Astrology on the coordinate plane. Astronomy on the coordinate plane Why are the zodiac signs indicated on the coordinate plane

There is no HTML version of the work yet.

Astronomy I'm on the coordinate plane

In the 6th grade, the topic “Coordinate plane and constructing points on it” is studied. Working with a task-game "Astronomy on the coordinate plane" allows students to consolidate acquired knowledge and skills; show creativity when studying this section; avoid difficulties when studying the topic “Function” (graphing functions in grades 7–11).

During the lesson, 10 minutes are allotted for constructing constellations (Fig. 1 – 4). 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 latter’s wishes. To save Kalisto from the persecution of the goddess, Zeus turned Kalisto 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. One day, Cassiopeia had the imprudence to boast of her beauty in the presence of the Nereids, the inhabitants of the sea. Offended, the envious Nereids complained to the god of the sea, Poseidon, and he released a terrible monster - Whale - onto the shores of Ethiopia. In order to pay off Keith, who was devastating the country, Cepheus was forced, on the advice of the oracle, to give his beloved daughter Andromeda to be devoured 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 ancient Greece Perseus performed one of his exploits: he penetrated a secluded island at the end of the world, where three terrible women lived - gorgons with balls of snakes on their heads instead of hair. The Gorgon's gaze turned all living things into stone. Taking advantage of the gorgons' sleep, Perseus cut off the head of one of them named Medusa. The winged horse Pegasus flew out of her body. The other two gorgons, having woken up, wanted to rush at Perseus, but he jumped on the winged Pegasus and, holding the precious booty in his hands - the head of Medusa, flew home.

Flying over Ethiopia, Perseus noticed Andromeda chained to a rock. Whale, having emerged from the depths of the sea, was already heading towards her. Perseus entered into mortal combat with the monster. The whale was defeated only after the chilling gaze of the dead head of Medusa fell on it. The whale was 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 Cetus appeared.

Homework (according to options): invite students to depict constellation data on a 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., Education, 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.

