Municipal budgetary educational institution

gymnasium No. 1 of the city of Khabarovsk

Urban scientific and practical conference"Step into Science"

Section of Mathematics

Research

"Zodiac signs

on the coordinate plane"

Completed:

Bobrovnikova Daria,

Soklakova Natalya,

Lozhnikova Anastasia

6B class students

Head: Korovaeva S.V.

Khabarovsk 2017

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

Theoretical chapter

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

1. History of origin of coordinates…………………………………...9

   Types of coordinate systems………………………………………………… 11

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

2. Practical chapter

Signs of the Zodiac in coordinates……………………………………………….20

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

References………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………… ………......25

Introduction

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

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

Project relevance:

There are many non-traditional tasks with novelty tasks that can be successfully used when studying the topic "Coordinate plane", but they were not included in school textbooks And teaching aids teachers.

Hypothesis: Do people need coordinates in Everyday life?

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

Goal of the work : To expand knowledge about coordinates and their application in everyday life.

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

Learn to "draw" in a rectangular coordinate system.

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

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

Select historical material.

Create didactic material "To help the teacher" for a general lesson on the topic "Coordinate plane"

Prepare a presentationsigns of the Zodiac on the coordinate plane»

Subject of study : What is a coordinate plane?

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

Before the study, there washypothesis : "To know in order to be able"

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

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

- Verbal: search and processing of the necessary information from literary sources and the Internet; preparation of the survey and analysis of the results; disclosure of findings;

Coordinates meet in our life hourly. In order to prove that we need a coordinate plane in practical life, we will give a few examples.

The coordinate system is used in the cinema, in transport, in geography there is a coordinate system. Coordinate systems only occur with two quantities? Everyone knows how to play naval combat, and coordinates are used in this game.

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

a) navigate the terrain, and, therefore, remember and, if necessary, tell who should have their address;

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

c) know what time it is.

Can you imagine what creepy life I would have waited for a non-addressed, constantly wandering humanity without a residence permit, deprived, moreover, of a clock and a calendar! Would lose the meaning of passports and borders. It would be impossible to schedule rail and air transport, etc. Finally, the human race itself would simply cease to exist.

Work plan:

Finding coordinates information around us.

Identify the types of coordinate systems, their features and purpose.

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

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

Draw a conclusion

Theoretical chapter

1. coordinates around us.

In our speech, you could hear the following phrase more than once: “Leave me your coordinates.” What does this expression mean? Guessed?! The interlocutor asks to write down his address or phone number. Each person has situations when it is necessary to determine the location: on the ticket, find a seat in the auditorium or in the train car. When playing games, we have to determine the location of the "enemy" ship, the pieces on the chessboard. different situations? But the essence of coordinates, which in Greek means “ordered” or, as they usually say, coordinate systems, is the same: this is the rule by which the position of an object is determined. The word "system" is also of Greek origin: "Theme" - something given, "sis" - 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 two parts of the address - latitude and longitude. We define latitude using a "parallel" - an imaginary line on the surface of the Earth drawn at the same distance from the equator. Longitude - along the "meridian" - an imaginary line on the surface of the Earth connecting the North and South Poles along the shortest distance. Parallels are lines of direction west - east, meridians show the direction north - south. Familiar? Rectangular coordinate system.

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

All this is found in modern life. But such a fact is interesting, how long has the coordinate system permeated the practical life of a person?

1. History of origin of coordinates

200 BCGreekscientistHipparchus introducedgeographerscal coordinates.He proposed to draw on a geographical mapparallels and meridians and label with numberslatitude and longitude . With these two numbersposition can be accurately determined.islands, villages, mountains or wellsin the desert and put them on a map orglobe,Learning to identifyopen world latitude and longitudethe location of the ship, the sailors got the opportunity to choose the direction they needleniya.East longitudeand north latitude are numberedlamy cosign"plus", and the westernlongitude and south latitude - with signcom"minus".So a couplenumbers fromsigns unambiguouslydefineputs a dot onglobe.

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

At the piss Jules Verne's body, some Roma we are built on situations associated with geographicdinats. These are the novels "AmazingAdventures of Uncle Antifera" and"The Children of Captain Grant".

