Biography of Pythagoras
The Pythagoreans always credited Pythagoras:
1. A triangle's angles are equivalent to two right angles when added together.
2. Pythagoras' theorem: the square on the hypotenuse of a right-angled triangle is equal to the sum of the squares on the other two sides. The Babylonians knew it 1000 years before Pythagoras, but Pythagoras proved it.
3. Geometrical algebra and the construction of figures in a given area. They used geometrical methods to solve various equations, for example.
4. The Pythagoreans are credited with discovering irrational numbers, although this appears doubtful because it contradicts Pythagoras' belief that all things are numbers, as number to him meant the ratio of two whole numbers.
5. The five basic solids (tetrahedron, cube, octahedron, icosahedron, dodecahedron). Pythagoras is thought to have mastered the first three but not the last two.
6. Pythagoras taught that the Earth was a sphere in the Kosmos (Universe), that the planets, stars, and the universe were all spherical because the sphere was the most perfect solid shape. He also claimed that the planets' trajectories were round. Pythagoras saw that the morning and evening stars, Venus, were the same.
7. Pythagoras was a mathematician who was interested in odd and even numbers, triangular numbers, and perfect numbers. Angles, triangles, areas, proportion, polygons, and polyhedral were all influenced by Pythagoreans.
8. Pythagoras linked music and mathematics as well. He'd been playing the seven-string lyre for a long time and had discovered how beautiful the vibrating strings sounded when the string lengths were proportionate to whole numbers, such as 2:1, 3:2, and 4:3. Pythagoreans also discovered that their expertise might be applied to a variety of other musical instruments.
9. There are various accounts of Pythagoras' death. He is reported to have been killed by an enraged mob, to have been caught up in a fight between the Agrigentum and the Syracusans and killed by the Syracusans, or to have been burned out of his Crotona school and subsequently starved to death in Metapontum. In at least two of the legends, Pythagoras refuses to crush a crop of bean plants in order to flee, and as a result, he is apprehended.
10. The Pythagorean Theorem is a cornerstone of mathematics, and it continues to fascinate mathematicians to the point where there are over 400 distinct proofs, including one by President Garfield.
