of representatives of the Fire or Air trigons, but they experience internal feelings with great strength and depth.

Of the signs of the Water trine, Scorpio is the strongest in body and spirit, the most meaningful, the most aggressive, not susceptible to unwanted influence from the outside and showing strong resistance to everything with which his soul does not agree. His patience, endurance, tenacity and perseverance are simply amazing.

9. List of references.

1. Book "Unsolved Mysteries of Humanity" JSC "Reader's Digest Publishing House", France, 2004.

2. Book "All the Secrets of the World" JSC "Reader's Digest Publishing House", France, 2001.

3. Book "Only the Facts" JSC "Reader's Digest Publishing House", Hong Kong, 2004.

4. http://images.yandex.ru

5. http://cat.convdocs.org/docs/index-47882.html

7. http://www.myshared.ru/slide/473666/

10. Conclusion.

In the course of my work, I became acquainted with the history of the origin of coordinates, learned about different types of coordinate systems, their features, origin and purpose. Having done a lot of work on studying the zodiac constellations, we came to the conclusion that the world of zodiac signs is that beautiful line that connects a person with the mysterious cosmos and distant stars. Studying the signs of the Zodiac, we built 4 signs on the coordinate plane. Having systematized the knowledge gained, we were able to conduct astrological research among students at our school.

3. Conclusions.

In the course of my work, we became acquainted with the history of the origin of coordinates, learned about different types of coordinate systems, their features, origin and purpose. Having done a lot of work on studying the zodiac constellations and plotting them on the coordinate plane, we came to the conclusion that the world of zodiac signs is that beautiful line that connects a person with the mysterious cosmos and distant stars. Having systematized the knowledge gained, we were able to conduct astrological research among school students.

Annex 1. Zodiac signs of school studentsAppendix 2. Elements of school students.

Objective of the project:

Study the zodiac constellations.

Construct an image of the constellation on the coordinate plane.

Conduct astrological research for 6th grade B students.

Project objectives:

get acquainted with the history of the origin of the coordinate plane;

expand the scope of knowledge within the chosen topic;

create cards"Constructions in a rectangular coordinate system."

Project issues:

1) Why do we need coordinates in a person’s life?

2) Who entered the coordinates and created the coordinate system?

3) What constructions can be performed in a rectangular coordinate system?.

Relevance of the project: Working in a rectangular coordinate system involves drawing it, constructing a single segment - working with measuring instruments, which allows you to combine visual and mental activity. Problems with the coordinate plane are interesting and varied, which contributes to better understanding of the topic and develops interest in the subject.

Stages of work on the project:

Determining the theme of the project.

Collection and systematization of materials in accordance with the topic.

Analysis of acquired knowledge, design of the project, creation of a presentation, information booklet.

Presentation and defense of the project.

List of information resources used:

References

Internet

ANNOTATION

Coordinates occur in our lives every hour.

The coordinate system is used in cinemas, in transport, and in geography there is a coordinate system.

Do coordinate systems have only two quantities?

Everyone can play sea battle, and this game uses coordinates.

How do pilots navigate the sky?

The position of the stars probably also has coordinates?

This is all found in modern life.

But an interesting fact is how long has the coordinate system permeated the practical life of a person?

What constructions can be performed in the coordinate plane?

The hypothesis of our project is: “To know in order to be able to”

1. Introduction…………………………………………...........………………………2

2. History of the origin of coordinates…………………………………….4

3. Types of coordinate systems……………………………………………5

4. The starry sky and the legend of the 12 signs of the Zodiac…………………………5-7

5. Twelve constellations.................................................... ...........................6-11

6. Zodiac signs in coordinates……………….............……………….12-13

7. Astrological studies 6 “B” class…………….......…….14-15

8. Interesting facts about the elements…………………………………………..16

9. Conclusion……………………………………………………………17

10. References……………………………………...……………..18

11.Appendix……………………………………………………………

Introduction.

We live in a huge world full of mysteries and wonders. Throughout its history, humanity has tried to unravel them, strived for new knowledge and discoveries....

Since childhood, everyone loves to look at the stars in the sky. I have always liked watching the starry sky.But then I had no idea that in addition to their beautiful location in the sky, you can learn about the zodiac constellations unique, interesting myths and legends, theories of origin and much more about the signs of the zodiac. We decided to explore the signs of the Zodiac using the coordinate plane, because we love mathematics.

Many people know about the zodiac constellations, but not everyone can find them. This work is aimed at constructing the signs of the Zodiac on the coordinate plane.

Coordinate translated from Greek means “ordered”; a coordinate system is a rule by which the position of an object is determined.

The word “system” is also of Greek origin: “Theme” is something given, “sis” is made up of parts. Thus, a “system” is something given, made up of parts (or a clearly dissected whole).

Coordinate systems permeate the entire practical life of a person. For example, using a geographic map, you can determine the address of any point using geographic coordinates. To do this, you need to know two parts of the address - latitude and longitude. Latitude is determined using a “parallel” - an imaginary line on the surface of the Earth drawn at the same distance from the equator. Longitude - along the “meridian” - an imaginary line on the surface of the Earth connecting the North and South Poles along the shortest distance. Parallels are lines of direction west - east, meridians show the direction north - south. Sound familiar? Rectangular coordinate system.

How do pilots navigate the sky? Does the position of stars in the sky also have coordinates?

This is all found in modern life. But an interesting fact is how long has the coordinate system permeated the practical life of a person?

2. History of the origin of the coordinate system.

The history of the origin of coordinates and the coordinate system begins a very long time ago; initially, the idea of the coordinate method arose in the ancient world in connection with the needs of astronomy, geography, and painting. The ancient Greek scientist Anaximander of Miletus (c. 610-546 BC) is considered the compiler of the first geographical map. He clearly described the latitude and longitude of a place using rectangular projections.

More than 200 years BC, the Greek scientist Hipparchus proposed encircling the globe on a map with parallels and meridians and introducing the now well-known geographical coordinates: latitude and longitude and designating them with numbers.

The idea of depicting numbers as dots, and giving numerical designations to the dots, originated in ancient times. The initial use of coordinates is associated with astronomy and geography, with the need to determine the position of luminaries in the sky and certain points on the surface of the Earth, when compiling a calendar, star and geographical maps. Traces of the application of the idea of rectangular coordinates in the form of a square grid (palette) are depicted on the wall of one of the burial chambers of Ancient Egypt.

Already in IIV. The ancient Greek astronomer Claudius Ptolemy used latitude and longitude as coordinates.

The main credit for creating the modern coordinate method belongs to the French mathematician Rene Descartes. A story has survived to this day that prompted him to make the discovery. Taking seats in the theater according to the purchased tickets, we do not even suspect who and when proposed the method of numbering seats by rows and seats that has become common in our lives.