D For a long time, only geography "description of the earth" used this wonderful invention, and only in the 14th century did the French mathematicianNicola Orsem (1323-1382) tried to apply it to "land measurement" - geometry.He offered to coverwith a rectangular grid and oncall latitude and longitude whatwe now callabscissa And op dynatoy .

H on the basis of this successful innovationnick coordinate method linking geometrics with algebra. Main forservant in the creation of this method belongslies to the great Frenchmasubject matterRene Descartes (1596 - 1650) . In his honor, such a coordinate system is calledcartesian, denoting the place of any point of 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 a point is denoted by the letter x, "longitude" - by the letter "y".

1. Types of coordinate systems

On this systembased on many ways of specifyingplaces. For example, there are two numbers on a ticket to a cinema: a row and a place - they can be considered as coordinatesseats in the hall. Likenye coordinates are taken aboutmats. Instead of one of the numbers, a letter is taken: vertical rowscell types are denoted by the letters latin alphabet, and the horizontalnye - numbers.So every cellchessboard is assigned a peer of letters and numbers, and chess players get the opportunity to writeplay your parts.The same principle forchanges on city plans.The city plan is divided into squaresnumbered with letters andnumbers, and on the reverse sidecount all the depicted streetsV alphabetical order Andpoint outWhat square are they in?

Exist on the plane and othersdifferent coordinate systems.

H to enterpolar system coordinate T , choosestarting point calledfieldcatfish(so the systemAndcalled"polar");from thisdots spenda beam calledpolar axis . Todetermine the coordinates of a pointon a plane, it is connected by a cutcom with a poleAndcalculate the lengththis segmentAndthe angle betweenand polar axis.

Existencewailalso the coordinates givenonenumber.Thiscoordinates on straight . It is enough to ask onenumber - distance from point to onreference point to indicate the linemy position is this point. INlifewe very oftenfacewith suchcoordinates.

For example, Railway Withmilestonesalongher or numberhouses on the street.

Three coordinates will be setpoint position inspace.Such a coordinate systemcalledspherical . Need tochoose someplospeed andenteronherCartesiancoordinate system, and our pointcompare the coordinates of its projectiononthisplane and distance fromit to the plane, takencosignplusForone half of the spacestva and cosignsminus - for othersgoy; so we getCartesian system mu coordinates in space .

spherical coordinate systemcommonly used at airports.A radiolo is being installed near the airfield.kator. This device can determinedistance to the aircraft, angle, underwhich the aircraft is visible over the horizonvolume, andcornerbetween direction toplane and heading north.

1. Starry Sky and Legends of the Twelve Signs of the Zodiac

A
Strology 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 were namedzodiacal (from 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.

a 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 the 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.

Sagittarius - once the great hero of Greece, Hercules, traveled with his wife. Near the river Even they met the centaur Nessus. Hercules wade across the river, and instructed the centaur to transport Dejanira. While the hero was already on the other side, 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, decided to take revenge on him by giving her his talisman with poison, supposedly returning her husband from another woman. Later, Dejanira 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, putting on these clothes, Hercules died in terrible agony. However, the evil Ness did not calm down, even when he got to the starry sky. A centaur, armed with a bow and arrows, threatens everyone from heaven - this is what the constellation SAGITTARIUS looks like.

Capricorn - when the day came winter solstice, the hour has come to be born to 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.

Twins One day the brothers decided to get married. And having chosen two beautiful princesses, they kidnapped them. But the beauties were already the brides of other heroes. A fierce struggle ensued between the rivals. In this fight, Castor was struck down by an opponent's arrow. Polydeuces bowed over the dying Castor, unable to restrain his sobs. Suddenly he sees: the mighty Zeus appeared before him and offered Pollux immortality. “Great father,” said the young man, “I cannot accept your gift. Send me death! I can't imagine life without Castor. May our lot be one." The peacekeeper allowed Polydeuces to give half of his immortality to Castor. Since then, GEMINI spend one day in the realm of the dead, and the other day on Olympus, among the gods.