14th regional scientific and practical conference of students Section mathematics Astronomy on the coordinate plane Completed by Danil Karmanov Student 5 “B” class MNBOU “Lyceum No. 76” Head Mathematics teacher Ekaterina Igorevna Bukurova Novokuznetsk 2015 Contents I. Introduction………………………… ……………………………………...….3 II. Main part……………………………………………………………..4 2.1 History of the origin of coordinates…………...…………………..4 2.2 Types of coordinate systems…………………………………………….5 2.3 The starry sky and legends about the twelve signs of the Zodiac………….6 2.4 Signs of the Zodiac in coordinates…………………… ………………..10 2.5Astrological characteristics of my class……………….……11 III. Conclusion…………………..…………………………………………12 IV. List of references………………………………………………………………...…..13 Appendix 1…………………………………………………… ………………14 2 I. Introduction I always liked watching the starry sky, when I was little, I thought that the stars in the sky were randomly located. But my mother told me that there is such a science as astronomy and I became interested in it. I 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. Statement 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. Purpose of the work: to consider the signs of the zodiac through the theory of the coordinate plane. Objectives: 1) 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 program in the 6th grade); 2) expand knowledge about coordinates and their application in human everyday life; 3) get acquainted with the history of the origin of coordinates; 4) consider different types of coordinate systems; 5) study the zodiac constellations; 3 6) construct an image of the constellation on the coordinate plane; 7) create didactic material “to help the teacher” for conducting a general lesson on the topic “coordinate plane”; 8) conduct astrological research for students in grade 5 “b”; 9) prepare a presentation “Astronomy on the coordinate plane.” In the process of work, I used the following research methods and techniques:  study of theoretical sources;  observation;  work with photographic materials;  consultation with teacher and parents. 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 200 years BC, the Greek scientist Hipparchus introduced geographic coordinates. He suggested drawing parallels and meridians on a geographical map and indicating 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. Having learned to determine the latitude and longitude of a ship’s location in the open world, sailors were able to choose the direction they needed. 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) proposed covering the plane with a rectangular 4 grid and calling latitude the abscissa and longitude the ordinate. This innovation gave birth to the coordinate method. The main credit for creating this method belongs to Rene Descartes. In his honor, such a coordinate system is called Cartesian. 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”. 2.2 Types of coordinate systems and their application 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. 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. 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. There are different coordinate systems on the plane. For example, the polar coordinate system. To introduce a polar coordinate system, A Angle Polis Polar axis is chosen as the initial pole (therefore, the point 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. 5 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 a scale (unit of length measurement) on each of them. We denote the intersection point by the letter O and its origin. We will consider these straight lines. So we have obtained a rectangular coordinate system on the 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 The 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 on 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. 6 Most of the names belong to animals, so these received zodiacal names (from the Greek zodiakos constellation - “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. 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. Long The Golden Fleece it was shining, and its horns curled into cool 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. 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 anguish, seeing nothing but sky and water, the maiden 7 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. Gemini - the brothers once 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. 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. 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 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. 8 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 - 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. Sagittarius – Once upon a time, the great Greek hero 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. Scorpio - Hera placed Scorpio in heaven because he killed the evil hunter Orion, who decided to exterminate all animals on earth. 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. 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 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. 