MYSTERIES OF THE EQUILATERAL TRIANGLE - HIKARI Ltd

Biographical Vignettes 149
Vignette 1 (Pythagoras of Samos: Circa 569-475 B.C.).
Aristotle attributed the motto “All is number.” to Pythagoras more than
a century after the death of the latter. Since all of Pythagoras’ writings, if
indeed there ever were any, have been lost to us, we have to rely on secondhand
sources written much later for details of his life and teachings [148, 165,
233]. Thus, a grain of skepticism is in order when assessing the accuracy of
these accounts. Pythagoras was born on the island of Samos off the coast of
Ionia (Asia Minor). He had a vast golden birthmark on his thigh which the
Greeks believed to be a sign of divinity. He studied Mathematics with Thales
and Anaximander in the Ionian city of Miletus and traveled widely in his
youth, visiting both Egypt and Babylon and absorbing their knowledge into his
evolving philosophy. He eventually settled in Croton in southern Italy where
he established a commune with his followers. The Pythagorean brotherhood
believed that reality was mathematical in nature and practiced a numerical
mysticism which included the tetraktys discussed in Chapter 1 as well as a
numerical basis for both music and astronomy. Amongst their mathematical
discoveries were irrational numbers, the fact that a polygon with n sides has
sum of interior angles equal to 2n − 4 right angles and sum of exterior angles
equal to four right angles, and the five regular solids (although they knew
how to construct only the tetrahedron, cube and octahedron). They also were
the first to prove the so-called Pythagorean theorem which was known to the
Babylonians 1000 years earlier. Due to political turmoil, the Pythagoreans
were eventually driven from Croton but managed to set up colonies throughout
the rest of Italy and Sicily. Pythagoras died, aged 94, after having returned to
Croton.
Vignette 2 (Plato of Athens: 427-347 B.C.).
Plato was born in Athens and studied under Theodorus and Cratylus who
was a student of Heraclitus [107, 166, 202]. He served in the military during
the Peloponnesian War between Athens and Sparta. After his discharge, he
originally desired a political career but had a change of heart after the execution
of his mentor, Socrates, in 399 B.C. He then traveled widely visiting
Eqypt, Sicily and Italy, where he learned of the teachings of Pythagoras. After
another stint in the military when he was decorated for bravery in battle, he
returned to Athens at age 40 and established his Academy which was devoted
to research and instruction in philosophy and science. Plato believed that
young men so trained would make wiser political leaders. Counted among the
Academy’s graduates were Theaetetus (solid geometry), Eudoxus (doctrine of
proportion and method of exhaustion) and Aristotle (philosophy). Above the
entrance to the Academy stood a sign “Let no one ignorant of Geometry enter
here.”. Plato’s principal writings were his Socratic dialogues wherein he elaborated
upon, among other topics, mathematical ideas such as his Theory of