Taurus - the Phoenician princess Europe was wonderfully charming. Once she went with her friends to the seashore to listen to the sound of the sea waves. Zeus, the Thunderer, seeing her, immediately inflamed with love for her and descended to Earth in the form of a bull with a round silvery spot on his forehead. Approaching the beautiful Europe, the bull lay down at her feet and turned his back. When the princess sat on the bull, he started off like an arrow and headed for the sea. The virgin called for help, but her friends could not catch up with her, and at that time the bull moved across 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 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 this form." Zeus - the bull sailed to the island of Crete, where Europe bore him glorious sons.

Virgo – seeing 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.

Scales - 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. All this means the same thing:man pouring water.

Aries - when Afamant decided to give his son Frixus 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 from a clear sky; a huge white cloud descended from the sky, the goddess of the clouds Nephele emerged from it, and next to her was a beautiful ram. Long The Golden Fleece it shone, and its horns twisted in tight curls. The goddess of the clouds exclaimed: “My children, I will save you! Get on this magical ram." Phrixus and Helle mounted a ram and flew off to a country called Colchis, where King Eet ruled. Eet caught the Ram and kept him for himself. Since then, the country of Colchis has become happy, because happiness was brought by this wonderful Aries.

Fish - Once the goddess of love and beauty Aphrodite and her son Eros were walking along the bank of the river, near which the 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.

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

Interesting facts about the elements.

Element of Fire. The 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, i.e. fire trine (triangle): Aries, Leo, Sagittarius. The fire trine is considered a creative trine.

Principle: action, activity, energy.

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.

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.

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: constancy of the internal with external variability

2. Practical chapter

Zodiac signs in coordinates

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

On each card there is an image of one of the signs and the coordinates of points (stars) and the ways of connecting these points are given. After they have been marked on the coordinate plane and connected in the indicated order, the image of the Zodiac sign will be the same as on the map of the starry sky.

In order to make cards we did:

Familiarize yourself with different coordinate systems

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

We studied the map of the starry sky (Appendix 1)

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

Transferred the points of each constellation to checkered paper (Appendix 3)

Arbitrarily introduced a coordinate system (Appendix 3)

We wrote out the coordinates of each point and marked the ways of their connection (Appendix 3)

Compiled brief description each of the constellations (Appendix 4)

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

Conclusion

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

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

How many stars (points) does a constellation consist of

How are they connected on the map?

Distance between points

Then we picked up the coordinates (x; y) for each star (point) and built them, keeping the scale, indicated the way the stars were connected.

After that, task cards were made for work in groups (Appendix 1). The materials of our work can help the teacher conduct a lesson to consolidate knowledge on the topic "Coordinate plane". In the course of completing tasks, students can test their knowledge and ability to mark points according to given coordinates and determine the coordinates of already marked points with interest. In the future, we plan to study in more detail the relative position of all the constellations, build them on the same coordinate plane, so that we can make a map of the starry sky.

Literature

Glazer G.I. History of mathematics at school: - M .: Education, 1981. - 239 p., ill.

Lyatker Ya. A. Descartes. M .: Thought, 1975. - (Thinkers of the past)

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

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

Mathematics - supplement to the newspaper "First of September", No. 7, No. 20, No. 17, 2003, No. 11, 2000.

Siegel F.Yu. Star alphabet: A guide for students. - M.: Enlightenment, 1981. - 191 p., Illus.

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

Annex 1

Annex 2

Appendix 3

Appendix 4

Litsenko Daniel

Project goals:

1. Expand knowledge about coordinates and their application in everyday life.

2. 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.

2. Study the zodiac constellations.

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

Download:

Preview:

Municipal budgetary educational institution

"Secondary School No. 4"

PROJECT

on the topic

“Coordinate plane and signs of the Zodiac”

(mathematics)

6A grade student

Litsenko Daniil Sergeevich

Project Manager:

Mathematic teacher

Katsevich Nadezhda Igorevna

Shchekino

2016

1. History of origin of coordinates. Coordinate system 4
2. Zodiac Signs 5
3. Zodiac signs in 6 coordinates
4. Conclusion 7
5. References 8

Project goals:

1. To expand knowledge about coordinates and their application in everyday life.
2. Consider the signs of the zodiac through the theory of the coordinate plane.
   

