Career

"constellations on the coordinate plane" research work in mathematics and astronomy. Astrology on the coordinate plane Pisces constellation on the coordinate plane

BUDGET GENERAL EDUCATIONAL INSTITUTION
"POLOGRUDOV SECONDARY EDUCATIONAL SCHOOL"
TARSKY MUNICIPAL DISTRICT OF THE OMSK REGION

PROJECT ON

"ASTOROLOGY
ON THE COORDINATE PLANE»

Performed:
6th grade student
Kuzheva Polina

Project relevance:
On a cloudless, moonless night, a majestic picture of the starry sky opens up to the gaze. At first glance, it seems that it is impossible to understand the star placer. But knowing the starry sky is interesting and useful. It has attracted people for a long time. Thousands of years ago, people mentally combined the brightest stars into various figures (constellations) and called them the names of the characters of myths and legends of animals and objects. Different peoples had their own myths and legends about the constellations, their own names, and the number of constellations in different peoples was different. In our work, we transferred the constellations from the starry sky to the coordinate plane.
Objective of the project:
Construct images of the zodiac constellations on the coordinate plane.

Project objectives:
get acquainted with the history of the origin of the coordinate plane;
expand your knowledge of the zodiac constellations;
create images of zodiac signs on the coordinate plane and set their coordinates

The history of the origin of the coordinate system

Coordinate in 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 divided whole).
Coordinate systems permeate the entire practical life of a person. For example, by geographical map Using geographic coordinates, you can determine the address of any point. To do this, you need to know the two parts of the address, latitude and longitude.
The history of the emergence of coordinates and coordinate systems begins a very long time ago, initially the idea of the coordinate method arose back in ancient world in connection with the needs of astronomy, geography, 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.
The idea of depicting numbers as dots, and giving dots numerical designations originated in ancient times. The initial use of coordinates is associated with astronomy and geography, with the need to determine the position of the stars in the sky and certain points on the surface of the Earth, when compiling a calendar, star and geographical maps. Traces of applying the idea of rectangular coordinates in the form of a square grid (pallet) are depicted on the wall of one of the burial chambers of Ancient Egypt.
Already in the II century. Ancient Greek astronomer Claudius Ptolemy used latitude and longitude as coordinates.
The main merit in the creation of the modern coordinate method belongs to the French mathematician Rene Descartes. A story has come down to our times that prompted him to discover. Taking seats in the theater according to the purchased tickets, we do not even suspect who and when proposed the method of numbering seats in rows and seats, which has become common in our life.
René Descartes first made a scientific description of the rectangular coordinate system in his Discourse on the Method in 1637. Therefore, the rectangular coordinate system is also called the Cartesian coordinate system. In the Cartesian coordinate system, negative numbers have received a real interpretation.
Pierre Fermat also contributed to the development of the coordinate method, but his work was 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 applied 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. 17th century German mathematician Wilhelm Leibniz.

zodiac constellations
Astrology is the science of the influence of stars, constellations and planets on man and on the Earth. Among the 88 constellations that adorn the night sky, a special place is occupied by those among which the Sun passes its yearly 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 received the names of the zodiac (from the Greek zodiac - "animal circle").
In fact, of course, the Earth moves around its luminary, but it seems to us that it is the Sun that changes its location. So did the ancient astronomers who named the zodiac constellations.
They noticed that the Sun always follows the same path across the sky and every month "stays" at the signs of the Zodiac: in January - at Capricorn, in February - at Aquarius, in March - at Pisces ... It has long been believed that the sign of the Zodiac, that is, the month of birth of a person determines his character, influences behavior and predetermines fate.

The beginning of the zodiac is considered to be the constellation Aries, here 2 thousand years
ago was the vernal equinox. Over the past time, it has moved a lot 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 one, astronomical spring begins. It is most convenient to observe the constellation in autumn, when the sun is far from it.
Constellation Taurus
Taurus is 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 that form a triangle (the muzzle of Taurus).
Constellation Gemini.
Gemini is the northernmost of the zodiac constellations. Observed in winter. Its brightest stars are Castor and Pollux. That was the name of the twin brothers who went with Jason on a campaign for the Golden Fleece. The brighter Pollux has an orange color. Upon closer examination, this star turns out to be a system of four stars.
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.” Between them, a “foggy star” (Nursery) is really visible.
Constellation Leo
The zodiac constellation Leo is best observed during the spring months. Finding it is easy: A clear trapezoid of four bright stars forms the body of the Lion, and a weaker chain of stars curved in an arc 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 radiated light energy it exceeds it by 140 times.
Constellation Virgo
The ancient Greeks called this constellation Parthenos, which means "virgin" in Greek. The celestial maiden is often depicted with a sheaf of ears of corn in her hands, and the name of her main star, Spica, means “ear” in Greek. The constellation was known in ancient times and was usually associated with the beginning of the harvest.
Constellation Libra
The small constellation of Libra appeared on star maps relatively recently. The name of the constellation is due to the fact that in ancient times there was a point in it autumn equinox. The ancient Roman poet Virgil wrote: “When Libra equalizes the hours of day and night and divides light and darkness equally in the world, then, farmer, bring your working oxen into the field.”
constellation scorpio
Scorpio is a constellation in the southern sky. The most prominent is the star Antares. This is a double star, a red giant, quite bright. With brilliance and color, Antares can compete with Mars. But it is not difficult to distinguish the luminaries. Mars shines evenly, and Antares, like all stars, twinkles.
Constellation Sagittarius
The constellation Sagittarius is located near the Milky Way. Ancient Greek myths tell of the wise centaur Chiron, who created the first model of the celestial sphere, and left one place for himself. But another centaur, the treacherous and cunning Krotos, took this place by deceit, becoming the constellation of Sagittarius. Zeus nevertheless placed Chiron in the sky, turning it into the constellation of the Centaur. And the evil Sagittarius even in the sky behaves militantly, aiming from a bow at Scorpio.
Constellation Capricorn
This mythical creature with the body of a goat and the tail of a fish gave the name to one of the constellations of the zodiac. An ancient Greek legend tells how the goat-footed god Pan, the patron saint of shepherds, met the hundred-headed giant Typhon and rushed into the water in horror. After that, Pan grew a fish tail, and he also became a water god. Constellation stars are not very interesting. Curiously, the star Algedi Capricornus is a double star. Physically, these 2 luminaries are not connected, they move away from each other in different directions. These stars are called optical binaries.
Constellation Aquarius
In this zodiac constellation different nations I saw a man pouring water. The name of the constellation most likely came from Mesopotamia. In the constellation Aquarius, about 90 stars can be seen with the naked eye. Here is one of the largest planetary nebulae.
Constellation Pisces
The "water" constellation Pisces is 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". With binoculars, it is visible as a bluish star, and a telescope allows you to see a satellite of the same color.