Scientific description of the rectangular coordinate systemRene Descartesfirst made in his work “Discourse on Method” in 1637. Therefore, the rectangular coordinate system is also called the Cartesian coordinate system. In the Cartesian coordinate system, negative numbers received a real interpretation.

Pierre Fermat also contributed to the development of the coordinate method, but his works were first published after his death.

Descartes and Fermat used the coordinate method only on the plane. The coordinate method for three-dimensional space was first used by Leonhard Euler already in the 18th century.

The terms “abscissa” and “ordinate” (derived from the Latin words “cut off” and “ordered”) were introduced in the 70-80s.XVIIV. German mathematician Wilhelm Leibniz.

3. Types of coordinate systems.

The position of any point in space (in particular, on a plane) can be determined using one or another coordinate system.

The numbers that determine the position of a point are called the coordinates of that point.

The most commonly used coordinate systems are rectangular.

In addition to rectangular coordinate systems, there are oblique systems. Rectangular and oblique coordinate systems are combined under the nameCartesian coordinate systems .

Sometimes coordinate systems are used on a plane, and in space - or coordinate systems.

A generalization of all the listed coordinate systems are coordinate systems.

But as they say, it is better to see once than to hear a hundred times.

A detailed acquaintance with them will happen much later.

4.Starry sky and the legend of the 12 signs of the Zodiac.

Astrology is the science of the influence of stars, constellations and planets on humans and the Earth. Among the 88 constellations that decorate the night sky, a special place is occupied by those among which the Sun passes its annual path. Twelve constellations on the path of the Sun: Aries, Taurus, Gemini, Cancer, Leo, Virgo, Libra, Scorpio, Sagittarius, Capricorn, Aquarius, Pisces. The Sun passes through every sign of the Zodiac, but according to the legend of Ancient Greece, the Sun passes through 13 signs. The thirteenth is Ophiuchus, but according to ancient traditions it is not included in the zodiac constellations.

Most of the names belong to animals, which is why these constellations are namedzodiac (from Greek zodiacos - “animal circle”).

Lion – a huge lion settled near Nemea. Horror gripped the people when they heard his roar. The people did not leave their homes, hunger set in, and illness began.

The valiant Hercules decided to kill the Nemean lion. Hercules wandered for a long time along the slopes of the mountains. The sun began to set. And then a terrifying roar reached the hero. In several jumps, Hercules reached the lion's den - a huge cave with two exits. When a giant beast emerged from the cave with a roar, Hercules showered it with arrows, but none of them even wounded the monster. Then Hercules threw away his bow and attacked the lion with a club. With a powerful blow to the head, the hero stunned the beast, grabbed him by the neck with his powerful hands and strangled him.

Having shouldered a huge carcass, Hercules went to Nemea. There he made a sacrifice to Zeus and established the Nemean Games in memory of this feat. And he began to wear lion skin instead of a cloak.

Capricorn - when the day of the winter solstice arrived, the hour had come for the great Zeus to be born. Rhea, the goddess, wrapped a stone in swaddling clothes and gave it to her formidable husband. The evil husband did not notice the substitution and swallowed it. The goddess hid the newborn Zeus in a deep cave on the island of Crete, leaving him in the care of the forest nymphs. And the goat Amalthea fed him with her milk. The years flew by. Zeus grew up and matured. Rebelling against his father, he freed his divine brothers and sisters, becoming the leader between them. Zeus did not forget his nurse, the goat Amalthea, placing her in the sky - this is the constellation CAPRICORN.

Libra - when Astraea was transported to the sky and turned into the constellation VIRGO. In her hands she holds SCALES - a symbol of justice, harmony and equality.

Pisces - once upon a time, the goddess of love and beauty Aphrodite and her son Eros walked along the bank of the river, near which the wild Typhon, who had escaped from the dungeon, hid. Suddenly the ferocious Typhon attacked them. Horrified by his wild appearance, the immortals rushed into the water, turned into sparkling fish and swam away from the vile monster. This is how Aphrodite and her son Eros were saved, and the constellation FISH shone in the sky in honor of this.

Scorpio - Hera placed Scorpio in heaven because he killed the evil hunter Orion, who decided to exterminate all animals on earth

5. Twelve constellations. Aries constellation

ago there was the point of the vernal equinox. Over the past time, it has shifted greatly and is now located in the constellation Pisces; it is still designated by the sign of the constellation Aries. When the sun is at this point and moves from the Southern hemisphere of the celestial sphere to the Northern, astronomical spring begins.It is most convenient to observe the constellation in the fall, when the sun is far from it.

Taurus constellation

Taurus - one of the most beautiful winter constellations. In November - December it is observed almost all night. 125 stars are visible to the naked eye. The brightest - Aldebaran - is red-orange in color (its temperature is about 3500°). Near Aldebaran it is easy to see a scattering of not very bright stars forming a triangle (the face of Taurus).

Constellation Gemini.

Twins - the northernmost of the zodiac constellations. Observed in winter. Its brightest stars are Castor and Pollux. This was the name of the twin brothers who went with Jason on a campaign for the Golden Fleece. The brighter Pollux is orange in color. Upon closer inspection, this star turns out to be a system of four stars.

Constellation Cancer

Constellation Leo

Zodiac constellation Leo best seen during the spring months. It’s easy to find: A clear trapezoid of four bright stars forms the torso of Leo, and a curved chain of weaker stars forms the head and mane of the king of beasts. Regulus is the main star of the constellation, which has 2 satellites, one of them is a star very similar to the Sun. Regulus is a white hot, rather large star, it is almost 3 times larger than the Sun, and in terms of the amount of emitted light energy it exceeds it 140 times.

Virgo constellation

The ancient Greeks called this constellation Parthenos, which in Greek means"Virgo". The heavenly maiden is often depicted with a sheaf of ears of grain in her hands, and the name of her main star, Spica, is translated from Greek as “ear of grain.” The constellation was known in ancient times and was usually associated with the beginning of the harvest.

Constellation Libra

Small constellation Libra appeared on star maps relatively recently. The name of the constellation is due to the fact that in ancient times it was the location of the autumnal equinox. The ancient Roman poet Virgil wrote: “When Libra equalizes the hours of day and night and divides equally light and darkness in the world, then, farmer, take your working oxen to the field.”

Scorpio constellation

Scorpion - constellation of the southern sky. The most prominent star is Antares. This is a double star, a red giant, quite bright. Antares can compete with Mars in brilliance and color. But it is not difficult to distinguish the luminaries. Mars shines evenly, and Antares, like all stars, flickers.

