Like Thales, Pythagoras is rather known for mathematics than for philosophy. Anyone who can recall math classes will remember the first lessons of plane geometry that usually start with the Pythagorean theorem about right-angled triangles: a²+b²=c². In spite of its name, the Pythagorean theorem was not discovered by Pythagoras. The earliest known formulation of the theorem was written down by the Indian mathematician Baudhāyana in 800BC. The principle was also known to the earlier Egyptian and the Babylonian master builders. However, Pythagoras may have proved the theorem and popularised it in the Greek world. With it, his name and his philosophy have survived the turbulences of history.
His immediate followers were strongly influenced by him, and even until today Pythagoras shines through the mist of ages as one of the brightest figures of early Greek antiquity. The Pythagorean theorem is often cited as the beginning of mathematics in Western culture, and ever since mathematics -the art of demonstrative and deductive reasoning- has had a profound influence on Western philosophy, which can be observed down to Russell and Wittgenstein.
Pythagoras’ influence found an expression in visual art and music as well, particularly in the renaissance and baroque epoch. The far-reaching imprint of his ideas is yet more impressive if we consider that he did not leave any original writings. Instead, all what is known about Pythagoras was handed down by generations of philosophers and historiographers, some of whom, like Heraclitus, opposed his views. In this light it is remarkable that Pythagoras’ teachings have survived relatively undistorted until the present day.
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| Painting Title: Homage to Pythagoras Size: 34" wide x 55" tall Medium: Acrylic on Board 2006 Artist: Marion Drennen |
He, or rather one of his followers, also proved that irrational numbers exist, as shown in the mathematical proof in the upper portion of the painting. Phi, written
is found in the relationships between the sides, the edges and the vertices of the Platonic Solids, and was considered by the Pythagoreans to be so significant that they were sworn to secrecy on the subject. When Hippasus of Metapontum divulged the secret of the existence of the irrational, he was thrown in the river and drowned. Phi, expressed to about 20,000 places is printed to the surface in the painting.
Pythagoras discovered the mathematics in music. By dividing a string into sections, so lengths have the ratios of 2:1, 3:2, 4:3, or 5:4 (octave, fifth, fourth, third), harmonic tunes result. He was quoted as having said, "There is geometry in the humming of the strings". In music theory, the diatonic scale, depicted on the left side of the theorem proof, is a 7-note musical scale with the pattern repeating at the octave (diatonic is translated by Greek, meaning literally "progressing through tones").
Pythagoreans discovered the dodecahedron, the fifth regular/Platonic solid.
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Actually, Neolithic people of Scotland 2000 BC knew about these shapes, as evidenced by the stone carvings they left behind. However, the Pythagoreans were enamored and studied these shapes.
If you fit any regular solid just inside a sphere, all the vertices touch the inside of the sphere. If you fit a sphere just inside any regular solid, it touches all the faces of that regular solid.
The Pythagoreans believed that the universe consisted of a central, spherical earth surrounded by one of the five regular solids, in turn surrounded by a crystalline sphere surrounded by another regular solid, and so on until five spheres surrounded the earth, each circumscribed about a regular solid. The planets and the stars were attached and, as they rotated, created musical harmonies. The Pythagoreans believed most people couldn’t hear this "harmony of the spheres" because they had grown accustomed to it from birth, but that Pythagoras alone could hear it.
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| Platonic Solids |
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