Who Was Pythagoras and Where Did He Come From?
Pythagoras was Greek, born on the island of Samos in North-east Aegean around 569BC (exact date is unknown). He studied Philosophy mainly, though also attended lectures on Cosmology and Geometry. His later life was highly eventful, particularly upon being captured by Cambyses II, the King of Persia, when he travelled to Egypt. It was soon after this that he was exposed to the world of mathematics...
The Pythagoreans
After his capture, he was taken to Babylon as a prisoner, where he learned Babylonian mathematics (as well as musical theory). Upon committing his life to mathematics, he later founded the school of Pythagoreans in Crotone, Italy. It is this mysterious cult of the Pythagoreans for which he is best known, for they had very different beliefs to mainstream society. Not only were they vegetarians, they were strictly against eating, or even touching, any sort of bean, probably because they thought beans were created from the same material as humans. They walked bare foot, and, most importantly, believed that the universe was mathematical, and that all numbers and symbols had spiritual meaning. This belief was based on the idea of Platonism, which suggests that all numbers exist, though not in the same space-time dimensions as our universe. They also strongly believed in the idea of certain humans having a higher level of soul purification, and thought pure mathematicians, and those who merely contemplated on life, lived in the highest plane of existence, or had the purest souls.
Pythagoras's Theorem and A Proof For It
Many mathematical theories were associated with being discovered by the Pythagoreans, though the most famous, of course, is Pythagoras's Theorem, which you most likely first came across in school. For any right angled triangle with sides 'a', 'b' and 'c', where 'c' is the hypotenuse (longest side): a^2 + b^2 = c^2. Pythagoras probably didn't have a proof for this (most likely he just believed it to be true), but many proofs have been found. The proof I've explained below is one of my favourites:
As you can see, there are four identical right-angled triangles in this square, arranged so that they form a smaller square inside, where all of the sides are the Hypotenuses of the four triangles. There are two ways to calculate the area of the large square: 1. The obvious way is to square the length of a side. Each side has length 'a+b', so the area is '(a+b)^2', which expands to give: 'a^2 + 2ab + b^2'
2. An alternative method is to add the areas of the four triangles and the smaller square. Each triangle has an area of 'ab/2', and the square has an area of c^2, so the total area is: '4(ab/2) + c^2', which simplifies to: '2ab + c^2'
Now, these two calculations both give the area of the large square, so we can equate them (make them equal to each other): a^2 + 2ab + b^2 = 2ab + c^2.
'2ab' will cancel on both sides, leaving:
a^2 + b^2 = c^2
The Death of Pythagoras (According to Legend)
Since Pythagoras lives so long ago, it is near impossible to be sure of certain details, such as how he died. According to legend, enemies of the Pythagoreans set fire to his house, forcing him to flee for his life. He soon came upon a bean field, and his belief that beans should not even be touched was so strong, he would not enter it. He declared that he would rather die that enter the field, and thus allowed his enemies to capture him and slit his throat. So the life of Pythagoras came to a sorrowful end; though the legacy he left behind shall live on until the end of time.
Thanks for reading everyone, hopefully it was an insightful experience for you. If you liked it, or if you have any queries, make sure you comment in the comments section below. Hopefully, within a couple of weeks or so, I'll have done another post about Leonard Euler. Keep checking back here for more awesome stuff about maths. Until next time!
Admin H.
2 + 2 = vagina
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