Tasks:

1. Learn about the origin of coordinates.
2. Learn the zodiac constellations.
3. Construct an image of the constellation on the coordinate plane.
   

History of origin of coordinates

200 BC Greek scientist Hipparchus entered geographic coordinates.He proposed to draw on a geographical mapparallels and meridiansand label with numberslatitude and longitude. Using 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. By learning to determine the latitude and longitude of the location of the ship in the open world, sailors were able to choose the direction they needed.

Eastern longitude and northern latitude are denoted 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.

For a long time, only geography "description of the earth" used this wonderful invention, and only in the 14th century did the French mathematician Nicola Oresme (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 callabscissa 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 Rene Descartes . In his honor, such a coordinate system is called cartesian, denoting the place of any point of 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 a point is denoted by the letter X, "longitude" - by the letter Y.

Coordinate system

Two mutually perpendicular coordinate lines intersecting at the point, which is the origin of each of them, formcoordinate system. The lines forming the coordinate system are calledcoordinate axes, each of which has its own name: horizontal - abscissa axis, vertical - y-axis . The plane on which the coordinate system is chosen is calledcoordinate plane.

Zodiac signs

Astrology is the science of the influence of stars, constellations and planets on man and on the Earth.

The signs of the zodiac are 12 sectors of 30 °, which in astrology divided odiacal belt, each of these sections is assigned certain metaphysical properties that play a role in the analysis horoscopes.

Among the many constellations (a constellation is an astronomical concept, meaning a section of the celestial sphere with boundaries established by virtue of historical tradition) decorating the night sky, a special place is occupied by those among which the Sun passes its yearly path, namely: Aries, Taurus, Gemini, Cancer, Leo, Virgo, Libra, Scorpio, Sagittarius, Capricorn, Aquarius, Pisces. Most of the names belong to animals, so these constellations were named zodiac (from the Greek zodiac - "animal circle").

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 point of the South 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”). Thus, it is possible to determine the location of any star in the sky.

Currently, the boundaries of the constellations are officially used, determined by the decision of the First General Assembly of the International Astronomical Union in 1922 (spherical, often irregularly shaped, polygons with boundaries running parallel to the latitudes and longitudes of the equatorial coordinate system).

Zodiac signs in coordinates

Based on the above, it is possible to build drawings of the twelve signs of the Zodiac on the coordinate plane, for this we need to know the coordinates of the points (stars) and the way they are connected.

For example, let's take my zodiac sign - Libra:

Coordinates	Connection paths	On the coordinate plane
1(-4;12)	1→2→4→5→6
2(10;7)	2→3 1→4
3(9;-5)
4(-10;4)
5(-1;-10)
6(-2;-12)

After building all the signs, you can make a map of the starry sky.

Conclusion

In my work, I combined two subjects: mathematics and astronomy. He spoke about the history of the emergence of coordinates and their creators, about the signs of the Zodiac and how you can build constellations of the signs of the Zodiac on the coordinate plane and determine the coordinates of each point-star. To do this, I looked at a map of the starry sky, studying the location and appearance of each of the 12 constellations:

• How many stars (points) does the constellation consist of;
• How are they connected to each other on the map;
• Distance between points.

Then I picked up the coordinates (x; y) for each star (point) and built them, indicating the connection path of the stars on the example of the Zodiac sign - Libra.

In the course of the work, I tested my knowledge and ability to apply the topic in mathematics: "Coordinate plane".

Literature

1. I.I. Zubaryova and A.G. Mordkovich Textbook of mathematics grade 6.
2. E. N. Bakhtina. Book of stars. Moscow "Interbook", 1997.
3. A. Savin. Coordinates // Kvant. 1977. No. 9
4. Internet - source zodiac-art.narod.ru
5. Internet source https://ru. wikipedia.org/.

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Municipal budgetary educational institution "Secondary school No. 4" PROJECT on the topic "Coordinate plane and signs of the Zodiac" by a student of grade 6A Litsenko Daniil Sergeevich Project leader: Mathematics teacher Katsevich Nadezhda Igorevna Shchekino 2016

Project objectives: To expand knowledge about coordinates and their application in everyday life. Consider the signs of the zodiac through the theory of the coordinate plane. Tasks: To get acquainted with the history of origin of coordinates. Learn the zodiac constellations. Construct an image of the constellation on the coordinate plane.

