The history of the Pythagorean theorem has several millennia. The assertion that the square of the hypotenuse is equal to the sum of the squares of the legs was known long before the birth of the Greek mathematician. However, the Pythagorean theorem, the history of creation and its proofs are connected for the majority with this scientist. According to some sources, the reason for this was the first proof of the theorem, which was given by Pythagoras. However, some researchers refute this fact.
Music and Logic
Before telling how the history of the Pythagorean theorem evolved, we briefly dwell on the biography of a mathematician. He lived in the VI century BC. The date of birth of Pythagoras is considered to be 570 BC. e., the place is the island of Samos. Little is known about the life of the scientist. Biographical data in ancient Greek sources are intertwined with obvious fiction. On the pages of treatises, he appears as a great sage, masterfully mastering the word and the ability to convince. By the way, that is why the Greek mathematician was nicknamed Pythagoras, that is, "convincing speech." According to another version, the birth of the future sage was predicted by Pythia. Her father named the boy Pythagoras.
The sage learned from the great minds of the time. Among the teachers of the young Pythagoras are Germodamant and Feriqid of Syros. The first instilled in him a love of music, the second taught philosophy. Both of these sciences will remain in the center of attention of the scientist throughout his life.
30 year training
According to one version, being an inquisitive young man, Pythagoras left his homeland. He went to seek knowledge in Egypt, where he stayed, according to various sources, from 11 to 22 years old, and then was captured and sent to Babylon. Pythagoras was able to benefit from his position. For 12 years, he studied mathematics, geometry, and magic in an ancient state. Pythagoras returned to Samos only at 56 years old. Here the tyrant Policrates ruled at that time. Pythagoras could not accept such a political system and soon went to the south of Italy, where the Greek colony Croton was located.
Today it is impossible to say for sure whether Pythagoras was in Egypt and Babylon. Perhaps he left Samos later and went straight to Croton.
Pythagoreans
The history of the Pythagorean theorem is connected with the development of the school created by the Greek philosopher. This religious and ethical fraternity preached a special lifestyle, studied arithmetic, geometry and astronomy, studied the philosophical and mystical aspects of numbers.
All the discoveries of the students of the Greek mathematician were attributed to him. However, the history of the emergence of the Pythagorean theorem is associated by ancient biographers only with the philosopher himself. It is assumed that he transmitted to the Greeks the knowledge gained in Babylon and Egypt. There is also a version that he really discovered a theorem on the relationship of legs and hypotenuse, not knowing about the achievements of other nations.
Pythagoras Theorem: Discovery History
Some ancient Greek sources describe the joy of Pythagoras when he managed to prove the theorem. In honor of such an event, he ordered a sacrifice to the gods in the form of a hundred bulls and made a feast. Some scholars, however, point to the impossibility of such an act due to the peculiarities of the Pythagorean views.
It is believed that in the treatise "Beginnings" created by Euclid, the author gives a proof of the theorem, the author of which was the great Greek mathematician. However, this view was not supported by all. Thus, the ancient neo-Platonic philosopher Proclus pointed out that the author of the proof given in the "Elements" is Euclid himself.
Be that as it may, but the first to formulate the theorem was still not Pythagoras.
Ancient Egypt and Babylon
The Pythagorean theorem, the history of which is considered in the article, according to the German mathematician Kantor, was known as far back as 2300 BC. e. in Egypt. The ancient inhabitants of the Nile Valley during the reign of Pharaoh Amenemkhet I knew the equality 3 2 + 4 ² = 5 ² . It is assumed that with the help of triangles with sides 3, 4 and 5, the Egyptian “rope tensioners” built right angles.
They knew the Pythagorean theorem in Babylon. On clay tablets dating back to 2000 BC and dating back to the reign of King Hammurabi, an approximate calculation of the hypotenuse of a right triangle was discovered.
India and China
The history of the Pythagorean theorem is also connected with the ancient civilizations of India and China. The treatise "Zhou-bi Xuan Jin" contains indications that the Egyptian triangle (its sides correspond as 3: 4: 5) was known in China in the XII century. BC e., and to the VI century. BC e. mathematicians of this state knew the general form of the theorem.
The construction of the right angle with the help of the Egyptian triangle was also described in the Indian treatise "Sulva Sutra", dating from the 7th-5th centuries. BC e.
Thus, the history of the Pythagorean theorem at the time of the birth of the Greek mathematician and philosopher totaled several hundred years.
Evidence
During its existence, the theorem has become one of the fundamental in geometry. The history of the proof of the Pythagorean theorem probably began with a consideration of an equilateral right triangle. Squares are built on his hypotenuse and legs. The one that "grew" on hypotenuse will consist of four triangles equal to the first. The squares on the legs in this case consist of two such triangles. A simple graphic image clearly shows the validity of the statement formulated in the form of the famous theorem.
Another simple proof combines geometry with algebra. Four identical right-angled triangles with sides a, b, c are drawn so that they form two squares: the outer one with side (a + b) and the inner one with side c. In this case, the area of the smaller square will be equal to 2 . The large area is calculated from the sum of the areas of the small square and all the triangles (the area of a right-angled triangle, recall, is calculated by the formula (a * c) / 2), i.e. with 2 + 4 * ((a * c) / 2), which is equal to 2 + 2av. The area of a large square can be calculated in another way as a product of two sides, that is (a + b) 2 , which is equal to a 2 + 2av + in 2 . It turns out:
and 2 + 2av + in 2 = s 2 + 2av,
and 2 + to 2 = s 2 .
There are many options for proving this theorem. Euclid, and Indian scientists, and Leonardo da Vinci worked on them. Often, ancient sages brought drawings, examples of which are located above, and did not accompany them with any explanations, except for the note “Look!” The simplicity of the geometric proof, provided there was some knowledge of the comments, was not required.
The history of the Pythagorean theorem, summarized in the article, debunkes the myth of its origin. However, it is difficult to even imagine that the name of the great Greek mathematician and philosopher will someday cease to be associated with it.