Pythagorean Theorem — or Pythagoras’ theorem: in any right-angled triangle, the area of the square whose side is the hypotenuse (the side opposite the right angle) is equal to the sum of the areas of the squares whose sides are the two legs (the two sides that meet at a right angle).
Pythagoras of Samos, the creator of one of the most famous equations of all time, has a rather obscure history. He wrote very little about himself, delegating the task of documenting his life and views to his followers. What we do know is that in his world of the mid-sixth century BCE, he was considered to be a thinker and a mystic.
In today’s world, Pythagoras’ school would be considered more like a religious cult than a philosophical establishment. His teachings included many eccentric doctrines including, the veneration for, and abstinence from, the eating of beans. He advocated reincarnation and the transmigration of souls. Most see him as the founder of the modern belief in numerology, later popularised by Nostradamus.
Pythagoras argued that the ultimate nature of reality is number, which he developed out of his theory of music. He claimed that music had a special power over the soul. The proof was found in the intervals between musical tones, which could be expressed as ratios between the first four integers, number 1 – 4. His discovery of irrational numbers did play havoc with his beliefs on the origin of the universe; however, they have proven to be a major and lasting development in mathematical thinking.
After his death, his followers split into two camps; one embraced his religious and mystical teachings, while the other pursued his scientific and mathematical philosophy. Ideas and beliefs, whether or not they prove to be valid, must be considered, lest we overlook the very insight that will bring us to the next stage of development.
“It is the mark of an educated mind to be able to entertain a thought without accepting it.”