Coordinates of the constellation Leo on the coordinate plane. Coordinate plane and zodiac signs

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 use in everyday life Based on a coordinate system, there are many ways to indicate a place. 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 they list all the streets depicted 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. His long golden fleece shone, and his horns curled in steep curls. The goddess of the clouds exclaimed: “My children, I will save you! Sit on this magical ram." Phrixus and Hella boarded a ram and flew to a country called Colchis, where King Eet ruled. Eet caught Aries and kept him for himself. Since then, the country of Colchis became happy, because happiness was brought by this wonderful Aries. 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 the Nemean lion. Hercules wandered for a long time along the slopes of the mountains. The sun began to set. And then a terrifying roar reached the hero. In several jumps, Hercules reached the lion's den - a huge cave with two exits. When a giant beast emerged from the cave with a roar, Hercules showered it with arrows, but none of them even wounded the monster. Then Hercules threw away his bow and attacked the lion with a club. With a powerful blow to the head, the hero stunned the beast, grabbed him by the neck with his powerful hands and strangled him. 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 Zodiac signs in coordinates In my work, I propose to construct drawings of the twelve Zodiac signs 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 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 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

BUDGETARY EDUCATIONAL INSTITUTION
"POLOGRUDOVSKAYA SECONDARY SCHOOL"
TARSKY MUNICIPAL DISTRICT OF OMSK REGION

PROJECT ON

"ASTOROLOGY
ON THE COORDINATE PLANE"

Performed:
6th grade student
Kuzheva Polina

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

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

History of the origin of the coordinate system

Coordinate translated from Greek means “ordered”; a coordinate system is a rule by which the position of an object is determined.
The word “system” is also of Greek origin: “Theme” is something given, “sis” is made up of parts. Thus, a “system” is something given, made up of parts (or a clearly dissected whole).
Coordinate systems permeate the entire practical life of a person. For example, using a geographic map, you can determine the address of any point using geographic coordinates. To do this, you need to know two parts of the address: latitude and longitude.
The history of the origin of coordinates and the coordinate system begins a very long time ago; initially, the idea of the coordinate method arose in the ancient world in connection with the needs of astronomy, geography, and painting. The ancient Greek scientist Anaximander of Miletus (c. 610-546 BC) is considered the compiler of the first geographical map. He clearly described the latitude and longitude of a place using rectangular projections.
The idea of depicting numbers as dots, and giving numerical designations to the dots, originated in ancient times. The initial use of coordinates is associated with astronomy and geography, with the need to determine the position of luminaries in the sky and certain points on the surface of the Earth, when compiling a calendar, star and geographical maps. Traces of the application of the idea of rectangular coordinates in the form of a square grid (palette) are depicted on the wall of one of the burial chambers of Ancient Egypt.
Already in the 2nd century. The ancient Greek astronomer Claudius Ptolemy used latitude and longitude as coordinates.
The main credit for creating the modern coordinate method belongs to the French mathematician Rene Descartes. A story has survived to this day that prompted him to make the discovery. Taking seats in the theater according to the purchased tickets, we do not even suspect who and when proposed the method of numbering seats by rows and seats that has become common in our lives.
Rene Descartes first made a scientific description of the rectangular coordinate system in his work “Discourse on Method” in 1637. Therefore, the rectangular coordinate system is also called the Cartesian coordinate system. In the Cartesian coordinate system, negative numbers received a real interpretation.
Pierre Fermat also contributed to the development of the coordinate method, but his works were first published after his death.
Descartes and Fermat used the coordinate method only on the plane. The coordinate method for three-dimensional space was first used by Leonhard Euler already in the 18th century.
The terms “abscissa” and “ordinate” (derived from the Latin words “cut off” and “ordered”) were introduced in the 70-80s. XVII century German mathematician Wilhelm Leibniz.

Zodiac constellations
Astrology is the science of the influence of stars, constellations and planets on humans and the Earth. Among the 88 constellations that decorate the night sky, a special place is occupied by those among which the Sun passes its annual path. Twelve constellations on the path of the Sun: Aries, Taurus, Gemini, Cancer, Leo, Virgo, Libra, Scorpio, Sagittarius, Capricorn, Aquarius, Pisces.
Most of the names belong to animals, so these constellations received the names of the zodiac (from the Greek zodiakos - “animal circle”).
In fact, of course, the Earth moves around its star, but it seems to us that it is the Sun that changes its location. The ancient astronomers thought so too, giving names to the zodiacal constellations.
They noticed that the Sun always walks across the sky one way and every month “visits” the signs of the Zodiac: in January - Capricorn, in February - Aquarius, in March - Pisces... It has long been believed that the sign of the Zodiac, that is, The month of a person’s birth determines his character, influences his behavior and predetermines his fate.

