Tag Archives: Right Triangle

Pythagoras and His Pythagorean Followers

27 Feb

The Pythagorean Theorem is known by many students as

a^2 + b^2 = c^2\!\,

But who came up with this? A Greek mathematician by the name of Pythagoras is credited for this discovery. He was born on the island of Samos, Greece in 569 B.C.. Around 518 B.C., Pythagoras settled down in a Greek colony in southern Italy called Crotona. It was here that he founded a religious and philosophical school where many of his followers, both men and women, lived and worked. These “Pythagoreans” were not allowed to have personal possessions and were vegetarians. The followers were also known as mathematikoi.

Pythagoras believed (and therefore his followers also believed) in the following:

  • All things are numbers. Mathematics is the basis for everything, and geometry is the highest form of mathematical studies. The physical world can understood through mathematics.
  • The soul resides in the brain, and is immortal. It moves from one being to another, sometimes from a human into an animal, through a series of reincarnations called transmigration until it becomes pure. Pythagoras believed that both mathematics and music could purify.
  • Numbers have personalities, characteristics, strengths and weaknesses.
  • The world depends upon the interaction of opposites, such as male and female, lightness and darkness, warm and cold, dry and moist, light and heavy, fast and slow.
  • Certain symbols have a mystical significance.
  • All members of the society should observe strict loyalty and secrecy.
[My favorite is that numbers have personalities, characteristics, strengths and weaknesses. Must be why 7 has a huge appetite and a problem with “numberalism” (get it? Because seven “ate” nine?? )]
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Anyway, because this society of Pythagoras’ was so secretive and the fact that they shared ideas and intellectual discoveries, no one knows for sure whether or not the theorems are actually ones Pythagoras came up with himself. Nonetheless, the Pythagoreans gave Pythagoras all the credit for the following:
  1. The sum of the angles of a triangle is equal to two right angles.
  2. The Theorem of Pythagoras (a.k.a. The Pythagorean Theorem) : For a right-angled triangle the square on the hypotenuse is equal to the sum of the squares on the other two sides. The Babylonians are actually the ones who understood this 1,000 years earlier, but Pythagoras proved it and hence, he gets the credit.
  3. Constructing figures of a given area and geometrical algebra. (So, for example, they solved various equations by geometrical means)
  4. The discovery of irrational numbers is attributed to the Pythagoreans, but this seems unlikely to have been the idea of Pythagoras since it does not align with his philosophy the all things are numbers (he believed that number meant the ratio of two whole numbers).
  5. The five regular solids (tetrahedron, cube, octahedron, icosahedron, dodecahedron).
Here is a problem that requires you to use the Pythagorean Theorem to solve:
Scott wants to swim across a river that is 400m wide. He begins swimming perpendicular to the shore he started from, but he ends up 100m down river from where he started because of the current. How far did he actually swim from his starting point?
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Click here to find the answer.
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Source (MLA Format): Douglass, Charlene. “Biography of Pythagoras.” Math Open Reference. 2005. Web. 21 Feb. 2012. <http://www.mathopenref.com/pythagoras.html&gt;.