Conclusion
In the course of work, we got acquainted with the history of the origin of coordinates, a rectangular coordinate system. Having carried out work on the study of 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.
With the help of a map of the starry sky and the zodiac constellations depicted on it, drawings of the signs of the Zodiac were built on the coordinate plane. For each star-point of any of the 12 signs, the coordinates are selected and the connection paths are indicated.

INTRODUCTION

Even in early childhood, on long dark evenings, I loved to look at the sky when there were no clouds on it. Then I noticed that the whole sky was covered with stars. When I watched these stars, I realized that they are arranged in a certain way. Later, at school, I learned that constellations - these are the sections into which the celestial sphere is divided for the convenience of orienting in the starry sky.

The history of the constellations is very interesting. Long ago, observers of the sky combined the most visible groups of stars into constellations and gave them various names. These were the names of mythical heroes or animals, characters of legends and tales - Hercules, Cepheus, Cassiopeia, Andromeda, Pegasus and others. INthe boundaries of 88 constellations were finally approved. But not all of them are bright and noticeable. Of the 88 constellations, only 47 are ancient. The 12 constellations are traditionally calledare those through which. Also in the zodiac constellations were singled out in a special group, and each of them was assigned its own sign. most richly bright stars winter sky. The most beautiful constellation in the winter sky is Orion (Appendix 1).

Currently, there are many legends that have come to us from Ancient Greece, and are associated with the zodiac constellations. Here is one of them about the constellations Ursa Major and Ursa Minor.

“The goddess Aphrodite had one of her maids the beautiful nymph Calisto. The almighty god Zeus decided to take Calisto as his wife against the wishes of Aphrodite. To save Calisto from the persecution of her mistress, Zeus turned Calisto into the Big Dipper, and her beloved dog into the Little Dipper and took them to heaven.

Studying in primary school the concepts of "coordinate ray" and "coordinate angle", I wondered how to depict constellations using a coordinate system. To do this, it became necessary to obtain additional information from the field of mathematics.

That's why purpose This work began to find out the possibility of creating graphic images of constellations using a coordinate system.

As object of study math is chosensubject of study - coordinate plane.

At the beginning of the work, I put forwardhypothesis : "Images of the zodiac constellations can be transferred to the coordinate plane and the location recorded using coordinates."

As tasks scientific research work I determined:

Learn the concept of a coordinate plane.

Determine the possibility of creating a graphic image on the coordinate plane (create a drawing using known coordinates).

Draw (transfer) constellations from an astronomical map (plane) to a coordinate one.

Recording an image using coordinates (reading an image using coordinates on a plane).

When writing a research paper, I used the followingmethods:

The study of literature.

observation.

Creation of images on the coordinate plane.

Comparison of the received image with the actual one.

MAIN PART

The essence of the coordinate system

Communicating with each other, people often say: "Leave your coordinates." For what? To make the person easy to find. It can be: phone number, home address, place of work, email address. The essence of a coordinate or coordinate system is that it is a rule by which the position of an object is determined.

Coordinates in Everyday life

Coordinate systems are all around us:

in order to correctly take your place in the cinema, you need to know two coordinates - a row and a place;

system of geographical coordinates (latitude - parallels and longitude - meridians);

those who played sea battles in childhood also remember that each cell on the playing field was determined by two coordinates - a letter and a number:

with the help of a coordinate grid, pilots and sailors determine the location of objects;

used on tourist maps to search for an attraction or a desired street;

in astronomical observations, the coordinate grid is superimposed on the firmament with the Earth in the center.

From the history of the coordinate system

How long have coordinate systems permeated the practical life of a person?

More than 100 years BC, the Greek scientist Hipparchus proposed to encircle the globe on the map with parallels and meridians and enter the now well-known geographical coordinates: latitude and longitude and designate them with numbers.

In IIcentury AD the famous ancient Greek astronomer Claudius Ptolemy already used longitude and latitude as geographical coordinates. But these concepts were first systematized in the 17th century by René Descartes. René Descartes (1596-1650) French philosopher, naturalist and 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.

Components of the coordinate plane

At and While studying the topic "Coordinate line" in elementary school, we learned how to find the position of a point on a line by a coordinate. And how to specify the position of a point on a plane? For this we need coordinate plane. Consider its components (see Fig. 1):

two perpendicular lines - coordinate axes (often called - rectangular coordinate system)

horizontal - abscissa axis (x), vertical - ordinate axis (y), axis arrows indicate positive directions,

origin of coordinates - point of intersection of lines,

unit segments are chosen equal in length on each coordinate axis,

coordinate quarters.

Rice. 1. Components of the coordinate plane

Determining the coordinates of a point on a plane. Creation of graphic images on a plane by given coordinates

Each point on the coordinate plane corresponds to a pair of numbers: its abscissa (x) and ordinate (y). Conversely, each pair of numbers (x; y) corresponds to a single point on the plane. The coordinates of the point are written in brackets separated by a semicolon, and the coordinate is always written first.X , second coordinateat(see Fig. 2).

ALGORITHM 1 . In order to determine the coordinates of a point, you need:

X ;

write the resulting value in first place - this is the abscissa of the point;

drop a perpendicular from a point to an axisy ;

write the resulting value to the second place - this is the ordinate of the point.

ALGORITHM 2 . In order to find a point by given coordinates, A(x ; y ), need to:

Rice. 2. Determining the coordinate of a point

As a result of building several points, you can get an image. An example of building an image according to given coordinates is given in Appendix 3.

Transfer of constellations from the astronomical map to the coordinate plane and comparison with the image on the map of the starry sky

P we are trying to transfer the simplest constellation "Cassiopeia" to the coordinate plane (see Fig. 3):

Fig.3. Constellation "Cassiopeia"

Applying the algorithm 1 described above, we find the coordinates of the points of the constructed image:(– 5; 0), (– 3; 2), (– 1; 0), (1; 0), (3; – 2).