The constellation Aries is considered to be the beginning of the zodiac; it is 2 thousand years old.
ago there was the point of the vernal equinox. Over the past time, it has shifted greatly and is now located in the constellation Pisces; it is still designated by the sign of the constellation Aries. When the sun is at this point and moves from the Southern hemisphere of the celestial sphere to the Northern, astronomical spring begins. It is most convenient to observe the constellation in the fall, when the sun is far from it.
Taurus constellation
Taurus is one of the most beautiful winter constellations. In November - December it is observed almost all night. 125 stars are visible to the naked eye. The brightest - Aldebaran - is red-orange in color (its temperature is about 3500°). Near Aldebaran it is easy to see a scattering of not very bright stars forming a triangle (the face of Taurus).
Constellation Gemini.
Gemini is the northernmost of the zodiac constellations. Observed in winter. Its brightest stars are Castor and Pollux. This was the name of the twin brothers who went with Jason on a campaign for the Golden Fleece. The brighter Pollux is orange in color. Upon closer inspection, this star turns out to be a system of four stars.
Constellation Cancer
The constellation Cancer is best observed in the spring. The Roman scientist Pliny the Elder wrote about him: “In the sign of Cancer there are two small stars called Donkeys, and among them is a small cloud called the Manger.” A “foggy star” (Manger) is really visible between them.
Constellation Leo
The zodiac constellation Leo is best observed during the spring months. It’s easy to find: A clear trapezoid of four bright stars forms the torso of Leo, and a curved chain of weaker stars forms the head and mane of the king of beasts. Regulus is the main star of the constellation, which has 2 satellites, one of them is a star very similar to the Sun. Regulus is a white hot, rather large star, it is almost 3 times larger than the Sun, and in terms of the amount of emitted light energy it exceeds it 140 times.
Virgo constellation
The ancient Greeks called this constellation Parthenos, which means "virgin" in Greek. The heavenly maiden is often depicted with a sheaf of ears of grain in her hands, and the name of her main star, Spica, is translated from Greek as “ear of grain.” The constellation was known in ancient times and was usually associated with the beginning of the harvest.
Constellation Libra
The small constellation Libra appeared on star maps relatively recently. The name of the constellation is due to the fact that in ancient times it was the location of the autumnal equinox. The ancient Roman poet Virgil wrote: “When Libra equalizes the hours of day and night and divides equally light and darkness in the world, then, farmer, take your working oxen to the field.”
Scorpio constellation
Scorpio is a constellation in the southern sky. The most prominent star is Antares. This is a double star, a red giant, quite bright. Antares can compete with Mars in brilliance and color. But it is not difficult to distinguish the luminaries. Mars shines evenly, and Antares, like all stars, flickers.
Sagittarius constellation
The constellation Sagittarius is located near the Milky Way. Ancient Greek myths tell about the wise centaur Chiron, who created the first model of the celestial sphere, and left one place for himself. But another centaur, the cunning and cunning Krotos, took this place by deception, becoming the constellation Sagittarius. Zeus nevertheless placed Chiron in the sky, turning it into the constellation Centaur. And the evil Sagittarius behaves belligerently even in the sky, aiming his bow at Scorpio.
Constellation Capricorn
This mythical creature with the body of a goat and the tail of a fish gave its name to one of the constellations of the zodiac. An ancient Greek legend tells how the goat-footed god Pan, the patron of shepherds, met the hundred-headed giant Typhon and threw himself into the water in horror. After this, Pan grew a fish tail, and he also became a water god. The stars of the constellation are not very interesting. Interestingly, the star Algedi Capricorn is a double star. Physically, these 2 luminaries are not connected; they are moving away from each other in different directions. These stars are called optical binaries.
Aquarius constellation
In this zodiac constellation, different peoples saw a man pouring water. The name of the constellation most likely came from Mesopotamia. In the constellation Aquarius, about 90 stars can be seen with the naked eye. One of the largest planetary nebulae is located here.
Constellation Pisces
The “water” constellation Pisces is the last in the circle of the zodiac. It is visible in the sky in autumn, and the Sun comes into it at the end of winter. The main star of Pisces is Alrisha, which means “lace”. Through binoculars it is visible as a bluish star, and a telescope allows you to see a satellite of the same color.