Sagittarius constellation

Sagittarius constellationlocated near the Milky Way. Ancient Greek myths tell about the wise centaur Chiron, who created the first model of the celestial sphere, and left one place for himself. But another centaur, the cunning and cunning Krotos, took this place by deception, becoming the constellation Sagittarius. Zeus nevertheless placed Chiron in the sky, turning it into the constellation Centaur. And the evil Sagittarius behaves belligerently even in the sky, aiming his bow at Scorpio

Constellation Capricorn

This mythical creature with the body of a goat and the tail of a fish gave its name to one of the constellations of the zodiac. An ancient Greek legend tells how the goat-footed god Pan, the patron of shepherds, met the hundred-headed giant Typhon and threw himself into the water in horror. After this, Pan grew a fish tail, and he also became a water god. The stars of the constellation are not very interesting. It is curious that the star Algedi Capricorn is double. Physically, these 2 luminaries are not connected; they are moving away from each other in different directions. These stars are called optical binaries.

Aquarius constellation

In this zodiac constellation, different peoples saw a man pouring water. The name of the constellation most likely came from Mesopotamia. INconstellation AquariusAbout 90 stars can be seen with the naked eye. One of the largest planetary nebulae is located here.

Constellation Pisces

"Water" constellation Pisces - the last in the circle of the zodiac. It is visible in the sky in autumn, and the Sun comes into it at the end of winter. The main star of Pisces is Alrisha, which means “lace”. Through binoculars it is visible as a bluish star, and a telescope allows you to see a satellite of the same color.

Ophiuchus

Ophiuchus is the thirteenth sign of the Zodiac in the period from November 29 to December 14 inclusive, and is not singled out separately, since the main character traits are the same as Sagittarius. But there is one remarkable characteristic - during this period people are born with very high energetic and intuitive potential - that is, among people born during the Ophiuchus period there are a lot of psychics, sorcerers, predictors, etc. Everyone knows that there are 12 zodiac constellations, but there will be more real constellations (or as they are scientifically called - star clusters). And one of these “extra” ones is between the constellation Scorpio and the constellation Sagittarius. This is “Ophiuchus” (who likes “Ophiuchus”), which in some way every year “grabs” the last 5 days of Scorpio and the initial 5 days of Sagittarius.

6. Zodiac signs in coordinates. a lion

Coordinates

Connection paths

On the coordinate plane

1 (-21;-4)

1→2→3→4→5→6→7→8→9→10→13→15→16

2 (-11;2)

4→10 and 6→9

3 (-8;1)

10→11 and 10→12

4 (3;3)

13→14 and 13→2

5 (4;6)

6 (8;9)

7 (14;10)

8 (13;7)

9 (10;7)

10 (7;0)

11 (14;-6)

12 (7;-5)

13 (-11;-4)

14 (2;-8)

15 (-13;-8)

16(-11;-13)

Capricorn

Coordinates

Connection paths

On the coordinate plane

1(-22;3)

12345678 and 36

2(-18;2)

791011

3(-11;2)

9126 and 1213

4(-13;-5)

5(-12;-6)

6(-3;2)

7(14;6)

8(16;11)

9(11;1)

10(4;-10)

11(2;-12)

12(-3;-2)

13(-4;-10)

Coordinates

Connection paths

On the coordinate plane

1(-21; -10)

143 and 42

2(-17; -11)

45678469101

3(-22; 0)

11213101415

4(-20;2)

14161718

7(-1;1)

8(-1;4)

9(8;10)

10(1;-2)

11(-2;-6)

12(-1;-9)

13(3;-9)

14(6;-4)

15(14;-4)

16(12;-1)

17(8;-11)

18(14;-14)

7. Astrological studies 6 “B” class.

Zodiac signs in 6 "B"

Zodiac signs

Cancer

Taurus

Scales

Aries

Scorpion

Capricorn

Aquarius

Virgo

a lion

Sagittarius

Twins

Fish

Elements 6 "B" class.

Elements 6 "B"

Fire

Earth

Air

Water

8. Interesting facts about the elements.

Fire Release. The characteristics of this element are warmth and dryness, which are accompanied by metaphysical energy, life and its power. There are 3 signs in the Zodiac that have these qualities, i.e. fire trine (triangle): Aries, Leo, Sagittarius. The Fire trine is considered a creative trine.

Principle: action, activity, energy.

Earth Element. The characteristics of this element are cold and dryness, metaphysical matter, strength and density. In the Zodiac, this element is represented by the earth's trine (triangle): Taurus, Virgo, Capricorn. The Earth trine is considered a materialistic trine. Principle: stability.

Air Element. Features of this element are warmth and humidity, flexibility, divisibility, adaptability. In the Zodiac, these qualities correspond to the air trine (triangle): Gemini, Libra and Aquarius. The trine of Air is considered the trine of ideas and intellectuality.

Principle: exchange, contact.

Water Element. Features of this element are cold and humidity, metaphysical sensitivity, feeling, perception. There are 3 signs of this quality in the Zodiac - a water trine (triangle): Cancer, Scorpio, Pisces. The Water trine is considered the trine of feelings and sensations.

Principle: internal constancy despite external variability

10. Conclusion.

During the work, we became acquainted with the history of the origin of coordinates, learned about different types of coordinate systems, their features, origin and purpose. Having done a lot of work on studying the zodiac constellations, we came to the conclusion that the world of zodiac signs is that beautiful line that connects a person with the mysterious cosmos and distant stars. Studying the signs of the Zodiac, we built 4 signs on the coordinate plane. Having systematized the knowledge gained, we were able to conduct astrological research on students of grade 6 “B”.

Literature

1. Atlas for 5th grade science.

2. The book “The Unsolved Mysteries of Humanity” JSC “Reader’s Digest Publishing House”, France, 2004.

2. Book “All the Secrets of the World” JSC “Reader’s Digest Publishing House”, France, 2001.

3. Book “Only the Facts” JSC Reader’s Digest Publishing House, Hong Kong, 2004.

4.Internet.

d) http://www.myshared.ru/sl

Municipal budgetary educational institution

Gymnasium No. 1 of Khabarovsk

City scientific and practical conference “Step into science”

Mathematics section

Research

"Zodiac signs

on the coordinate plane"

Completed:

Bobrovnikova, Daria

Soklakova Natalya,

Lozhnikova Anastasia

6B grade students

Head: Korovaeva S.V.