Let's compare the resulting image with the image of the constellation on the map of the starry sky ( see fig. 4 ):

Fig.4. The constellation "Cassiopeia" on the map of the starry sky

Now we transfer to the coordinate plane the constellations Ursa Major and Mala oh dipper(See Fig. 5) :

Fig.5. Constellations Ursa Major and Ursa Minor»

Let's determine the coordinates of the points of the resulting image:

Ursa Minor: (6; 6), (- 3; 5.5), (- 8; 5), (0; 7.5), (3; 7), (- 5; 7)

Big Dipper:

(– 15; – 7), (– 3; – 6), (5; – 10), (– 6; – 5,5), (– 10; – 5), (6; – 6), (– 1; – 10)

WITH compare the obtained images with the images of the constellations on the map of the starry sky(see Fig. 6, 7):

R Fig.6. The constellation "Ursa Minor" on the map of the starry sky

Fig.7. The constellation "Ursa Major" on the map of the starry sky

Similarly, images of all constellations can be transferred to the coordinate plane. The resulting images of some constellations and their coordinates are given in Appendix 4.

CONCLUSION

Thus, as a result of the research, I have solved the tasks. Namely, I learned the coordinate plane and related concepts. In addition, I was able to determinethe ability to create a graphic image on the coordinate plane, that is, create a drawing using known coordinates, as well as transfer images of constellations from an astronomical map to the coordinate plane.

As a result of the study, the proposed hypothesis was confirmed. I proved that images of the zodiac constellations can be transferred to the coordinate plane and the location can be written using coordinates.

Currently, the coordinate method is widely used in everyday life. Modern systems Satellite navigation allows you to determine the coordinates of an object, as well as monitor and control objects, including moving ones. This topic is also of great interest today and may become the topic of a new research development in the future.

LITERATURE

Children's encyclopedia: in 12 volumes. T. 2 World of celestial bodies. Numbers and figures. - M., Pedagogy., 1972. - S. 56 - 64, 306 - 308.

Erganzhieva L.N., Sharygin I.F. visual geometry. // Tutorial for students in grades 5-6. - Moscow., 1995. - S. 127 - 135.

Ishmuratova K. Journey to the world of constellations. // Mathematics. - 2008. - No. 5. - P. 5 - 6.

Pisklina O. Astronomy on the coordinate plane. // Mathematics. - 2001. - No. - S. 5 - 7.

Pyatibratova S.I. Fundamentals of student research. // Guidelines for pre-profile and profile training of schoolchildren focused on student research work. - St. Petersburg, 2005. - 25 p.

Fridman L.M. We study mathematics. // A book for students in grades 5-6 of educational institutions. - Moscow "Enlightenment"., 1995. - P. 174 - 175, 180 - 181.

Encyclopedic Dictionary of a Young Mathematician. - Moscow "Pedagogy"., 1985. - S. 151 - 153.

Annex 1

THE MOST BEAUTIFUL CONSTELLATION OF THE WINTER SKY

There is no other constellation in the entire sky that would contain as many interesting and easily accessible objects for observation as Orion, located near the constellation Taurus.

Orion was the son of the god of the seas, Poseidon. He was a famous hunter and boasted that there was no animal that he could not defeat. Orion cleared the island of Chios from wild animals and began to ask the king of this island for the hand of his daughter, but Orion died from a scorpion sting sent by Hera. Zeus placed him in the sky in such a way that he could always get away from his persecution, and indeed, these two constellations are never visible in the sky at the same time.

The constellation of Orion is the brightest winter constellation. In shape, it looks like a bow, in the middle there is a chain of three stars located on a straight line. This is Orion's belt. The star Alpha Orion is called Betelgeuse Arabic means "hunter's shoulder". From this star, light has been coming to us for more than 650 years. Betelgeuse is a red giant. The red light indicates that this star is colder than our Sun (its surface temperature is almost half that of the Sun). Another famous star in Orion is Rigel. It is very bright, bluish-white. It emits light almost 64,000 times more than our Sun. This is also a star - a giant, even a super-giant, but still smaller than Betelgeuse. Interestingly, Rigel is a triple star, that is, a couple more satellite stars revolve around the main giant star. Under the belt of Orion, you can find a hazy speck with the naked eye. This is the Orion Nebula, no less famous than the Andromeda Nebula. Orion is accompanied by two dogs - Big Dog and Small Dog. "Dog" in Latin sounds like "canis". The period of summer heat, when Sirius appears, and the rest from daily work associated with this, the ancient Romans called "holidays", which means "dog days". In those days, vacations were considered an unsettling time. It was believed that the dog star caused rabies in dogs and fever in humans. And now we look at Sirius not with fear, but with admiration. Just like the stars of Orion.

Appendix 2

LEGENDS AND POETRY ABOUT THE CONSTELLATIONS

Currently, there are many legends that have come to us from Ancient Greece and are associated with the zodiac constellations. Here is one of them.

« In ancient times, the king of the Ethiopians Cepheus had a beautiful wife - Queen Cassiopeia. Once Cassiopeia had the imprudence to boast of her beauty in the presence of nereids - inhabitants of the sea. Offended, the envious Nereids complained to the god of the sea, Poseidon, and he unleashed a terrible monster, Kita, on the shores of Ethiopia.

In order to pay off the Whale, who was devastating the country, Cepheus was forced, on the advice of the oracle, to give his beloved daughter Andromeda to be eaten by the monster. She was chained to a coastal rock. Every minute Andromeda expected that a Whale would emerge from the depths of the sea and swallow her.At this time, the hero of ancient Greece, Perseus, performed one of his feats: he penetrated a secluded island at the end of the world, where three terrible women lived - gorgons with tangles of snakes on their heads instead of hair. The look of the Gorgon turned everything living into stone. Taking advantage of the dream of the Gorgons, Perseus cut off the head of one of them named Medusa. The winged horse Pegasus fluttered out of her body. Two other gorgons, waking up, wanted to rush to Perseus, but he jumped on the winged Pegasus and, holding precious prey in his hands - the head of Medusa, flew home.

Flying over Ethiopia, Perseus noticed Andromeda chained to a rock. Keith was already heading towards her, emerging from the depths of the sea. Perseus entered into a mortal battle with the monster. It was possible to overcome the whale only after the chilling look of the dead head of Medusa fell on it. The whale petrified, turning into a small island. Perseus unchained Andromeda, brought her to Cepheus, and subsequently married her.

The fantasy of the ancient Greeks placed the main characters of this myth in the sky. This is how the names of the constellations Cepheus, Cassiopeia, Andromeda, Perseus, Pegasus, and Kita appeared.»

The names of the constellations are also often mentioned in poetic works:

Looking at the belt of the Zodiac,
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.
I bought myself a scale in April,
they wanted to live in peace
but in May the terrible Scorpio
they were deprived of rest and sleep.
He was killed by the beautiful Sagittarius,

June's father's unfortunate son,

in July, brother Capricorn
the dream of the Lion and the Virgin saved,
and in August, for many days
Uncle Aquarius arrived.
From Pisces ear it is in September
cooked and ate in the yard,
fried Aries in October,
Taurus slaughtered in November.
And finally in December
a pair of twins was born.