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. Eastern longitude and northern latitude are denoted by numbers with a plus sign, and western longitude and southern latitude by a minus sign. For a long time, only geography - "description of the earth" - used this wonderful invention, and only in the 14th century, the French mathematician Nicolas Orem (1323-1382) proposed covering the plane with a rectangular grid and calling latitude and longitude what we now call the abscissa and ordinate. History of origin of coordinates

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 Rene Descartes. 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" - with the letter U. The history of the origin of coordinates (continued)

Two mutually perpendicular coordinate lines intersecting at the point, which is the origin of each of them, form a coordinate system. The straight lines that form the coordinate system are called coordinate axes, each of which has its own name: horizontal - the abscissa axis, vertical - the y-axis. The plane on which the coordinate system is chosen is called the coordinate plane. Coordinate system

Astrology is the science of the influence of stars, constellations and planets on man and on the Earth. The signs of the zodiac are 12 sectors of 30 ° each, into which the zodiac belt is divided in astrology, each of these sections is assigned certain metaphysical properties that play a role in the analysis of horoscopes. Among the many constellations, a special place is occupied by those among which the Sun passes its yearly path, namely: 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"). Zodiac signs

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 point of the South 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”). Thus, it is possible to determine the location of any star in the sky. Currently, the boundaries of the constellations are officially used, determined by the decision of the First General Assembly of the International Astronomical Union in 1922 (spherical, often irregularly shaped, polygons with boundaries running parallel to the latitudes and longitudes of the equatorial coordinate system). Signs of the Zodiac (continued)

Based on the above, it is possible to build drawings of the twelve signs of the Zodiac on the coordinate plane, for this we need to know the coordinates of the points (stars) and the way they are connected. For example, let's take my Zodiac sign - Libra: Signs of the Zodiac in coordinates Coordinates 1(-4;12) 2(10;7) 3(9;-5) 4(-10;4) 5(-1;-10) 6 (-2;-12) Connection paths 1→2→4→5→6 2→3 and 1→4 On the coordinate plane

and whether my mother's zodiac sign is 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) 11 (14;-6) 12 (7;-5) 13 (-11;-4) 14 (2; -8) 15 (-13;-8) 16 (-11;-13) Connection paths 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 On the coordinate plane

After building all the signs, you can make a map of the starry sky:

In my work, I combined two subjects: mathematics and astronomy. He spoke about the history of the emergence of coordinates and their creators, about the signs of the Zodiac and how you can build constellations of the signs of the Zodiac on the coordinate plane and determine the coordinates of each point-star. To do this, I examined a map of the starry sky, studying the location and appearance of each of the 12 constellations: How many stars (points) does a constellation consist of; How are they connected to each other on the map; Distance between points. Then I picked up the coordinates (x; y) for each star (point) and built them, indicating the connection path of the stars on the example of the Zodiac sign - Libra. In the course of the work, I tested my knowledge and ability to apply the topic in mathematics: "Coordinate plane". Conclusion

I.I. Zubareva and A.G. Mordkovich Textbook of mathematics grade 6. E. N. Bakhtina. Book of stars. Moscow "Interbook", 1997. A. Savin. Coordinates // Kvant. 1977. No. 9 Internet source zodiac-art.narod.ru Internet source https://ru. wikipedia.org/. Literature

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. Omnipotent god Zeus decided to marry Calisto 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.

While studying the concepts of “coordinate ray” and “coordinate angle” in elementary school, 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 goal 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 research - coordinate plane.

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

As tasks 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, 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 of the constellation Ursa Major and Mal 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 satellite navigation systems allow 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. // Textbook 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.

Annex 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 ancient greece Perseus performed one of his feats: he penetrated a secluded island at the end of the world, where three scary women- Gorgons with coils 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 a chilling look fell on him dead head Jellyfish. 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.

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

Coordinate plane and zodiac signs

(project)

Executor:

Saygina Anastasia Vladimirovna

Supervisor:

Savelieva Anastasia Alexandrovna

Sol - Iletsk.