Khabarovsk 2017

Introduction………………………………………………………………………………………...3

Theoretical chapter

1.1 Coordinates around us…………………………………………….7

1.4.Starry sky and legends about the twelve signs of the Zodiac……………13

2. Practical chapter

Zodiac signs in coordinates…………………………………………….20

Conclusion…………………………………………………………………………………......22

References………………………………………………………24 Appendices……………………………………………………… ……….....25

Introduction

This work contains two main aspects of the study: theoretical and practical. The first side of the research work is to identify the basic concepts: the history of the origin of the coordinate plane, who and how represented the coordinate plane, what is the significance of the coordinate plane and the signs of the zodiac.

The second part is to construct 12 zodiac signs in the coordinate plane.

Relevance of the project:

There are many non-traditional tasks with novelty tasks that can be successfully used when studying the topic “Coordinate plane”, but they are not included in school textbooks and methodological manuals teachers.

Hypothesis: Do people need coordinates in Everyday life?

Problem: Is it possible to build various interesting drawings on the coordinate plane, using coordinates?

Goal of the work : Expand knowledge about coordinates and their application in human everyday life.

Learn to construct points in the Cartesian coordinate system and determine the coordinates of given points. (This goal is highlighted because I started working on the project on my own much earlier than we started studying it in the program)

Learn to “draw” in a rectangular coordinate system.

Construct the zodiac signs using the theory of the coordinate plane.

To achieve the goal it was necessary to solve the followingtasks:

Select historical material.

Create a didactic material “To help the teacher” for conducting a general lesson on the topic “Coordinate plane”

Prepare a presentation “ZZodiac signs on the coordinate plane»

Subject of study : What is a coordinate plane?

Object of study : How to find the location of an object on a plane and in space?

Before the study there washypothesis : “To know in order to be able”

To achieve this goal, the following methods and techniques were used in the work:

- Problem: the presence of a posed problem - a hypothesis: what you need to know to find objects on the globe and on the map. Do people need coordinates in everyday life?

- Verbal: search and processing of necessary information from literary sources and the Internet; preparing a survey and analyzing the results; disclosure of findings;

Coordinates occur in our lives every hour. In order to prove that we need a coordinate plane in practical life, we will give several examples.

The coordinate system is used in cinemas, in transport, and in geography there is a coordinate system. Do coordinate systems have only two quantities? Everyone can play sea battle, and this game uses coordinates.

How do pilots navigate the sky? The position of the stars probably also has coordinates? This is all found in modern life. But an interesting fact is how long the coordinate system has permeated the practical life of a person.Mathematics is abstract. But it began with serving people. What about astronomy? Without astronomy people could not:

a) navigate the area, and, therefore, remember and, if necessary, inform who your address should be;

b) determine the days of the week and thereby skip Saturday and Sunday; finally,

c) know what time it is.

Can you imagine what a terrible life would await humanity without an address, constantly wandering without registration, and also deprived of a clock and a calendar! Passports and borders would lose the meaning. It would be impossible to create a schedule for rail and air transport, etc. Finally, the human race itself would simply cease to exist.

Work plan:

Search for information coordinates around us.

Identify types of coordinate systems, their features and purpose.

Consider starry sky and legends about the twelve signs of the Zodiac.

Study the zodiac constellations and plot them on the coordinate plane.

Draw a conclusion

Theoretical chapter

Coordinates around us.

In our speech, you may have heard the following phrase more than once: “Leave me your coordinates.” What does this expression mean? Did you guess it?! The interlocutor asks you to write down your address or phone number. Every person has situations when it is necessary to determine a location: use a ticket to find a seat in an auditorium or in a train carriage. When playing games, we have to determine the location of the “enemy” ship, a piece on a chessboard. Different situations? But the essence of coordinates, which translated from Greek means “ordered” or, as they usually say, coordinate systems is one thing: this is the rule by which the position of an object is determined. The word “system” is also of Greek origin: “Theme” is something given, “sis” is made up of parts. Thus, a “system” is something given, made up of parts (or a clearly dissected whole). Coordinate systems permeate the entire practical life of a person. For example, using a geographic map, you can determine the address of any point using geographic coordinates. To do this, you need to know two parts of the address - latitude and longitude. Latitude is determined using a “parallel” - an imaginary line on the surface of the Earth drawn at the same distance from the equator. Longitude - along the “meridian” - an imaginary line on the surface of the Earth connecting the North and South Poles along the shortest distance. Parallels are lines of direction west - east, meridians show the direction north - south. Sound familiar? Rectangular coordinate system.

How do pilots navigate the sky? Does the position of stars in the sky also have coordinates?

This is all found in modern life. But an interesting fact is how long has the coordinate system permeated the practical life of a person?

200 BCGreekscientistHipparchus enteredgeographyical coordinates.He suggested drawing on a geographical mapparallels and meridians and designate with numberslatitude and longitude . With these two numbersposition can be accurately determinedislands, villages, mountains or wellsin the desert and put them on a map orglobe,Having learned to determineopen world latitude and longitudelocation of the ship, sailors were able to choose the direction they neededlaziness.East longitudeand northern latitude are denoted by numberslami withsign"plus", and Westernlongitude and southern latitude - from thecom"minus".So the couplenumbers withsigns clearlydefineplaces a point onglobe.

For example,pair +70°, +60° defines the pointin the center of Vaigach Island, locatedfoot in the Kara Sea.

At the pussy body of Jules Verne, some Roma we are built on situations, related to geographical coordsdinats. These are the novels "Amazing"the adventures of Uncle Antifer" and"The Children of Captain Grant".

D For a long time, only geography - "land description" - used this wonderful invention, and only in the 14th century the French mathematicianNicola Orsem (1323-1382) I tried to apply it to “earth measurement” - geometry.He suggested covering thespeed with a rectangular mesh and oncall latitude and longitude whatwe now callabscissa And op dinata .

N and on the basis of this successful innovationnick coordinate method associated geogeometry with algebra. Main forservant in the creation of this method belongslies to the great Frenchmasubject matterRene Descartes (1596 - 1650) . In his honor this coordinate system is calledCartesian, denoting the location of any point on the plane by the distances from this point to the “zero latitude” - the abscissa axis and the “zero meridian” - the ordinate axis.

According to the tradition introduced by Descartes, the “latitude” of a point is denoted by the letter x, and the “longitude” by the letter “y”.

On this systemmany ways of indicatingplaces. For example, on a cinema ticket there are two numbers: row and place - they can be considered as coordinatesseats in the hall. Similarnew coordinates accepted about checkmatah. Instead of one of the numbers, a letter is taken: vertical rowsThe rows of cells are designated by the letters laTin alphabet, and the horizontalnew - in numbers.Thus, each cellthe chessboard is matched with a peer of a letter and a number, and chess players are able to writethrow away your parties.The same principle forchanges on city plans.The city plan is divided into squaresnumbered with letters andnumbers, and on the reverse side there isall the streets shown are includedIn alphabet orderAndindicatewhat square are they in?