Internet Conference "Digital Horizons"

Creative work on the topic:

"Zodiac signs on the coordinate plane"

Work completed: student of 9 "A" class

MOU "Secondary school r.p. Red textile worker

Saratov district of the Saratov region"

Shirobokova Anna Valerievna

Scientific adviser: Physics teacher

honorary worker of general education

Sviridenko Olga Vladimirovna

Saratov, 2010

1. Introduction. Setting the goal of the work, problems and tasks .............................................. ........................3

2. Main part.............................................. ................................................. ......................................

2.1. History of coordinates creation............................................................... ................................................. ..........

2.2. Types of coordinate systems ............................................... ................................................. .................4

2.3. Coordinate systems in astronomy .............................................................. ................................................. ..5

2.4. A bit of history about the signs of the zodiac .............................................. ................................................. ..6

2.5. 12 signs of the zodiac ............................................... ................................................. ...............................

2.5.1. Aries constellation .................................................................. ................................................. ...............................7

2.5.2. Constellation Taurus .................................................................. ................................................. .........................

2.5.3. Constellation of Gemini .............................................................. ................................................. ...................8

2.5.4. Constellation Cancer .................................................................. ................................................. ...............................

2.5.5. Constellation Leo................................................... ................................................. .............................9

2.5.6. Constellation Virgo .................................................................. ................................................. ...............................

2.5.7. Constellation Libra .................................................................. ................................................. .........................10

2.5.8. Constellation Scorpio .................................................................. ................................................. .................

2.5.9. Constellation Sagittarius .................................................................. ................................................. ....................eleven

2.5.10. Constellation Capricorn.................................................................. ................................................. ...................

2.5.11. Constellation Aquarius .................................................................. ................................................. ....................12

2.5.12. Constellation Pisces .................................................................. ................................................. ...........................13

3. Conclusions ............................................... ................................................. ................................................. .

4. Bibliography .................................................... ................................................. ................................................

Appendix 1. Signs of the zodiac in 9 "A" class .............................................. ............................................14

Annex 2. Elements 9 "A" class .............................................. ................................................. .......15

1. Introduction.
The starry sky... binds me through boundless distances

with worlds and systems of worlds in boundless time

their periodic rotation,

their beginning and duration.

I.Kant

We live in a vast world full of mysteries and wonders. Throughout its history, mankind has been trying to solve them, striving for new knowledge and discoveries....

I have been interested in astronomy since childhood. I always liked to watch the starry sky, find the constellations and consider them. But then I had no idea that in addition to the 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 signs of the zodiac, and much more. Therefore, I decided to start studying the constellations and by all means 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 the zodiac constellations, but not everyone can find them in the starry sky. In this work, an attempt was made to construct images of the signs of the zodiac on the coordinate plane.

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

Tasks:

1) Get acquainted with the history of the origin of coordinates; consider different types of coordinate systems.

2) Study the zodiac constellations.

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

4) Conduct astrological research of students of 9 "A" class.

2. The main part.

2.1. History of coordinates creation.

For 200 years BC, the Greek scientist Hipparchus introduced geographical coordinates. He proposed to draw parallels and meridians on a geographical map and indicate latitude and longitude with numbers. . In the 14th century, the French mathematician N. Orsem proposed to call latitude the abscissa, and longitude the ordinate. On this innovation, the method of coordinates arose. The main merit in the creation of this method belongs to Rene Descartes.

2.2. Types of coordinate systems:

1. Spherical coordinate system

Spherical coordinates:

- object radius vector. Cartesian coordinate system

is the polar distance, which is sometimes

is called the colatitude, which varies from 0°

up to 180°.

- longitude, varying from 0° to 360°.

2. Coordinates on a straight line.

3. Polar coordinate system.
polar coordinates

points P are called the radius vector,

ρ - distance from point P to given point

O (poles) and polar angle φ is the angle between

line OP and given line,

passing through the pole (polar axis).

2.3. Coordinate systems in astronomy.

In ace In astronomy, coordinate systems are used that are associated either with the horizon, or with the celestial equator, or with the ecliptic, or with the plane of symmetry of the Milky Way. In the horizontal coordinate system, the position of an object relative to the observer is determined by the azimuth and elevation, that is, the height of the object above the horizon. Azimuth in astronomy is usually measured from the direction

to the South (the azimuth of the South point is considered equal to zero) to the direction of the object, counting the angle towards the West up to 360°. Thus, the azimuth of the North point is 180°. The elevation angle (or height) is determined from the condition that it is equal to 0 ° for sea level, and 90 ° for the zenith point (in the direction “directly overhead”). Instead of the elevation angle, the zenith distance is often used: 90° minus the elevation angle. When using a horizontal coordinate system, it is convenient to work with a theodolite that has two graduated scales: for measuring angles in the horizontal and vertical (determined by a plumb line) planes. Thus, it is possible to determine the location of any star in the sky. Since, when searching for comets, you have to move the telescope along the horizon many times (either to the East or to the West), the use of a horizontal coordinate system is very convenient. However, this convenience is limited by the location of observation: the horizontal coordinates of an object measured at a given location cannot be directly compared with horizontal coordinates determined elsewhere.
The equatorial coordinate system associated with the rotation of the Earth is free from this shortcoming. The vertical axis in this system is the axis of rotation of the globe, which is a straight line passing through the North and South Poles of the Earth. Its intersection with the celestial sphere determines the North and South poles of the sky, called the poles of the world. If the angular distance of 180 ° between these two poles is divided in half and, remaining at equal distances from both poles, mentally draw a circle across the sky, then what is called the celestial equator will be obtained.

If from the direction to the celestial equator (0°) we count the angle in the direction to the North Pole of the World (90°) with a plus sign, and in the direction of the South Pole of the World (-90°) - with a minus sign, then the angular coordinate will be determined, which is called declination (it is similar to geographic latitude). We now divide the celestial equator into 24 "time" zones, thereby determining the angular coordinate corresponding to geographic longitude. It is called right ascension and is measured in hours, minutes and seconds. The point on the celestial equator at which the Sun is located on the day of the vernal equinox is taken as the beginning of its countdown. Right ascension is counted counterclockwise from the vernal equinox when looking at the equator from the north celestial pole.