2016

Content

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

Main part

1. History of coordinates creation…………... …………………………5

   Types of coordinate systems and their application in everyday life…………………………………………………………………..7

   Starry sky and legends about the twelve signs of the Zodiac………10

Practical part.

1. Astrological characteristic 6 "a" class………………… 17

   Signs of the Zodiac in coordinates…………….………………………20

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

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

Application.

I .Introduction

When I was little and looked up, I saw bright lights chaotically arranged in the night sky. I have always enjoyed watching the stars in the sky. I grew up and my mother told me that there is such a science - astronomy, and I became interested in it, began to study the constellations, find and examine them in the starry sky. It turns out that in addition to a 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 do 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:

learn how to build points in the Cartesian coordinate system and determine the coordinates of given points (this task is highlighted because this topic is being studied under the 6th grade program in the fourth quarter);

expand knowledge about coordinates and their application in everyday life;

get acquainted with the history of the origin of coordinates;

consider different types of coordinate systems;

study the zodiac constellations;

construct an image of the constellation on the coordinate plane;

to conduct astrological research of students of the 6th "a" class;

prepare a presentation "Coordinate plane and signs of the zodiac";

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

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

study of theoretical sources;

observation;

work with photographic materials;

consultation with a teacher.

I started my research by studying theoretical sources. First of all, the Internet helped me in this.

II . Main part

2.1 History of coordinate creation

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

More than 100 years BC, the Greek scientist Hipparchus proposed 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 the II century AD. the famous ancient Greek astronomer Claudius Ptolemy already used longitude and latitude as geographical coordinates.

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

But these concepts were first systematized in the 17th century by Rene Descartes (Appendix No. 1). 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.

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

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

Based on the coordinate system, there are many ways to specify a location. For example, there are two numbers on a ticket to a cinema: a row and a seat - they can be considered as the coordinates of a seat in the hall.

Fig.2

Similar coordinates are accepted in chess. Instead of one of the numbers, a letter is taken: the vertical rows of cells are indicated by the letters of the Latin alphabet, and the horizontal rows by numbers. Thus, each cell of the chessboard is assigned a pair of letters and numbers, and chess players get the opportunity to write down their games.

Fig.3

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

Fig.4

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

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

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

For example, a railroad with milestones along it, or numbers of houses on the street.

Rectangular Cartesian coordinate system on the plane.

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

Fig.5

each of them is a scale (a unit of length). The point of intersection of these lines will be denoted by the letter O and we will consider it as the starting point. So we got a rectangular coordinate system on the plane. To build a point with coordinates (X; Y): first you need to go along the abscissa (x) axis from the origin to X units, and then along the ordinate (y) axis to Y units. Thus, we will get a point with the given coordinates.

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

Astrology is the science of the influence of stars, constellations and planets on 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

Fig.6

have been namedzodiacal (from Greek zodiac - "animal circle").

Fig.7

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.

Aries.

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

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

Twins.

Once upon a time there were two brothers: Pollux (who is with a club) and Castor (who is with reins). Their mother was the same, but their fathers were different. But they were also twins. Pollux's father was Zeus, and Castor's was an ordinary earthly person.
The difference is that if your father is a god, then you are immortal.
So, these twins adored each other, doted on each other's souls. Always been together, naughty. And once, after another battle, Castor was mortally wounded. And then Pollux turned to Zeus (his father) and said: "Without a brother, I do not need immortality!"
And the gods placed them in the sky as a symbol of brotherly devotion.

Cancer .

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

End of form

a lion .

Not far from Nemea, a huge lion settled. 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 the 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.

Virgo.

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

End of form

Scales.

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

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

Sagittarius - once the great hero of Greece, Hercules, traveled with his wife. Near the river Even they met the centaur Nessus. Hercules wade across the river, and instructed the centaur to transport Dejanira. While the hero was already on the other side, 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, decided to take revenge on him by giving her his talisman with poison, supposedly returning her husband from another woman. Later, Dejanira 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, putting on these clothes, Hercules died in terrible agony. However, the evil Ness did not calm down, even when he got to the starry sky. A centaur, armed with a bow and arrows, threatens everyone from heaven - this is what the constellation SAGITTARIUS looks like.