Exist on the plane and othersdifferent coordinate systems.

H to enterpolar system coordinate T , choosestarting point calledfieldsom(therefore the systemAndcalled"polar");from thispoints spendray calledpolar axis . Todetermine the coordinates of a pointon a plane, it is connected by a cutcom with poleAndcalculate the lengththis segmentAndthe angle between itand polar axis.

Existencehowlalso the coordinates specifiedonenumber.Thiscoordinates on straight . It is enough to ask one thingnumber - distance from point tostarting point to indicate straightmy position of this point. INlifewe very oftenwe collidewith suchcoordinates.

For example, a railway withkilometer pillarsalongher or numbershouses on the street.

Three coordinates will be givenposition of the point inspace.Such a coordinate systemcalledspherical . Need tochoose somebadspeed andenteronherCartesiancoordinate system, and our pointlet's compare the coordinates of its projectiononthisplane and distance fromit to the plane, takenwithsignplusForone half of the spacesquality and societysignsminus - for othersgoy; so we getCartesian system mu coordinates in space .

Spherical coordinate systemusually used at airfields.A radio is installed near the airfieldconvict This device can determinedistance to the aircraft, angle, underwhich the plane is visible above the horizonTom, andcornerbetween direction toplane and heading north.

A
strology is the science of the influence of stars, constellations and planets on humans and the Earth. Among the 88 constellations that decorate the night sky, a special place is occupied by those among which the Sun passes its annual path. Twelve constellations on the path of the Sun: Aries, Taurus, Gemini, Cancer, Leo, Virgo, Libra, Scorpio, Sagittarius, Capricorn, Aquarius, Pisces. Most of the names belong to animals, which is why these constellations are namedzodiac (from Greek zodiacos - “animal circle”).

a lion – a huge lion settled not far from Nemea. Horror gripped the people when they heard his roar. The people did not leave their homes, hunger set in, and illness began.

Having shouldered a huge carcass, Hercules went to Nemea. There he made a sacrifice to Zeus and established the Nemean Games in memory of this feat. And he began to wear lion skin instead of a cloak.

Cancer - when Hercules went to fight the hydra, a huge Cancer crawled out of the reeds to meet him and grabbed Hercules by the leg. The angry Hercules crushed him, thereby inadvertently eliminating another enemy.

Sagittarius – once the great hero of Greece Hercules was traveling with his wife. Near the River Even they met the centaur Nessus. Hercules forded the river and instructed the centaur to transport Dejanira. While the hero was already on the other bank, he heard the cry of his wife: seduced by her beauty, the rude centaur decided to kidnap her, taking her downstream. “My arrows are faster than you!” Nessus knew that the piercing arrow of Hercules was deadly, and, foreseeing his inevitable death, he decided to take revenge on him by giving her his talisman with poison, supposedly returning her husband from another woman. Later, Deianira learned that Hercules had brought a beautiful slave, Iola, and became jealous of him. She sent him clothes rubbed with poison, hoping that he would return to her, but, having put on these clothes, Hercules died in terrible agony. However, the evil Nessus did not calm down, even when he found himself in the starry sky. A centaur, armed with a bow and arrow, threatens everyone from the heavens - this is exactly what the constellation SAGITTARIUS looks like.

Capricorn - when the day of the winter solstice arrived, the hour had come for the great Zeus to be born. Rhea, the goddess, wrapped a stone in swaddling clothes and gave it to her formidable husband. The evil husband did not notice the substitution and swallowed it. The goddess hid the newborn Zeus in a deep cave on the island of Crete, leaving him in the care of the forest nymphs. And the goat Amalthea fed him with her milk. The years flew by. Zeus grew up and matured. Rebelling against his father, he freed his divine brothers and sisters, becoming the leader between them. Zeus did not forget his nurse, the goat Amalthea, placing her in the sky - this is the constellation CAPRICORN.

Twins - One day the brothers decided to get married. And having chosen two beautiful princesses, they kidnapped them. But the beauties were already brides of other heroes. A fierce struggle ensued between the rivals. In this battle, Castor was struck down by an enemy arrow. Polydeuces bent over the dying Castor, unable to hold back his sobs. Suddenly he sees: the powerful Zeus appeared before him and offered Polydeuces immortality. “Great father,” said the young man, “I cannot accept your gift. Send death to me! I can’t imagine life without Castor. Let our lot be one.” The world ruler allowed Polydeuces to give half of his immortality to Castor. Since then, GEMINS spend one day in the kingdom of the dead, and the other day on Olympus, among the gods.

Taurus - The Phoenician princess Europe was wonderfully charming. One day she and her friends went to the seashore to listen to the sound of the sea waves. Zeus the Thunderer, seeing her, immediately became inflamed with love for her and descended to Earth in the guise of a bull with a round silver spot on his forehead. Approaching the beautiful Europa, the bull lay down at her feet and offered his back. When the princess sat on the bull, he took off like an arrow and headed towards the sea. The maiden called for help, but her friends could not catch up with her, and at that time the bull moved through the sea like a dolphin, because his brother Poseidon himself cleared the way for him. Full of melancholy, seeing nothing but sky and water, the maiden asked: “Who are you?” and heard in response: “Do not be afraid of me, I am Zeus and only love for you prompted me to take on this form.” Zeus the bull sailed to the island of Crete, where Europe bore him glorious sons.

Virgo - Having seen human greed and malice, the gods decided to leave this vicious world. Virgin Astraea, goddess of justice, daughter of the almighty Zeus and the goddess of justice Themis, the latter left the earth. Astraea was transported to the sky and turned into the constellation VIRGO.

Scales - when Astraea was transported to the sky and turned into the constellation VIRGO. In her hands she holds SCALES - a symbol of justice, harmony and equality.

Aquarius - in memory of the Great Flood, Zeus lit the constellation AQUARIUS in the sky. The Greeks called it Hydrochos, the Romans called it Acuarius, and the Arabs called it Sakib - alma. All this means the same thing:man pouring water.

Aries - when Athamas decided to give his son Phrixus to the gods as a sacrifice, and his sister Gella stood nearby and mourned the inevitable death of her brother, when suddenly a thunderclap was heard in the clear sky; A huge white cloud descended from the sky, the cloud goddess Nephele came out of it, and next to her was a beautiful ram. His long golden fleece shone, and his horns curled in steep curls. The goddess of the clouds exclaimed: “My children, I will save you! Sit on this magical ram." Phrixus and Hella boarded a ram and flew to a country called Colchis, where King Eet ruled. Eet caught Aries and kept him for himself. Since then, the country of Colchis became happy, because happiness was brought by this wonderful Aries.