The equatorial coordinate system is primarily used to determine the positions of stars, but it is also used for the Moon and planets. However, the ecliptic coordinate system is especially convenient for the latter. In it, unlike the equatorial system, where the role of the main coordinate plane is played by the plane of the earth's equator, the plane of the earth's orbit serves the same purpose. If the intersection of the plane of the earth's equator with the celestial sphere gave the line of the celestial equator, then the intersection of the plane of the earth's orbit with the celestial sphere determines the so-called ecliptic line.

The ecliptic coordinate system was widely used in the old days when astrology dominated. Along the line of the ecliptic are 12 constellations, called the zodiac and conventionally denoted by special signs of the zodiac. So, for example, the point of the vernal equinox for a long time was in the zodiac constellation Aries, which is denoted by the symbol t, resembling a ram in shape.

Due to the precessional movement of the Earth's axis relative to the axis of the ecliptic, which has a period of 26 thousand years, the vernal equinox is constantly shifting and is currently in the constellation Pisces. Therefore, when indicating the position of an object in the sky using equatorial or ecliptic coordinates, it is necessary to clarify, to the equinox, which year the coordinate system is related to. When determining the position of a comet in the equatorial coordinate system, it is convenient to make measurements relative to the nearest star, for which we know the equatorial coordinates well.

2.4. A bit of history about the signs of the zodiac.

The allocation of the zodiac as a region of the celestial sphere, along which the visible path of the moon, and then the sun and planets, passes, occurred in Babylon. The first mention of the allocation of the zodiacal zone in the written sources of Babylon is contained in a series of cuneiform tablets "Mul Apin" (MUL.APIN - the constellation of the Plow), dating from the end of the beginning of the 7th century BC: these texts list 18 constellations on the "path of the Moon" and it is indicated that the Sun and five planets move along the same path, and a group of equatorial (and, accordingly, close to the ecliptic) stars is also distinguished. In the 7th-6th centuries BC. the number of divisions of the zodiacal zone was doubled, i.e. The zodiac is divided into 36 sections of 10°.

The Babylonian zodiac system also served as a system of celestial coordinates: the ecliptic longitudes of the luminaries were counted within the zodiacal area from its western border to the east.

The division of the zodiac into 12 parts probably occurred at the beginning of the 5th century BC, when 10 ° sections were grouped in three - in any case, references appear in this period zodiac horoscopes; in the Babylonian astronomical "diaries" 12 zodiac constellations are mentioned from the end of the 5th - the beginning of the 4th centuries BC. The division of the zodiac into 18-36-12 sections was due to the fact that the sexagesimal number system was adopted in Babylon, and they divided the ecliptic (and the circle in general) into 360 angular shares, which approximately corresponded to the number of days in a year - the zodiac arcs of the ecliptic in this system expressed in round numbers.

The ten-day system with 10 ° sections was perceived by Egyptian astronomy, and each decanal deity was put in correspondence with decanal deities (in the Greek name - “decans”), in Hellenistic Egypt they used a combined system - an example is the so-called Dendera zodiac - a bas-relief located on the ceiling of one of the rooms of the Temple of Hathor in Dendera, where along with the twelve zodiac sections are divided into decanal triplets.

Greek astronomy took the zodiac system of the Babylonians in the version with the division into 12 constellations (12 was sacred number- number Olympic gods V Greek mythology), the first mention in Greek sources of the zodiac in modern understanding found in Eudoxus of Cnidus, the founder of ancient Greek theoretical astronomy, the author of the theory of homocentric spheres around 370 BC. The further spread of the twelve-part zodiac system in the Hellenistic world was facilitated by the conquests of Alexander the Great, during which Babylon became part of the Seleucid state and, thus, the Hellenistic world.

2.5. 12 signs of the zodiac.

Zodiac constellations, zodiac, zodiac circle (from the Greek ζωδιακός, "animal") - 12 constellations located along the apparent annual path of the Sun among the stars - the ecliptic. Although the Sun also passes through the 13th constellation - the constellation of Ophiuchus, but it ancient tradition not included in the zodiac constellations.

Ecliptic - line on celestial sphere, along which, from the point of view of an earthly observer, the Sun makes its annual movement relative to the stars (this movement takes place in the direction opposite to the daily rotation of the celestial sphere)

In general, the figures of the constellations on the Egyptian zodiacs are very similar to the drawings of the same constellations in ancient European writings on astronomy. All twelve zodiac constellations in the "ancient Egyptian" version are usually recognized without much difficulty - and, fortunately, it is not required to decipher them. However, as we have found, there are some important features of the constellation figures in the Egyptian zodiacs that are not found in European drawings. These features, apparently, have not been noticed before. Meanwhile, they are important for deciphering the zodiacs in general. We are talking about the fact that the figures of the constellations on the Egyptian zodiacs were sometimes combined with the symbols of the planets, thereby forming a more complex symbol - so to speak, "astronomical hieroglyph".
2.5.1. Aries constellation.

Beginning The beginning of the zodiac is considered to be constellation Aries, here 2 thousand years ago was the point of the vernal equinox. Over the past time, it has moved a lot 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 one, astronomical spring begins.

It is most convenient to observe the constellation in autumn, when the sun is far from it.
2.5.2. Constellation Taurus.

2.5.3. Constellation Gemini.

Twins is the northernmost of the zodiac constellations. Observed in winter. Its brightest stars are Castor and Pollux. That was the name of the twin brothers who went with Jason on a campaign for the Golden Fleece. The brighter Pollux has an orange color. Upon closer examination, 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.” Between them, a “foggy star” (Nursery) is really visible.

2.5.5. Constellation Leo.

zodiacal constellation lion The best time to see it is during the spring months. Finding it is easy: A clear trapezoid of four bright stars forms the body of the Lion, and a weaker chain of stars curved in an arc 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 radiated light energy it exceeds it by 140 times.

2.5.6. Constellation Virgo.

The ancient Greeks called this constellation Parthenos, which in Greek means "Virgo". The celestial maiden is often depicted with a sheaf of ears of corn in her hands, and the name of her main star, Spica, means “ear” in Greek. 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 point of the autumn equinox. The ancient Roman poet Virgil wrote: “When Libra equalizes the hours of day and night and divides light and darkness equally in the world, then, farmer, bring your working oxen into the field.”