Capricorn.

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

Zeus grew up strong boy. Once, while dabbling, he pushed the horn of milk away from him so strongly that it splashed out in a long stream high up and hit the sky. There it spilled into a wide white band, which people called the Milky Way.

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

Fish.

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

Practical part.

2.4 Astrological characteristic 6 "a" class

To compile the astrological characteristics of the 6 "a" class, I conducted a survey:

- "Who are you by zodiac sign?»,

- "Do you know what your constellation looks like?"

and plotted the results data.

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

2.5 Signs of the Zodiac in coordinates

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

14th regional scientific-practical conference of students Mathematics section Astronomy on the coordinate plane Completed by Danil Karmanov Pupil of 5 "B" class MNBOU "Lyceum No. 76" Head Teacher of mathematics Bukurova Ekaterina Igorevna Novokuznetsk 2015 Contents I. Introduction……………………………………………………… ……………………………………...….3 II. Main part……………………………………………………………..4 2.1History of origin of coordinates…………...…………………..4 2.2 Types of coordinate systems……………………………………………….5 2.3 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. References…………………………………………………………..13 Annex 1……………………………………………………… ………………14 2 I. Introduction I always liked to watch the starry sky, when I was little, I thought that the stars in the sky are randomly arranged. 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 a 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. Statement 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. The purpose of the work: to consider the signs of the zodiac through the theory of the coordinate plane. Tasks: 1) learn to build 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 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 a general lesson on the topic "coordinate plane"; 8) to conduct astrological research of students of the 5th "b" class; 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 teachers and parents. I started my research by studying theoretical sources. First of all, the Internet helped me in this. II. Main part 2.1 The history of the creation of coordinates 200 years before our era, the Greek scientist Hipparchus introduced geographical coordinates. He suggested drawing parallels and meridians on a geographical map and marking 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 put them on a map or globe. By learning to determine the latitude and longitude of the location of the ship in the open world, sailors were able to choose the direction they needed. 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) proposed covering the plane with a rectangular 4 grid and calling 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. 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, "longitude" - by the letter "y". 2.2 Types of coordinate systems and their application in everyday life There are many ways to indicate a place based on a coordinate system. For example, there are two numbers on a ticket to a cinema: a row and a seat - they can be considered as the coordinates of a seat in the hall. Similar coordinates are accepted in chess. Instead of one of the numbers, a letter is taken: the vertical rows of cells are indicated by the letters of the Latin alphabet, and the horizontal rows by numbers. Thus, each cell of the chessboard is assigned a pair of letters and numbers, and chess players get the opportunity to write down their games. The same principle applies to city plans. The plan of the city is divided into squares numbered with letters and numbers, and on the reverse side all the depicted streets are listed in alphabetical order and indicate in which square they are located. There are various coordinate systems on the plane. For example, the polar coordinate system. To enter a polar coordinate system, A Angle Polis Polar axis is chosen as the initial pole (therefore, the point, the system is called and 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 the pole and the length of this segment and the angle between it and the polar axis are calculated. 5 There are also coordinates given by a single number. These are the coordinates on the line. It is enough to set one number - the distance from the point to the origin, to indicate the position of this point on the straight line. In life, we often encounter such coordinates. For example, a railroad with milestones along it, or numbers of houses on the street. Rectangular Cartesian coordinate system on the plane. To introduce a rectangular Cartesian coordinate system on a plane, you need to draw two mutually perpendicular lines, choosing a positive direction on each of them, indicating it with an arrow, and choosing a scale (a unit of length measurement) on each of them. The point of intersection will be denoted by the letter O and its origin. we will consider these lines. So we got a rectangular coordinate system on the plane. To build a point with coordinates (X; Y): first you need to go along the abscissa (x) axis from the origin to X units, and then along the ordinate (y) axis to Y units. Thus, we will get a point with the given coordinates. 2.3 Starry sky and legends about the twelve signs of the Zodiac Astrology is the science of the influence of stars, constellations and planets on 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. 