Fish - One day, the goddess of love and beauty Aphrodite and her son Eros walked along the bank of a river, near which the wild Typhon, who had escaped from the dungeon, hid. Suddenly the ferocious Typhon attacked them. Horrified by his wild appearance, the immortals rushed into the water, turned into sparkling fish and swam away from the vile monster. This is how Aphrodite and her son Eros were saved, and the constellation FISH shone in the sky in honor of this.

Scorpion – Hera placed Scorpio in heaven because he killed the evil hunter Orion, who decided to exterminate all animals on earth.

Interesting facts about the elements.

Element of Fire. The characteristics of this element are warmth and dryness, which are accompanied by metaphysical energy, life and its power. There are 3 signs in the Zodiac that have these qualities, i.e. fire trine (triangle): Aries, Leo, Sagittarius. The Fire trine is considered a creative trine.

Principle: action, activity, energy.

Element of Earth. The characteristics of this element are cold and dryness, metaphysical matter, strength and density. In the Zodiac, this element is represented by the earth's trine (triangle): Taurus, Virgo, Capricorn. The Earth trine is considered a materialistic trine. Principle: stability.

Element of Air. Features of this element are warmth and humidity, flexibility, divisibility, adaptability. In the Zodiac, these qualities correspond to the air trine (triangle): Gemini, Libra and Aquarius. The trine of Air is considered the trine of ideas and intellectuality.

Principle: exchange, contact.

Element of Water. Features of this element are cold and humidity, metaphysical sensitivity, feeling, perception. There are 3 signs of this quality in the Zodiac - a water trine (triangle): Cancer, Scorpio, Pisces. The Water trine is considered the trine of feelings and sensations.

Principle: internal constancy despite external variability

2. Practical chapter

Zodiac signs in coordinates

In our work, we propose to construct drawings of the twelve signs of the Zodiac on a coordinate plane.

Each card has an image of one of the signs and gives the coordinates of the points (stars) and the paths to connect these points. After they have been marked on the coordinate plane and connected in the specified order, the image of the Zodiac sign will be the same as on the star map.

In order to make the cards we did:

We got acquainted with various coordinate systems

We learned to construct points in the rectangular-Cartesian coordinate system (we will only study this topic in the fourth quarter)

We studied the star map (Appendix 1)

We examined each constellation in detail, studied how many stars each constellation consists of, the distance between the points, how they are connected to each other on the map (Appendix 2)

We transferred the points of each constellation onto checkered paper (Appendix 3)

Randomly introduced a coordinate system (Appendix 3)

We wrote down the coordinates of each point and marked the paths to connect them (Appendix 3)

Compiled brief description each of the constellations (Appendix 4)

Picked up Interesting Facts about people born under this zodiac sign (Appendix 4)

Conclusion

In this work we tried to combine two subjects: mathematics and astronomy. The theoretical part tells about the history of the origin of coordinates and their creators. we learned that there are different coordinate systems, how widely and where they are used in human everyday life. In addition, in our work you can learn about the legends of the starry sky and the origin of the names of the signs of the Zodiac.

The practical part of our work was to construct all twelve constellations of the Zodiac signs on the coordinate plane and determine the coordinates of each star point. To do this, we looked at a map of the starry sky, studying the location and appearance of each of the 12 constellations:

How many stars (points) does a constellation consist of?

How are they connected to each other on the map?

Distance between points

Then we selected the coordinates (x; y) for each star (point) and plotted them, maintaining the scale, and indicated the path of connecting the stars.

Then we prepared task cards for working in groups (Appendix 1). The materials from our work can help the teacher conduct a lesson to consolidate knowledge on the topic “Coordinate plane”. During the completion of tasks, students can test with interest their knowledge and skills in marking points at given coordinates and determining the coordinates of already marked points. In the future, we plan to study in more detail the relative positions of all constellations, plot them on the same coordinate plane, so that we can draw up a map of the starry sky.

Literature

Glazer G.I. History of mathematics in school: - M.: Prosveshchenie, 1981. – 239 p., ill.

Lyatker Ya. A. Descartes. M.: Mysl, 1975. – (Thinkers of the past)

Matvievskaya G. P. Rene Descartes, 1596–1650. M.: Nauka, 1976.

A. Savin. Coordinates Quantum. 1977. No. 9

Mathematics – supplement to the newspaper “First of September”, No. 7, No. 20, No. 17, 2003, No. 11, 2000.

Siegel F.Yu. Star alphabet: A manual for students. – M.: Education, 1981. – 191 pp., illus.

Steve Parker, Nicholas Harris. Illustrated encyclopedia for children. Secrets of the universe. Kharkov Belgorod. 2008

Annex 1

Appendix 2

Appendix 3

Appendix 4

Municipal educational budgetary institution “Secondary school No. 1 of Sol-Iletsk”

Coordinate plane and zodiac signs

(project)

Executor:

Saygina Anastasia Vladimirovna

Supervisor:

Savelyeva Anastasia Alexandrovna

Sol - Iletsk.

2016

Content

Introduction……………………………………………………………………...….3

Main part

History of the creation of coordinates…………... …………………………5
Types of coordinate systems and their use in everyday life…………………………………………………………………………………..7
Starry sky and legends about the twelve signs of the Zodiac………10

Practical part.

Conclusion…………………..……………………………………………25

Bibliography…………………………………………………... …..26

Application.

I .Introduction

When I was little and looked up, I saw bright lights randomly located in the night sky. I always liked watching the starry sky. I grew up and my mother told me that there is such a science - astronomy and I became interested in it, began to study the constellations, find and examine them in the starry sky. It turns out that in addition to their beautiful location in the sky, you can learn about the zodiac constellations unique, interesting myths and legends, theories of origin, names and locations of the main stars in the zodiac signs and much more. Therefore, I decided to start researching the constellations and certainly connect their location with the coordinate plane, because I also like to study mathematics, which is directly related to astronomy.

Formulation of the problem: Many people know about the existence of zodiac constellations, but not everyone can find them in the starry sky. In this work, an attempt is made to construct images of zodiac signs on a coordinate plane.

Goal of the work: consider the signs of the zodiac through the theory of the coordinate plane.

Tasks:

learn to construct points in the Cartesian coordinate system and determine the coordinates of given points (this task is highlighted because this topic begins to be studied according to the 6th grade program in the fourth quarter);

expand knowledge about coordinates and their application in human everyday life;

get acquainted with the history of the origin of coordinates;

consider different types of coordinate systems;

study the zodiac constellations;

construct an image of the constellation on the coordinate plane;

conduct astrological research for 6th grade students;

prepare a presentation “Coordinate plane and zodiac signs”;

create didactic material “to help the teacher” for conducting a general lesson on the topic “coordinate plane”;

In the process of work, I used the following research methods and techniques:

study of theoretical sources;

observation;

working with photographic materials;

consultation with the teacher.