2.5.8. Constellation Scorpio.

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

2.5.9. Constellation Sagittarius.

Constellation Sagittarius located near the Milky Way. Ancient Greek myths tell of the wise centaur Chiron, who created the first model of the celestial sphere, and left one place for himself. But another centaur, the treacherous and cunning Krotos, took this place by deceit, becoming the constellation of Sagittarius. Zeus nevertheless placed Chiron in the sky, turning it into the constellation of the Centaur. And the evil Sagittarius even in the sky behaves militantly, aiming from a 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 saint of shepherds, met the hundred-headed giant Typhon and rushed into the water in horror. After that, Pan grew a fish tail, and he also became a water god. Constellation stars are not very interesting. It is curious that the star Algedi Capricorn is double. Physically, these 2 luminaries are not connected, they move away from each other in different directions. These stars are called optical binaries.

2.5.11. Constellation Aquarius.

In this zodiac constellation, different nations 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. Here is one of the largest planetary nebulae.

2.5.12. 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” in translation. With binoculars, it is visible as a bluish star, and a telescope allows you to see a satellite of the same color.

3. Conclusions.

In the course of my work, I got acquainted with the history of the emergence of coordinates, learned about the various types of coordinate systems, their features, origin and purpose. Having done a lot of work on studying the zodiac constellations and building them on the coordinate plane, I 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. By systematizing the acquired knowledge, I was able to conduct astrological research for students in grade 9 “A”.
4. Bibliography.

O. Pisklina,
school number 3, Tutaevo,
Yaroslavl region

Astronomy i on the coordinate plane

In the 6th grade, the topic "Coordinate plane and the construction of points on it" is studied. Working with a task-game "Astronomy on the coordinate plane" allows students to consolidate their knowledge and skills; show creativity in the study of this section; avoid difficulties when studying the topic "Function" (plotting function graphs in grades 7 - 11).

On the construction of constellations (Fig. 1 - 4) 10 minutes are allotted in the lesson. When constructing the constellations Ursa Major and Ursa Minor (Fig. 11), students should tell the legend about them.

Legend 1

..The ancient Greeks had a legend about the constellations Ursa Major and Ursa Minor. The almighty god Zeus decided to marry the beautiful nymph Calisto, one of the servants of the goddess Aphrodite, against the wishes of the latter. To save Calisto from the persecution of the goddess, Zeus turned Calisto into Ursa Major, her beloved dog into Ursa Minor and took them to heaven.

Legend 2

In ancient times, the king of the Ethiopians Cepheus had a beautiful wife - Queen Cassiopeia. Once Cassiopeia had the imprudence to boast of her beauty in the presence of nereids - inhabitants of the sea. Offended, the envious Nereids complained to the god of the sea, Poseidon, and he unleashed a terrible monster, Kita, on the shores of Ethiopia. In order to pay off the Whale, who was devastating the country, Cepheus was forced, on the advice of the oracle, to give his beloved daughter Andromeda to be eaten by the monster. She was chained to a coastal rock. Every minute Andromeda expected that a Whale would emerge from the depths of the sea and swallow her.

At this time, the hero of ancient Greece, Perseus, performed one of his feats: he penetrated a secluded island at the end of the world, where three terrible women lived - gorgons with tangles of snakes on their heads instead of hair. The look of the Gorgon turned everything living into stone. Taking advantage of the dream of the Gorgons, Perseus cut off the head of one of them named Medusa. The winged horse Pegasus fluttered out of her body. Two other gorgons, waking up, wanted to rush to Perseus, but he jumped on the winged Pegasus and, holding precious prey in his hands - the head of Medusa, flew home.

The fantasy of the ancient Greeks placed the main characters of this myth in the sky. This is how the names of the constellations Cepheus, Cassiopeia, Andromeda, Perseus, Pegasus, and Kita appeared.

Homework (according to options): invite students to depict constellation data on the coordinate plane. And for the final lesson, prepare messages about them (Fig. 5–10).

Constellation "Swan"

Constellation "Leo"

Constellation "Cepheus"

Constellation "Andromeda"

(– 2; 9),
(0; 7),
(1; 4),
(2; – 2),
(– 2; – 1)
(– 2; 5),
(– 4; 4)

Constellation "Perseus"

(– 5; – 3),
(– 2; – 2),
(0; – 1),
(2; – 2),
(4; – 1),
(5; 0),
(6; 2)
(0,5; 1),
(1; 3)

Constellation Ursa Major

(– 15; – 7), (– 3; – 6), (5; – 10),
(– 6; – 5,5), (– 10; – 5), (6; – 6), (– 1; – 10)

Literature

1. Children's encyclopedia. T. 2, - M., Enlightenment, 1964.
2. Levin B., Radlova L. Astronomy in pictures. - M., Children's literature, 1988.
3. Geographical atlas "The world around us". - Minsk, GUGK USSR, 1989.

Municipal budgetary educational institution

Isaevskaya basic comprehensive school

Zodiac signs on

coordinate plane

Done: 6th grade students

Banko Tatyana Sergeevna

Vorobyov Sergey Stanislavovich

Head: Shevakov Andrey Ivanovich

mathematic teacher

Kh.Isaev

2016

Brief annotation

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 meaning of the coordinate plane and the signs of the zodiac.

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

The results of a survey among classmates. Who was born, under what sign of the zodiac.

1. Introduction.

We live in a vast world full of mysteries and wonders. Throughout its history, mankind has been trying to solve them, striving for new knowledge and discoveries....

Still from childhood they love to look at the stars in the sky. We have always enjoyed watching starry sky. But then we had no idea that in addition to the 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 will be able to 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 of school students.

Content

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

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

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

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

6. Signs of the Zodiac in coordinates………………...........……………….

7. Astrological studies of schoolchildren…………….......………..

8. Interesting Facts about the elements………………………………………..

9. References………………………………………………………….

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

2.History of origin of coordinates.

For 200 years BC, the Greek scientist Hipparchus introduced geographical coordinates. He suggested drawing parallels and meridians on a geographical map and marking latitude and longitude with numbers. With these two numbers, you can accurately determine the position of an island, village, mountain or well in the desert and put 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 a minus sign. Thus, a pair of numbers with signs uniquely defines a point on the globe.

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

For a long time only geography "description of the earth" - 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 the abscissa and ordinate.

Based on this successful innovation, the method of coordinates arose, linking geometry with algebra. The main merit in the creation of this method belongs to the great French mathematician René Descartes (1596 - 1650). In his honor, such a coordinate system is called Cartesian, denoting the location of any point in the plane with 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 the point is denoted by the letter x, "longitude" - the letter "y".

It is necessary to select a certain plane and introduce a Cartesian coordinate system on it, and to our point we compare 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 minus signs for the other; so 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 man and on the Earth. Among the 88 constellations that adorn the night sky, a special place is occupied by those among which the Sun passes its yearly 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 each sign of the Zodiac, but according to ancient Greek legend, the Sun passes through 13 signs. The thirteenth is Ophiuchus, but according to ancient traditions, he is not considered among the zodiac constellations.

