Class 1/20/12 - 2.1.2 & 2.1.3

Salut mes amants des maths! 

Today's lecture corresponded to sections 2.1.2 and 2.1.3 dealing with Thales and Pythagoras and his school, respectively. As we enter the subject of Greek mathematics and it's contributions to the general math field, we will discuss various prominent figures who played a significant role in the development of what today is moder math. 

Thales (c. 624-547 BCE) of Miletus was one of such prominent figures who was said to have discovered several theorems in addition to provided numerous proofs. He is know for proving the following theorems: 

1. A circle is bisected by any diameter
2. Base angles of isosceles triangles are congruent
3. Angles between 2 intersecting straight lines are congruent. 
4. Two triangles are congruent if they have 2 angles and 1 side conrguent (ASA) 
5. An angle in a semicircle is 90 degrees.  (This theorem is illustrated below)

Although Thales was credited with many proofs and discoveries, for many of these presumed accomplishments, we are not exactly aware of how Thales "proved" any of these results, but it appears that he was able to advance some logical arguments. 

Also, Dr. Daddel spoke of Pythagoras and his school which led to the Pythagorean Brotherhood. There's not a lot of information about Pythagoras (c. 572-497 BCE), but there do exist many extensive but unreliable stories about his life with respect to the amount of time he spent when and where. It is said that after he was forced to leave his native land, he then settled in Crotona and gathered around him a group of disciples that were labeled Pythagoreans, in what was considered a religious and philosophical school. The general philosophy of this school is that the universe in all its aspects could be simply represented by numbers; unfortunately, this strong belief conflicted with their discovery of the concept of incommensurability.  The Pythagoreans studied different types of numbers (i.e. odd, eve, triangular, oblong, etc.) They were able to visually depict such numbers using dots and pebbles. 

Until next time, mes amis! 

A+! 

-MB