Conclusion
During the work, we became acquainted with the history of the origin of coordinates, the rectangular coordinate system. Having carried out work on studying the zodiac constellations, we came to the conclusion that the world of zodiac signs is that beautiful line that connects a person with the mysterious cosmos and distant stars.
Using a map of the starry sky and the zodiac constellations depicted on it, drawings of the zodiac signs were constructed on the coordinate plane. For each star-point of any of the 12 signs, coordinates are selected and connection paths are indicated.

Municipal budgetary educational institution

Gymnasium No. 1 of Khabarovsk

City scientific and practical conference “Step into science”

Mathematics section

Research

"Zodiac signs

on the coordinate plane"

Completed:

Bobrovnikova, Daria

Soklakova Natalya,

Lozhnikova Anastasia

6B grade students

Head: Korovaeva S.V.

Khabarovsk 2017

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

Theoretical chapter

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

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

2. Practical chapter

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

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

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

Introduction

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

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

Relevance of the project:

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

Hypothesis: Do people need coordinates in everyday life?

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

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

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

Learn to “draw” in a rectangular coordinate system.

Construct the zodiac signs using the coordinate plane theory.

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

Select historical material.

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

Prepare a presentation “ZZodiac signs on the coordinate plane»

Subject of study : What is a coordinate plane?

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

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

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

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

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

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

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

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

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

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

c) know what time it is.

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

Work plan:

Search for information coordinates around us.

Identify types of coordinate systems, their features and purpose.

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

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

Draw a conclusion

Theoretical chapter

Coordinates around us.

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

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

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

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

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

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

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

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

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

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

Exist on the plane and othersdifferent coordinate systems.

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

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

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

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

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

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

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.

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Interesting facts about the elements.

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

Principle: action, activity, energy.

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

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

Principle: exchange, contact.

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

Principle: internal constancy despite external variability

2. Practical chapter

Zodiac signs in coordinates

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

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

In order to make the cards we did:

We got acquainted with various coordinate systems

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

We studied the star map (Appendix 1)

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

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

Randomly introduced a coordinate system (Appendix 3)

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

We compiled a brief description of each of the constellations (Appendix 4)

We picked up interesting facts about people born under this zodiac sign (Appendix 4)

Conclusion

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

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

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

How are they connected to each other on the map?

Distance between points

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

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

Literature

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

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

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

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

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

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

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

Annex 1

Appendix 2

Appendix 3

Appendix 4

Varnavskaya Anastasia

D This material was developed for participation in a scientific conference in mathematics in the 2013 - 2014 academic year. Subject "Zodiac signs oncoordinate plane" was chosen by the student due to her interest in how to connect astrology with mathematics. This work is supported by a presentation.

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

Tasks:

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

2) Study the zodiac constellations.

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

4) Conduct astrological research for students in grade 6 “A”.

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Slide captions:

MBOU Secondary School No. 121 Coordinate plane and signs of the Zodiac Completed by: Varnavskaya Anastasia, 6 “A” class Supervisor: mathematics teacher Yulia Igorevna Shutova. Nizhny Novgorod, 2014

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

The main goal: consideration of the signs of the Zodiac through the theory of the coordinate plane. Objectives: 1) Get acquainted with the history of the origin of coordinates. 2) Study the zodiac constellations. 3) Construct an image of the constellation on the coordinate plane. 4) Conduct astrological research for students in grade 6 “A”.

History of the creation of the coordinate system 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.