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

In fact, of course, the Earth moves around its luminary, but it seems to us that it is the Sun that changes its location. So did the ancient astronomers who named the zodiac constellations.

They noticed that the Sun always follows the same path across the sky and every month "stays" at the signs of the Zodiac: in January - at Capricorn, in February - at Aquarius, in March - at Pisces ... It has long been believed that the sign of the Zodiac, that is, the month of birth of a person determines his character, influences behavior and predetermines fate. Each sign of the Zodiac has its own legend about the origin, here are a few of them:

Lion - a huge lion settled near Nemea. Horror seized the people when they heard his roar. The people did not leave their dwellings, famine set in, diseases began.

The valiant Hercules decided to kill Nemean lion. Hercules wandered for a long time on the slopes of the mountains. The sun began to set. And then a terrifying roar reached the hero. In a few jumps, Hercules reached the lion's lair - a huge cave with two exits. When a giant beast roared out of the cave, 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 it by the neck with his mighty hands and strangled it.

Having shouldered a huge carcass, Hercules went to Nemea. There he sacrificed to Zeus and established the Nemean Games in memory of this feat. And he began to wear a 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, who grabbed Hercules by the leg. Enraged, Hercules crushed him, thereby inadvertently eliminating another enemy.

Capricorn - when the day of the winter solstice came, the hour came for the birth of the great Zeus. Rhea - the goddess, having wrapped a stone in diapers, 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 the forest nymphs in charge. And the goat Amalthea nursed him with her milk. The years have flown by. Zeus grew up and matured. Rebelling against his father, he freed his divine brothers and sisters, becoming chief among them. Zeus did not forget and his nurse goat Amalthea, placing her in the sky - this is the constellation CAPRICORN.

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

Libra - when Astrea was transferred 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. Among the Greeks it is called - Hydrohos, among the Romans - Aquarius, among the Arabs - Sakib - alma. They all mean the same thing: a person pouring water.

Pisces - once the goddess of love and beauty Aphrodite and her son Eros walked along the bank of the river, near which wild Typhon hid, who got out of the dungeon. Suddenly the ferocious Typhon attacked them. In horror at its wild appearance, the immortals rushed into the water, turned into sparkling fish and swam away from the vile monster. So 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 labyrinth, people have combined the brightest stars into geometric figures, or constellations, they gave them the names of heroes, gods and animals. With the help of a teacher, I built the 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 ARIES.

The constellation Aries was highly revered in antiquity. supreme god 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. In the sky, by the way, there are a number of constellations 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 was the constellation Taurus, since New Year started 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 that constellation was associated with the bull (calf), where the Sun, as it were, conquered winter and heralded the arrival of spring and summer. In general, many ancient peoples revered this animal, 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 the Minotaur. Heroes of Hellas Hercules, Theseus, Jason subdued the bulls.

WHERE ARE THE GEMINI IN HEAVEN? (Slide 8)

In this constellation, two bright stars are very close to each other. They got their name in honor of the Argonauts Dioscuri - Castor and Pollux - twins, sons of Zeus, the most powerful of the Olympic gods. Castor was famous as a skilled charioteer, and Pollux as an unsurpassed fist fighter. They participated in the campaign of the Argonauts and the Calydonian hunt. But one day the Dioscuri did not share the booty with their cousins, the giants Idas and Linkey. In the battle with them, the brothers were badly 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 the patrons of sailors caught in a storm.

CONSTELLATION CANCER. (Slide 9)

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

CONSTELLATION LION. (Slide 10)

About 4.5 thousand years ago, the point of the summer solstice was in this constellation, and the Sun appeared 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 “great fire”, and the Chaldeans associated the fierce lion with the no less fierce heat that was every summer. They believed that the Sun receives additional strength and warmth, being among the stars of the lion. In Egypt, this constellation was also associated with the summer period: flocks of lions, fleeing the heat, migrated from the desert to the Nile valley, which at that time was flooding. Therefore, the Egyptians placed on the gates of irrigation canal locks that directed water to the fields, images in the form of a lion's head with an open mouth.

VIRGO. (Slide 11)

The Virgo constellation, located next to Leo, this constellation was sometimes represented by a fabulous 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 evidence that in this constellation, ancient observers saw Astrea, the daughter of Themis and the god Zeus - the goddess of justice, a symbol of purity and innocence, who left the Earth because of the crimes of people. Virgo is usually depicted with the rod of Mercury and an ear, which indicates the connection of this star with human agricultural activities. It is possible that the beginning of any agricultural work coincided with her appearance in the sky.

SCALES -

THE ONLY "NON-LIFE" CONSTELLATION. (Slide 12)

Over two thousand years ago, this constellation was the point of the autumnal equinox. The equality of day and night could be one of the reasons why the zodiac constellation was named Libra. Scales - a symbol of balance - could simply remind the 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 Astrea regularly “inspected” the Earth (armed with scales and blindfolded in order to judge everything objectively and mercilessly punish deceivers, liars and anyone who dared to commit all kinds of unjust acts). So Zeus decided that Libra's daughter should be placed in the sky.

CONSTELLATION SCORPIO. (Slide 13)

Not only because of the external similarity, this constellation was assigned the role of a poisonous creature. The sun entered this region of the sky in late autumn, when all nature seemed to die, in order to be reborn again, like the god Dionysus, in early spring. next year. The sun was considered “stung” by some poisonous creature (by the way, in this area of the sky there is also the constellation of the Serpent!), “from that it hurt” all winter, remaining weak and pale. It was he, the heavenly Scorpio, who frightened the most unfortunate Phaethon, the son of the god Helios, who decided to ride across the sky in his fiery chariot, not 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, turned out to be in it. Scorpio is a constellation where new stars often flare up.

WHO IS THE STAR SAGITTER AIMING? (Slide 14)

Even Scorpio himself is afraid of the evil Sagittarius, at whom he aims with a bow. Sometimes you can find the image of Sagittarius in the form of a centaur with two faces: one is turned back, the other is forward. In this he resembles the Roman god Janus. The first month of the year, January, is associated with the name of Janus. And the Sun is in Sagittarius in winter. Thus, the constellation, as it were, symbolizes 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 is a mythical creature with the body of a goat and the tail of a fish. According to the most common ancient Greek legend, the goat-footed god Pan, the son of Hermes, the patron saint of shepherds, was frightened by the hundred-headed giant Typhon and rushed into the water in horror. He has since become a water god and has grown a fish tail. Transformed by the god Zeus into a constellation, Capricorn became the lord of the waters and the harbinger of storms. It was believed that he sends heavy rains to the earth. Among many ancient peoples, the goat was revered as a sacred animal; divine services were performed 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 \u200b\u200ba "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)

The constellation of Aquarius is associated with 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 as flowing from the vessel of Aquarius. In Egypt, the constellation Aquarius was observed in the sky during the days of the highest water level in the Nile River. It was believed that the god of water overturns a huge ladle into the Nile. It is possible that the legend about one of the exploits of Hercules is connected with the constellation Aquarius - cleaning the Augean stables (for which the hero needed to dam three rivers).