2.3 Signs of the Zodiac in coordinates In my work, I propose to construct drawings of the twelve signs of the Zodiac on the coordinate plane in order to create didactic material “to help the teacher” for conducting a general lesson on the topic “coordinate plane”. Each card has an image of one of the zodiac 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. After constructing all the signs, you can create a map of the starry sky. The cards I created are in Appendix 1. 10 2.4 Astrological characteristics of my class To compile the astrological characteristics of class 5B, I conducted a survey “Who are you according to your zodiac sign?”, “Do you know what your constellation looks like?” and made charts based on the results. From which it can be seen that in our class there are most Leos (13%), Capricorns (13%), Scorpios (3%) and Aquarius (17%). This means that our class is: adventurous, sincere, kind, generous, proud, hardworking, serious, honest. And it also turned out that (75%) of students do not know what their constellation looks like. 11 III. Conclusion In this work I tried to combine two subjects: mathematics and astronomy. The theoretical part tells about the history of the origin of coordinates and their creators. I learned that there are different coordinate systems, how widely and where they are used in human daily life. In addition, in my 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 my work was to construct all twelve constellations of the Zodiac signs on the coordinate plane and compile cards for teaching material for the teacher. To do this, I studied the appearance of each of the 12 constellations:  how many stars (points) the constellation consists of  how they are connected to each other  the distance between the points Then I built them using coordinates (x; y) for each star. The materials from my 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. At the end I present an astrological portrait of my class. We will study the topic “Coordinate Plane” in 6th grade, so I am interested in continuing to study this material. 12 IV. References 1. E. N. Bakhtina. Book of Stars. Moscow “Interbook”, 1997. 2. A. Savin. Coordinates // Quantum. 1977. No. 9 3. Internet source zodiac-art.narod.ru 4. Internet source http://5klass.net 5. Internet source http://www.cleverstudents.ru/vectors/cartesian_rectangular_coordinates.htm l 13 Appendix 1 Constellation Aries Coordinates Paths of connection 1→2→3→4→5→6→4 1(-13;10) 4→7→9→2 2(-13;6) 9→10 and 7→8 and 1 →3 3(-10;7) 4(2;4) 5(6;5) 6(7;1) 7(1;-1) 8(8;-2) 9(-14;-3) 10 (-18;-7) On the coordinate plane Constellation Taurus Coordinates 1(-14;7) 2(-5;3) 3(-17;0) 4(-3;-3) 5(-1;-3) Connection paths 12345106789 and 82 101112 10141517 and 1516 and 1518 and 1013 On coordinate plane 6(1;0) 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) 14 Constellation Gemini Coordinates 1( -8;11) 2(-11;9) 3(-4;8) 4(-8;3) 5(-11;-1) 6(-7;-10) 7(-5;-1) 8(-2;-8) 9(-2;13) 10(-1;11) 11(8;8) 12(2;1) 13(2;-7) 14(6;-5) 15( 8;-6) 16(11;-7) 17(-7;9) 18(1;8) Connection paths On the coordinate plane 1→17→4→5→6 4→7→8 17→3→18→ 10→9 18→12→14→15→16 17→2 and 18→11 and 12→13 Constellation Cancer Coordinates 1(-10;3) 2(-3;4) 3(-6;-8) 4 (2;-3) 5(1;6) 6(6;12) Connection paths On the coordinate plane 123456 25 15 Constellation Leo Coordinates 1 (-21;-4) 2 (-11;2) 3 (-8;1) 4 (3;3) 5 (4;6) 6 (8;9) 7 (14;10) 8 (13;7) 9 (10;7) 10 (7;0) Connection paths On the coordinate plane 1→2→3→4→5→6→7→8→9→10→13→15 →16 4→10 and 6→9 10→11 and 10→12 13→14 and 13→2 11 (14;-6) 12 (7;-5) 13 (-11;-4) 14 (2;-8) 15 (-13;-8) 16 (-11;- 13) Constellation Virgo Coordinates 1 (6;7) 2 (10;6) 3 (10;3) 4 (6;0) 5 (3;-1) 6 (-1;-5) 7 (-3;- 9) 8 (-10;-10) 9 (-12;-7) 10 (-16;-9) 11 (-19;-3) 12 (-12;-2) 13 (-6;-3) 14 (-1;2) 15 (-4;7) Connection paths 1→2→3→4→5→1 5→6→7→8→9→12→13→14→15 14→5 9→10 and 12→11 On the coordinate plane 16 Constellation Libra Coordinates 1(-4;12) 2(10;7) 3(9;-5) 4(-10;4) 5(-1;-10) 6(- 2;-12) Connection paths On the coordinate plane 1→2→4→5→6 2→3 and 1→4 Constellation Sagittarius Coordinates 1(7;5) 2(10;9) 3(11;1) 4( 8;-4) 5(7;-2) 6(8;2) 7(3;4) 8(0;1) 9(-4;-7) 10(-3;-10) 11(-12 ;-3) 12(-10;-8) 13(-2.4) 14(1.5) 15(0;9) 16(-2;9) 17(-6;11) 18(-5; 13) Connection paths On the coordinate plane 1234561 and 63 678910 91112 111314151614 16 1718 and 147 17 Constellation Scorpio Coordinates 1(-19;2) 2 (-15;2) 3 (-14;2) 4(-16;0) 5(-18;0) 6(- 19;-2) 7(-16;-4) 8(-11;-5) 9(-7;-4) 10(-6;-1) Connection paths 1→2→3→4→5→6 →7→8→9→10→11→ 12→→13→14→15→16→17→1 On the coordinate plane 11(-5;3) 12(0;7) 13(3;9) 14(6 ;9) 15(8;14) 16(10;14) 17(12;11) 18(11;7) 19(10;4) 20(6;6) Constellation Aquarius Coordinates Path of conjunction 1(-21; -10) 143 and 42 2(-17; -11) 45678469101112 13101415 3 (-22; 0) 14161718 4(-20;2) 5(-19;5) 6(-14; 3) On the coordinate plane 7(-13; -3) 8(-14; -5) 9(-5; 4) 10(-4; 11) 11(-7; 10) 12(-11; 11) 13(-8; 13) 14(4;16) 15(-2;- 2) 16(11;0) 17(16;3) 18(17;2) 18 Constellation Capricorn Coordinates 1(-22;3) 2(-18;2) 3(-11;2) 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) Connection paths On the coordinate plane 12345678 and 36 791011 9 126 and 1213 Constellation Pisces Coordinates Connection paths 1→2→3→4→5→6→7→8→9→10→11→ 1(-10;13) →12→13→14→15→ 16→17→18→19→14 2(-12;11) 1→3 3(-10;8) 4(-14;3) 5(-15;0) 6(-19;-5) 7( -22;-10) 8(-17;-8) 9(-14;-8) 10(-11;-6) 11(-8;-6) 12(-5;-7) 13(6; -6) 14(11;-7) 15(11;-12) 16(15;-11) 17(17;-9) 18(17;-7) 19(15;-7) On the coordinate plane 19