I began my research by studying theoretical sources. First of all, the World Wide Web helped me with this.

II . Main part

2.1 History of the creation of coordinates

People ancient world traveled quite far, and of course, they did not have to draw maps and mark on them the location of mountains and rivers, cities and countries, convenient roads and dangerous places... But using a ready-made map, it is difficult to find a city on it if you only know its name. Therefore, all travelers should be eternally grateful to the ancient Greek scientist Hipparchus.

More than 100 years BC, the Greek scientist Hipparchus proposed encircling the globe on a map with parallels and meridians and introducing the now well-known geographical coordinates: latitude and longitude and designating them with numbers.

In the 2nd century AD. The famous ancient Greek astronomer Claudius Ptolemy already used longitude and latitude as geographical coordinates.

In the 14th century. French mathematician N. Oresme introduced, by analogy with geographical ones, coordinates on a plane. He proposed to cover the plane with a rectangular grid and call latitude and longitude what we now call abscissa and ordinate. This innovation turned out to be extremely productive. On its basis, the coordinate method arose, connecting geometry with algebra. A point on the plane - a geometric object - is replaced by a pair of numbers (x; y), that is, an algebraic object.

But these concepts were first systematized in the 17th century by Rene Descartes (Appendix No. 1). Rene Descartes (1596-1650) - French philosopher, natural scientist, mathematician. Descartes' goal was to describe nature using mathematical laws. The author of the coordinate plane, which is why it is often called the Cartesian coordinate system.

After the publication of the work “Geometry”, Rene Descartes’ coordinate system won recognition in scientific circles. Already at the end of the 17th century. The concept of “coordinate plane” has become widely used in the world of mathematics. Despite the fact that several centuries have passed since the creation of this system, it is still widely used in mathematics and even in life.

2.2. Types of coordinate systems and their use in everyday life

There are many ways to indicate a location based on a coordinate system. For example, on a movie ticket there are two numbers: row and seat - they can be considered as the coordinates of the seat in the theater.

Fig.2

Similar coordinates are accepted in chess. Instead of one of the numbers, a letter is taken: the vertical rows of cells are designated by letters of the Latin alphabet, and the horizontal rows by numbers. Thus, each square of the chessboard is assigned a pair of letters and numbers, and chess players are able to record their games.

Fig.3

The same principle applies to city plans. The city plan is divided into squares numbered using letters and numbers, and on the reverse side all the streets depicted are listed in alphabetical order and indicate in which square they are located.

Fig.4

There are different coordinate systems on the plane. For example, the polar coordinate system.

To introduce a polar coordinate system, you select a starting point called a pole (which is why the system is called “polar”); from this point a ray is drawn, called the polar axis. To determine the coordinates of a point on a plane, it is connected by a segment to a pole and the length of this segment and the angle between it and the polar axis are calculated.

There are also coordinates specified by a single number. These are the coordinates on a straight line. It is enough to specify one number - the distance from the point to the origin to indicate the position of this point on a straight line. In life, we very often encounter such coordinates.

For example, a railway with kilometer posts along it or house numbers on the street.

Rectangular Cartesian coordinate system on a plane.

To introduce a rectangular Cartesian coordinate system on a plane, you need to draw two mutually perpendicular straight lines, choosing a positive direction on each of them, indicating it with an arrow, and selecting

Fig.5

each of them has a scale (unit of length measurement). Let us denote the point of intersection of these lines by the letter O and consider it the origin of reference. This is how we got a rectangular coordinate system on a plane. To construct a point with coordinates (X;Y): first you need to go along the abscissa axis (x) from the origin by X units, and then along the ordinate axis (y) by Y units. This way we will get a point with the given coordinates.

2.3 Starry sky and legends about the twelve signs of the Zodiac

Astrology is the science of the influence of stars, constellations and planets on humans and the Earth. Among the 88 constellations that decorate the night sky, a special place is occupied by those among which the Sun passes its annual path. Twelve constellations on the path of the Sun: Aries, Taurus, Gemini, Cancer, Leo, Virgo, Libra, Scorpio, Sagittarius, Capricorn, Aquarius, Pisces. Most of the names belong to animals, so these constellations

Fig.6

got nameszodiac (from Greek zodiacos - “animal circle”).

Fig.7

Aries.

According to legend, an Aries, shaped like a ram, saved two children from imminent death, after which it was awarded a place in the starry sky. Zeus loved this sign most of all and made it the first zodiac circle. In addition, it is his golden skin ( The Golden Fleece) was hung on an oak tree. As we remember, the Argonauts hunted for the Golden Fleece. This is how precious Aries is.

Calf.
The great Olympian Zeus the Thunderer was a great admirer of the fair sex. Trying to protect his lovers from the jealousy and anger of his crowned wife Hera, he indulged in all sorts of tricks. One day, flying over the city of Sidon, he saw an idyllic picture: young girls walked along a spring meadow, danced in circles and wove wreaths of bright flowers. The most beautiful of all was a girl dressed in purple cloth with a gold pattern woven on it. It was Europa - the young daughter of the Sidonian king. Zeus descended to earth and appeared in the meadow in the form of a wonderful white bull, whose fur shimmered with gold, and on its forehead there was a silver spot, shaped like a moon. The girls surrounded him, began to pet him and feed him fresh grass and sweets. And the bull, sitting down on the grass at Europa’s feet, began to lick her arms and legs. Laughing, Europe kissed his forehead and sat on his broad back. At the same moment, the bull jumped up, rushed into the sea and swam quickly, cutting through the azure waves.
At first, Europe was very frightened, but when she saw that the waves parted in front of her bull, and beautiful Nereids, dolphins and other inhabitants of the sea were swimming next to them, she calmed down, snuggling in the soft fur of the bull. Soon the native island of Zeus, Crete, appeared on the horizon. There, Europe became the wife of Zeus and bore him two sons, Minos and Rhadamanthus.

Twins.

Once upon a time there were two brothers: Pollux (who carried a club) and Castor (who carried reins). They had one mother, but different fathers. But they were twins. Pollux's father was Zeus, and Castor's was an ordinary earthly man.
The difference is that if your father is a god, then you are immortal.
So, these twins adored each other, doted on each other. They were always together, playing mischief. And one day, after another battle, Castor was mortally wounded. And then Pollux turned to Zeus (his father) and said: “Without a brother, I don’t need immortality!”
And the gods placed them in the sky as a symbol of brotherly devotion.

