Pythagoras

Pythagoras was an ancient Greek mathematician and philosopher who was one of the most influential men in all of history. Even though he was a mathematician, his contributions help all sorts of fields of study, including math, science, music and astronomy. Most of his contributions, and those of his followers, the Pythagoreans, are known and used throughout the world. Almost everyone knows his theorem that the sum of the squares of the lengths of the two shorter sides of a right triangle is equal to the square of the length hypotenuse.

Pythagoras was born on the Greek Island of Samos. He traveled around the known world visiting Babylonia and Egypt along with seeing other parts of Greece. Early on in his life several other philosophers, such as Anaximander majorly influenced him. Pythagoras was a patron of the ancient Greek Olympic games, even though he criticized them. He died at some point around the turn of the century in Metapontion.

He started a religious and philosophical order known as the Pythagoreans and most of his work was completed between himself and his followers. His society was founded in Croton, in southern Italy.

The society was made up of two groups, the pupils and the learned, or teachers. These people set up the world's first organized schools.

They were a very strict order and had many restrictions, such as no meat or beans, and the new members couldn't even speak until they had listened to the teaching of their master for 5 years.

Even after the first 5 years the pupil's work was too be left anonymous, the discoveries made were either credited to the master or to the school itself.

The Pythagoreans believed that everything in the universe revolved around mathematics, such as music and the magicks. Every number had a soul and a specific meaning and value to the universe.

We here at the WM Times traveled across the globe and back in time to interview the famous Pythagoras and find out about some of his discoveries and theorems.

WM Times: So Pythagoras you made many contributions to geometry, can you tell us a few of them?

Pythagoras: Sure. You of course know of my a2+b2 = c2, but I created this method at first just to prove that a triangle was a right triangle. I also discovered a formula to find out how many degrees there are in a polygon. I came up with (n-2)180= the number of degrees in a polygon, where n represents the number of sides in the polygon. For example, a triangle has three sides, 3-2=1, 1x180=180, which is the total sum of all the inner angles of a triangle. Along with that I found out that the sum of all the outer angles of a polygon is always equal to three hundred sixty degrees. This is true for every single polygon, regardless of the number of the sides.

WM T: That's impressive, and you came up with all of this by yourself?

P: Not entirely, my followers, the Pythagoreans, contributed some of my work.

WM T: I've heard rumors that you didn't come up with the a2+b2 = c2 theorem at all, that while you spent a brief period in Babylonia, you stole the idea, an idea found on a stone tablet from over one thousand years before your time.

P: That is ridiculous, maybe these people thought it up first, but it was my people and I who prove it to be true.

WM T: Your discoveries and ideas were not limited to just math, what else did you come up with?

P: Well. I did a lot of work with proportions in other fields. I looked at and showed the difference in pitch in ratio to the length of string plucked. It was not as I expected. I found out that half way along the string is not half the pitch. I also looked to the stars and saw that the further away a planet is from where it orbited the longer it would take to go around the sun. Oh yes and you told me a few minutes ago that I was quite incorrect in my teachings about the Earth being in the center of the universe.

WM T: Sticking to your errors, did you ever discover anything that contradicted one of you previous ideas?

P: Of course I did. I believed that every single number was rational. Then in my work with right triangles, I found irrational numbers and proved myself wrong.

WM T: One final question, why? Why all the philosophy and mathematical discovery?

P: I did it because I am not content with accepting things as they are. I need explanations and reasons. Through this, I discovered a lot of different things, many being very useful.


Work Cited

“Pythagoras.” Microsoft Encarta 2001 Ed.

Very little significant information, but it's all accurate.

Burnet, John. Early Greek Philosophers. http:/plato.evansville.edu/public/burnet/ch2a.htm#38

Some good illustrations of theorems.

“Introduction to the Pythagoreans” http://www.drury.edu/ess/History/Ancient/pythagoreans1.html

Talked about the Pythagoreans.

“Pythagoras” http://www.pythagoras.com/

Proved the Pythagorean theorems.

“Pythagoras." Internet Encyclopedia of Philosophy. http://www.utm.edu/research/iep/p/pythagor.htm

Good biography.

"Pythagoras of Samos” http://www-groups.dcs.st-and.ac.uk/~history/Mathematicians/Pythagoras.html

A very good biography.

“Pythagorean Theorem” http://www.cut-the-knot.com/pythagoras/

Also proved the Pythagorean theorems.