In the 14th century, the French mathematician N. Orsem proposed 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. Nicolas Orsem (1323-1382) Hipparchus René Descartes (1596 - 1650)

Types of coordinate systems Coordinates on a straight line (Cartesian) Polar coordinate system Spherical coordinate system

Cartesian coordinate system

12 Zodiac signs

y x 1 0 Aquarius

y x 1 0 Taurus

y x Capricorn

y x Gemini

y x Scorpio

y x Sagittarius

Lost sign - Ophiuchus

Exploring my class

Conclusion In the course of my work, I became acquainted with the history of the origin of coordinates, learned about different types of coordinate systems, their features, origin and purpose. Having done a lot of work on studying the zodiac constellations, I came to the conclusion that the world of zodiac signs is that beautiful line that connects a person with the mysterious cosmos and distant stars. Having studied the signs of the Zodiac, I constructed 4 signs on the coordinate plane. Having systematized the knowledge gained, I was able to conduct astrological research on students in grade 6 “A”.

Thank you for your attention!

Objective of the project:

Study the zodiac constellations.

Construct an image of the constellation on the coordinate plane.

Conduct astrological research for 6th grade B students.

Project objectives:

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

expand the scope of knowledge within the chosen topic;

create cards"Constructions in a rectangular coordinate system."

Project issues:

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

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

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

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

Stages of work on the project:

Determining the theme of the project.

Collection and systematization of materials in accordance with the topic.

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

Presentation and defense of the project.

List of information resources used:

References

Internet

ANNOTATION

Coordinates occur in our lives every hour.

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

Do coordinate systems have only two quantities?

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

How do pilots navigate the sky?

The position of the stars probably also has coordinates?

This is all found in modern life.

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

What constructions can be performed in the coordinate plane?

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

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

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

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

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

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

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

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

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

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

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

11.Appendix……………………………………………………………

Introduction.

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

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

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

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

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

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

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

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

2. History of the origin of the coordinate system.

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

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

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

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

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

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

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

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

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

3. Types of coordinate systems.

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

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

The most commonly used coordinate systems are rectangular.

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

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

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

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

A detailed acquaintance with them will happen much later.

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

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

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

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

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

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

Capricorn - when the day of the winter solstice arrived, the hour had come for the great Zeus to be born. Rhea, the goddess, wrapped a stone in swaddling clothes and 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.

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

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

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

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

5. Twelve constellations. Aries constellation

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

Taurus constellation

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

Constellation Gemini.

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

Constellation Cancer

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

Constellation Leo

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

Virgo constellation

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

Constellation Libra

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

Scorpio constellation

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

Sagittarius constellation

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

Constellation Capricorn

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

Aquarius constellation

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

Constellation Pisces

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

Ophiuchus

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

6. Zodiac signs in coordinates. a lion

Coordinates

Connection paths

On the coordinate plane

1 (-21;-4)

1→2→3→4→5→6→7→8→9→10→13→15→16

2 (-11;2)

4→10 and 6→9

3 (-8;1)

10→11 and 10→12

4 (3;3)

13→14 and 13→2

5 (4;6)

6 (8;9)

7 (14;10)

8 (13;7)

9 (10;7)

10 (7;0)

11 (14;-6)

12 (7;-5)

13 (-11;-4)

14 (2;-8)

15 (-13;-8)

16(-11;-13)

Capricorn

Coordinates

Connection paths

On the coordinate plane

1(-22;3)

12345678 and 36

2(-18;2)

791011

3(-11;2)

9126 and 1213

4(-13;-5)

5(-12;-6)

6(-3;2)

7(14;6)

8(16;11)

9(11;1)

10(4;-10)

11(2;-12)

12(-3;-2)

13(-4;-10)

Coordinates

Connection paths

On the coordinate plane

1(-21; -10)

143 and 42

2(-17; -11)

45678469101

3(-22; 0)

11213101415

4(-20;2)

14161718

7(-1;1)

8(-1;4)

9(8;10)

10(1;-2)

11(-2;-6)

12(-1;-9)

13(3;-9)

14(6;-4)

15(14;-4)

16(12;-1)

17(8;-11)

18(14;-14)

7. Astrological studies 6 “B” class.

Zodiac signs in 6 "B"

Zodiac signs

Cancer

Taurus

Scales

Aries

Scorpion

Capricorn

Aquarius

Virgo

a lion

Sagittarius

Twins

Fish

Elements 6 "B" class.

Elements 6 "B"

Fire

Earth

Air

Water

8. Interesting facts about the elements.

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

Principle: action, activity, energy.

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

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

Principle: exchange, contact.

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

Principle: internal constancy despite external variability

10. Conclusion.

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

Literature

1. Atlas for 5th grade science.

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

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

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

4.Internet.

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