INTRODUCTION

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

The history of the constellations is very interesting. Long ago, sky observers grouped the most prominent groups of stars into constellations and gave them various names. These were the names of mythical heroes or animals, characters from 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 called- these are the ones through which it passes. Also in The zodiacal constellations were allocated to a special group, and each of them was assigned its own sign. Most rich bright stars winter sky. The most beautiful constellation in the winter sky is Orion (Appendix 1).

Currently, there are many legends that came 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 the beautiful nymph Calisto as one of her servants. The almighty god Zeus decided to take Calisto as his wife against the wishes of Aphrodite. To save Kalisto from the persecution of her mistress, Zeus turned Kalisto into Ursa Major and her beloved dog into Ursa Minor and took them to heaven.”

Studying in primary school 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 mathematics was chosen, andsubject of research - coordinate plane.

At the beginning of my work I put forwardhypothesis : “Images of the zodiacal constellations can be transferred to a coordinate plane and the location recorded using coordinates.”

As tasks research work I identified:

Explore 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 astronomical map(plane) to coordinate.

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

When writing a research paper I used the followingmethods:

Studying literature.

Observation.

Creating images on the coordinate plane.

Comparison of the received image with the actual one.

MAIN PART

The essence of the coordinate system

When communicating with each other, people often say: “Leave your coordinates.” For what? So that the person is easy to find. This could be: telephone number, home address, place of work, email address. The essence of coordinates or a coordinate system is that it is a rule by which the position of an object is determined.

Coordinates in everyday life

Coordinate systems surround us everywhere:

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

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

those who played naval battle as children also remember that each cell on the playing field was determined by two coordinates - a letter and a number:

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

used on tourist maps to search for attractions or the desired street;

during astronomical observations, a coordinate grid is superimposed on the vault of heaven 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 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 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 Rene Descartes. 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.

Components of the coordinate plane

When and While studying the topic “Coordinate Line” in elementary school, we learned to find the position of a point on a line using a coordinate. How to indicate the position of a point on a plane? For this we need coordinate plane. Let's look at its components (see Fig. 1):

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

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

the origin of coordinates is the point of intersection of lines,

unit segments are chosen to be 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 at given coordinates

Each point on the coordinate plane corresponds to a pair of numbers: its abscissa (x) and ordinate (y). And vice versa, each pair of numbers (x; y) corresponds to a single point on the plane. The coordinates of a point are written in parentheses separated by a semicolon, and the coordinate is always written firstX , 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 in second place - this is the ordinate of the point.

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

Rice. 2. Determining the coordinates of a point

As a result of constructing several points, an image can be obtained. An example of constructing an image using given coordinates is given in Appendix 3.

Transferring constellations from an astronomical map to a coordinate plane and comparing them with the image on a star chart

P We are trying to transfer the simplest constellation “Cassiopeia” to the coordinate plane (see Fig. 3):

Fig.3. Constellation Cassiopeia

Using 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 star map ( see Fig. 4 ):

Fig.4. Constellation "Cassiopeia" on the star map

Now let’s transfer the constellations Ursa Major and Ursa Minor to the coordinate plane. oh Ursa(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 resulting images with images of constellations on a star map(see Fig. 6, 7):

R is.6. Constellation "Ursa Minor" on the star map

Fig.7. Constellation "Ursa Major" on the star map

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 solved the assigned problems. Namely, I studied 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 put forward hypothesis was confirmed. I proved that images of the zodiac constellations can be transferred to a coordinate plane and the location can be recorded 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 new research development in the future.