Cancer .

There is an opinion that the constellation got its name as a reminder of the huge cancer that bit Hercules when the son of Zeus fought with the snake-like Lernaean Hydra.
The terrible hydra had nine heads, poisonous breath and was the daughter of the giant dragon Typhon. Hydra lived in a swamp near Lerna. The monster terrified the inhabitants of the town, attacked people, and devastated the Lernaean country. It was difficult to cope with the monster; it was believed that if you cut off its head, then two would immediately grow in its place. King Eurystheus of Mycenae, wanting to get rid of Hercules, ordered the hero to deal with the hydra, secretly hoping for his death in battle. His nephew Iolaus came to the aid of Hercules. He burned the monster's heads, which the athlete chopped off. During the battle, a huge crayfish crawled out to help the hydra and bit Hercules on the leg. But the hero defeated him too. Hera, who hated Hercules, sent the cancer to heaven, turning it into a constellation as a sign of gratitude for helping the Lernaean Hydra.

End of form

a lion .

A huge lion settled not far from Nemea. Horror gripped the people when they heard his roar. The people did not leave their homes, hunger set in, and illness began.

Having shouldered a huge carcass, Hercules went to Nemea. There he made a sacrifice to Zeus and established the Nemean Games in memory of this feat. And he began to wear lion skin instead of a cloak.

Virgo.

According to Greek legends, the Virgin was Rhea, the mother of Zeus and the wife of Kronos. She was later identified with the daughter of Zeus and Themis Astraea, who was known as the goddess of justice. Initially, a Golden Age reigned on the planet, which was developed thanks to Kronos. After Zeus took a leading position on Olympus, the Silver period began in the history of mankind. People had to earn their bread with their own labor. Prometheus was able to get fire for them, and they were able to find a use for it. Having created weapons, people entered the Copper Age. The Iron Age brought war and destruction. It was at this time that the gods left the earth forever; they preferred the peace of Olympus to civil strife and strife on earth. Astraea became the last of the gods to leave earthly existence. She is considered a defender of justice, who has risen above all earthly squabbles and, in the form of the constellation Virgo, shines in the firmament.

End of form

Scales.

Scales associated with the goddess of justice Themis, who had a beloved assistant daughter named Dike (the term "jurisdiction" is associated with her name). This girl walked around the world and weighed people's actions. Dike's eyes were closed, because vision deceives. But the symbol of the myth was not the girl herself, but her instrument, the symbol of justice - Libra.

Scorpion – when Helios (in ancient Greek philosophy- God of the Sun), took as his wife the daughter of the goddess of the sea - Clymene, and they had a son named Phaethon. When Phaeton grew up, he turned to his father with a request to allow him to drive the fiery chariot for one day. The parents tried to dissuade their son for a long time, citing the fact that he did not have immortality like his father, and it would be very difficult for an ordinary person to cope with the chariot. Phaeton, due to his persistence, was still able to convince his father, and, having driven out onto the road, he barely had the strength to keep the cart level. But suddenly, unexpectedly, a real monster appeared in front of him in the guise of a scorpion. Phaeton was so frightened that he could not cope with the horses, and they rushed up to the heavenly gates. As soon as they reached the stars, the horses turned around and rushed back, and, approaching the Earth, forests and fields caught fire from the fire of the chariot, and the ocean boiled. Then the Gods prayed to Zeus to help and stop the destruction of everything earthly. Zeus threw lightning at the chariot and put out the fire, and Phaeton fell into the river.

Capricorn.

The ancient Greek myth about the legendary goat Amalthea is associated with the constellation Capricorn. As is known, fearing the prophecy, Cronus swallowed his children born of the goddess Rhea. Therefore, Rhea gave birth to her last child, Zeus, in a secluded grotto on the island of Crete and left him under the care of her faithful assistants - nymphs. This time, instead of a child, Rhea gave Kron a swaddled stone and Kron did not notice the substitution. So Zeus remained alive and grew up on a distant island. In order not to arouse suspicion, Crona Rhea could not leave home often. Therefore, the nymphs had to feed Zeus not with their mother’s milk, but with goat’s milk. Zeus's nurse was the goat Amalthea. She became so attached to her baby Zeus that she gave him one of her horns, from which he drank healing milk.

Zeus grew up to be a strong boy. One day, while playing around, he pushed the horn of milk away from him so hard that it splashed out in a long stream high up and into the sky. There it spread out into a wide white stripe, which people called the Milky Way.

Aquarius - the traditional symbol of Aquarius is Ganymede, a young man holding an overturned amphora in his hand. Ganymede was kidnapped by an eagle disguised as Zeus. This mortal, son of Tros, according to some legends, was the founder of the city of Troy. Having become the cupbearer of the gods of Olympus, the Trojan heir poured ambrosia. He personified the constellation Aquarius, that is, the carrier of water.

Fish.

King Priam had a brother Titon, who charmed the winged goddess of dawn Eos with his beauty, who kidnapped Titon and took him to her place on the edge of Earth and Heaven. The gods gave him immortality, but did not give him eternal youth. Days and years passed and left merciless marks on his face.
Once Titon noticed in the distance the goddess of love Aphrodite, walking with her son Eros, who was ready at any moment to shoot a love arrow from a drawn bow into the heart of a god or a mortal. Dressed in gold-woven clothes, with a wreath of fragrant flowers on her head, Aphrodite walked holding her son’s hand. And where the beautiful goddess walked, wonderful flowers grew and the air smelled of freshness and youth. Fascinated by her beauty, Tithon rushed after Aphrodite, who began to run away with her son. A little more, and Tithon should have overtaken them. To escape his pursuit, Aphrodite and Eros threw themselves into the Euphrates River and turned into fish. The gods placed two fish in the sky among the constellations, connected by a wide and long ribbon, personifying great maternal love.

Practical part.

2.4 Astrological characteristics of class 6 “a”

To compile the astrological characteristics of grade 6 “a”, I conducted a survey:

- “Who are you? zodiac sign?»,

- “Do you know what your constellation looks like?”

and made charts based on the results.

From which it is clear that (85%) students do not know what their constellation looks like. And also how it turned out that in our class there are most Aries and Pisces, 4 people each. This means that our class is: adventurous, sincere, kind, hardworking, serious, honest.

2.5 Zodiac signs in coordinates

In our work, we propose to construct drawings of the twelve signs of the Zodiac on a coordinate plane in order to create didactic material “to help the teacher” for conducting a general lesson

View document contents "Astrology on the coordinate plane"

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"Astrology on the coordinate plane"