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

The very arrangement of the stars in the sky inspires the idea of two fish tied together with a ribbon or rope. The origin of the name of the constellation Pisces is very ancient. In this constellation, the Sun entered the season of rich fishing. The goddess of fertility was depicted as a woman with a fish tail, which, according to legend, appeared to her when she and her son, frightened by a monster, rushed into the water.

SIGNS AND CONSTELLATIONS OF THE ZODIAC

Background stars located in the plane of the ecliptic are combined into the so-called zodiac 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 originated in ancient times. The very word "zodiac" (in Greekzodiakos) comes from the word "zoon”- “animal”, since most of the constellations have been given the names of various animals by folk fantasy.

Zodiac
(1961 Valishin Yu.I.)

Looking at the belt of the zodiac,
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.
I bought myself a scale in April,
They wanted to live in peace
But in March, the terrible Scorpio
They were deprived of peace and sleep.
He was killed by the beautiful Sagittarius,
June's father's unfortunate son,
In July, brother Capricorn
The dream of the Lion and the Virgin saved,
And in August for many days
Uncle Aquarius arrived.
From Pisces ear it is in September
Cooked and ate in the yard,
Roasted Aries in October
Taurus slaughtered in November
And finally in December
A pair of twins was born.

2.5.1. Aries constellation.

The beginning of the zodiac is considered to beconstellation Aries , here 2 thousand years ago was the point of the vernal equinox. Over the past time, it has moved a lot 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 one, astronomical spring begins.

It is most convenient to observe the constellation in autumn, 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 a scattering of not very bright stars that form a triangle (the muzzle of Taurus).
2.5.3. Constellation Gemini.Twins is the northernmost of the zodiac constellations. Observed in winter. Its brightest stars are Castor and Pollux. That was the name of the twin brothers who went with Jason on a campaign for the Golden Fleece. The brighter Pollux has an orange color. Upon closer examination, this star turns out to be a system of four stars.

2.5.4. Constellation Cancer.

2.5.5. Constellation Leo.

2.5.6. Constellation Virgo.

2.5.7. Constellation Libra.

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

2.5.10. Constellation Capricorn.

2.5.11. Constellation Aquarius.

2.5.12. 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” in translation. With binoculars, it is visible as a bluish star, and a telescope allows you to see a satellite of the same color.

7. Astrological studies of students of the Isaev school.

Elements of students of the Isaev school.

8. Interesting facts about the elements.

Element of Fire. The features of this element are warmth and dryness, which are accompanied by metaphysical energy, life and its strength. 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 governing force of instinct, spirit, thought and mind, forcing you to go forward, to believe, to hope, to defend your convictions. The main driving force of Fire is ambition. Fire gives zeal, impatience, carelessness, self-confidence, irascibility, impetuosity, courage, courage, militancy. In the human body, it maintains life, is responsible for the temperature regime and stimulates the metabolism.

People whose horoscopes highlight the trine of the element of Fire have a choleric temperament. These people will never go unnoticed, they will achieve the recognition of others, especially in the 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 outstanding penetrating power. The element of Fire gives organizational talent, a thirst for activity and enterprise. Fire knows the strength of its own dignity.

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

The earth creates forms, laws, gives concreteness, stability, stability. Earth structures, analyzes, classifies, creates a foundation. It has such qualities as inertia, confidence, practicality, reliability, patience, rigor. In the body, the Earth gives inhibition, petrification through contraction and compression, slows down the process of metabolism.

People whose horoscopes express the element of the Earth have a melancholy temperament. These are people of sober mind and prudence, very practical and businesslike. The goal of life for them is always real and achievable, and the path to this goal is already planned in their youth. If they deviate from their goal, then very little, 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 a fantasy and vivid, vivid imagination as the signs of the Water trine, they lack utopian ideas, like the signs of Fire, but they stubbornly go towards 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 reaching their intended goal.

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

Air defines contacts and relationships. The element of Air endows a person with such qualities as mobility, activity, liveliness, changeability, flexibility, agility, receptivity, omnipresence, infinity, 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 they pass it all on to other people in a processed form in their own way. They instantly adapt to any changes and changes in life. They are characterized by spiritual flexibility, lability of the psyche, mobility of the mind, they are tireless, as long as they are passionate about some business. Monotony makes them tired.

Element of Water. The 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 trine of water is considered the trine of feelings and sensations. Principle: the constancy of the internal with external variability. Water is emotion inner world, preservation, memory. It is plastic, changeable, secretive. Gives such qualities as uncertainty, daydreaming, imaginative thinking, softness of manifestation. In the body, it slows down the metabolism, manages fluids, the work of the 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 of an inner life than an outer one. People of the trine of Water are usually contemplative, they think both about their own good and about the good of their loved ones, however, at times they are indifferent, lethargic, 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 trines of Fire or Air, but they experience internal feelings with great strength and depth.

Of the signs of the trigon of Water, Scorpio is the strongest in body and spirit, the most meaningful, the most aggressive, not amenable to undesirable outside influences and exerting strong resistance to everything that his soul does not agree with. His patience, endurance, tenacity and perseverance are simply amazing.

9. List of references.

1. The book "Unsolved mysteries of mankind" CJSC "Publishing House Reader's Digest", France, 2004.

2. Book "All the secrets of the world" CJSC "Publishing House Reader's Digest", France, 2001.

3. The book "Only facts" CJSC "Publishing House Reader's Digest", 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 got acquainted with the history of the emergence of coordinates, learned about the various types of coordinate systems, their features, origin and purpose. Having done a lot of work on the study of 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, built 4 signs on the coordinate plane. By systematizing the acquired knowledge, we were able to conduct astrological studies of students of our school.

3. Conclusions.

In the course of my work, we got acquainted with the history of the emergence of coordinates, learned about the various types of coordinate systems, their features, origin and purpose. Having done a lot of work on studying the zodiac constellations and building 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. By systematizing the acquired knowledge, they were able to conduct astrological studies of school students.

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