LITERATURE

Children's encyclopedia: in 12 volumes. T. 2 The world of celestial bodies. Numbers and figures. – M., “Pedagogy”., 1972. – P. 56 – 64, 306 – 308.

Erganzhieva L.N., Sharygin I.F. Visual geometry. // Tutorial for students in grades 5-6. – Moscow., 1995. – P. 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. – P. 5 – 7.

Pyatibratova S.I. Fundamentals of student research. // Methodological recommendations for pre-professional and specialized training of schoolchildren focused on student research work. – St. Petersburg, 2005. – 25 p.

Friedman L.M. We study mathematics. // Book for students in grades 5-6 of general education institutions. – Moscow “Enlightenment”., 1995. – P. 174 – 175, 180 – 181.

Encyclopedic dictionary of a young mathematician. – Moscow “Pedagogy”., 1985. – P. 151 – 153.

Annex 1

THE MOST BEAUTIFUL CONSTELLATION OF THE WINTER SKY

There is no other constellation in the entire sky that would contain so 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 the bite of a scorpion sent by Hera. Zeus placed him in the sky in such a way that he could always escape his pursuit, and indeed, these two constellations are never visible in the sky at the same time.

The constellation Orion is the brightest winter constellation. It is shaped like a bow, in the middle there is a chain of three stars located in a straight line. This is Orion's belt. The star Alpha Orionis is called Betelgeuse, which is Arabic means "hunter's shoulder". The light from this star has been coming to us for more than 650 years. Betelgeuse is a red giant. The red light indicates that this star is cooler 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 almost 64,000 times more light than our Sun. This is also a giant star, even a supergiant, but still smaller than Betelgeuse. It is interesting that Rigel is a triple star, that is, another pair of satellite stars revolve around the main giant star. Below Orion's belt you can see a nebulous speck with the naked eye. This is the Orion Nebula, no less famous than the Andromeda Nebula. Orion is accompanied by two dogs - Canis Major and Canis Minor. "Dog" in Latin sounds like "canis". The period of summer heat when Sirius appears, and the associated rest from everyday work, was called “vacation” by the ancient Romans, which means “dog days”. In those days, the holidays were considered an anxious time. There was a belief that the “dog star” caused rabies in dogs and fever in people. And now we look at Sirius not with fear, but with admiration. The same as for the stars of Orion.

Appendix 2

LEGENDS AND POETIC WORKS ABOUT CONSTELLATIONS

Currently, there are many legends that came 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. One day, Cassiopeia had the imprudence to boast of her beauty in the presence of the Nereids, the inhabitants of the sea. Offended, the envious Nereids complained to the god of the sea, Poseidon, and he released a terrible monster - Whale - onto the shores of Ethiopia.

In order to pay off Keith, who was devastating the country, Cepheus was forced, on the advice of the oracle, to give his beloved daughter Andromeda to be devoured 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 exploits: he entered a secluded island at the end of the world, where three terrible women lived - gorgons with balls of snakes on their heads instead of hair. The Gorgon's gaze turned all living things into stone. Taking advantage of the gorgons' sleep, Perseus cut off the head of one of them named Medusa. The winged horse Pegasus flew out of her body. The other two gorgons, having woken up, wanted to rush at Perseus, but he jumped on the winged Pegasus and, holding the precious booty 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 Cetus appeared.»

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

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 May the terrible Scorpio
It took away their 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 was stabbed to death in November.
And in December, in the end,
a pair of Geminis was born.

By clicking on the "Download archive" button, you will download the file you need completely free of charge.
Before downloading this file, think about those good abstracts, tests, term papers, dissertations, articles and other documents that lie unclaimed on your computer. This is your work, it should participate in the development of society and benefit people. Find these works and submit them to the knowledge base.
We and all students, graduate students, young scientists who use the knowledge base in their studies and work will be very grateful to you.

To download an archive with a document, enter a five-digit number in the field below and click the "Download archive" button