6 Most of the names belong to animals, so these are called zodiac (from the Greek zodiac constellation - "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. Aries - when Afamant decided to give his son Frixus 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 from a clear sky; a huge white cloud descended from the sky, the goddess of the clouds Nephele emerged from it, and next to her was a beautiful ram. His long golden fleece shone, and his horns twisted in tight curls. The goddess of the clouds exclaimed: “My children, I will save you! Get on this magical ram." Phrixus and Helle mounted a ram and flew off to a country called Colchis, where King Eet ruled. Eet caught the Ram and kept him for himself. Since then, the country of Colchis has become happy, because happiness was brought by this wonderful Aries. Taurus - the Phoenician princess Europe was wonderfully charming. Once she went with her friends to the seashore to listen to the sound of the sea waves. Zeus, the Thunderer, seeing her, immediately inflamed with love for her and descended to Earth in the form of a bull with a round silvery spot on his forehead. Approaching the beautiful Europe, the bull lay down at her feet and turned his back. When the princess sat on the bull, he started off like an arrow and headed for the sea. The virgin called for help, but her friends could not catch up with her, and at that time the bull moved across 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 this form." Zeus - the bull sailed to the island of Crete, where Europe bore him glorious sons. Gemini - one day the brothers decided to marry. And having chosen two beautiful princesses, they kidnapped them. But the beauties were already the brides of other heroes. A fierce struggle ensued between the rivals. In this fight, Castor was struck down by an opponent's arrow. Polydeuces bowed over the dying Castor, unable to restrain his sobs. Suddenly he sees: the mighty Zeus appeared before him and offered Pollux immortality. “Great father,” said the young man, “I cannot accept your gift. Send me death! I can't imagine life without Castor. May our lot be one." The peacekeeper allowed Polydeuces to give half of his immortality to Castor. Since then, GEMINI spend one day in the realm 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, who grabbed Hercules by the leg. Enraged, Hercules crushed him, thereby inadvertently eliminating another enemy. 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 the 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. 8 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. Virgo - seeing 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. Sagittarius - once the great hero of Greece, Hercules, traveled with his wife. Near the river Even they met the centaur Nessus. Hercules wade across the river, and instructed the centaur to transport Dejanira. While the hero was already on the other side, 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, decided to take revenge on him by giving her his talisman with poison, supposedly returning her husband from another woman. Later, Dejanira 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, putting on these clothes, Hercules died in terrible agony. However, the evil Ness did not calm down, even when he got to the starry sky. A centaur, armed with a bow and arrows, threatens everyone from heaven - this is 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 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 9, 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. 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 the 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. 2.3 Signs of the Zodiac in coordinates In my work, I propose to build drawings of the twelve signs of the Zodiac on the coordinate plane in order to create didactic material "to help the teacher" for a general lesson on the topic "coordinate plane". On each card there is an image of one of the signs of the zodiac and the coordinates of points (stars) and the ways of connecting these points are given. After they have been marked on the coordinate plane and connected in the indicated order, the image of the Zodiac sign will be the same as on the map of the starry sky. After building all the signs, you can make 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 according to the results. From which it can be seen that in our class there are most lions (13%), capricorns (13%), scorpions (3%) and Aquarius (17%). This means that our class is: adventurous, sincere, kind, generous, proud, hardworking, serious, honest. And also as it turned out that (75%) of students do not know what their constellation looks like. 11 III. Conclusion In this work I have tried to combine two subjects: mathematics and astronomy. The theoretical part tells about the history of the emergence of coordinates and their creators. I learned that there are different coordinate systems, how widely and where they are used in a person's 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 build all twelve constellations of the signs of the Zodiac on the coordinate plane and make cards for didactic 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 interconnected  the distance between the points Then I built them using the coordinates (x; y) for each star. The materials of my work can help the teacher conduct a lesson to consolidate knowledge on the topic "Coordinate plane". In the course of completing tasks, students can test their knowledge and ability to mark points according to given coordinates and determine the coordinates of already marked points with interest. At the end, I present an astrological portrait of my class. We will study the topic “Coordinate plane” in the 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 // Kvant. 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 →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 Taurus constellation 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 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 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 Sagittarius constellation 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 of the Way of connection 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 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