1. The Man They Called: Pythagoras
The beginning of time
572 B.C. – 501 B.C.

2. Event’s circa 600BC-500BC Cyrus the Persian: Religious Beginnings:
Persian Empire’s Expansion
Religious Beginnings:
Buddhism
Confucius
Lao-Tze

3. Early Life Born on Island of Samos circa 580 B.C.
Studied in Egypt, and even Babylonia.

4. Education
Taken prisoner out of Egypt and was transported to Babylon where he reached perfection in arithmetic, music, and other mathematical sciences.

5. Establishing a School
After years of traveling and studying, he settled in Croton where he established a school.
Main Mathemata (subjects) of study were:
Arithmetic
Music
Geometry
Astronomy
(Logic, grammar, rhetoric would later be added)

6. The Effects of School
A sacred brotherhood was created at the school by the followers of Pythagoras and called themselves Pythagoreans.
Believed the key in explaining the universe was in Numbers
Thesis: “Everything is Number”

7. Contributions to Mathematics
First to study the Theory of Numbers, and their relations to each other.
Astronomy: “Harmony of Spheres”
Pythagorean’s Theorem:
: a2+b2=c2 for right triangles
History of Pythagorean theorem and proofs

8. A Proof of Pythagorean’s Theorem
Start with four triangles, except that, this time, they combine to form a square with the side (a+b) and a hole with the side c. We can compute the area of the big square in two ways. Thus
(a + b)2 = 4·ab/2 + c2
simplifying which we get the needed identity.
The square has a square hole with the side (a-b). Summing up its area (a-b)2 and 2ab, the area of the four triangles (4·ab/2), we get
c2 = (a-b)2+2ab = a2-2ab+b2+2ab = a2+b2

9. Contributions to Number Theory
Was first to study the properties of Numbers:
Odd or even properties
Triangular Numbers: {1,3,6,10…n(n+1)/2}
Perfect Numbers: {6,28…}
Gave Number’s Personalities:
Number was Everything
[2=woman, 3=man, 10=universe]

10. The Ending A Revolution around 500BC occurred in the city of Croton
During this revolution many Pythagoreans were murdered
Pythagoras is believed to have been murdered at this time.(500BC)
The brotherhood lasted for 2 more centuries after Pythagoras’s death.

11. Discoveries
Many of the advances of mathematics at this time were made by Pythagoreans, NOT Pythagoras but in the time, it was customary to give all credit to the “Master” of the school.
Considered a legend by the people:
Astronomer
Mathematician
Philosopher
Saint
Prophet

12. Sources/ References Pythagorean Theorem:
Pythagoras of Samos
History of Pythagoras
Burton, David. Elementary Number Theory, Forth Edition. McGraw-Hill Companies, San Francisco, (pg )
Boyer, Carl B. A History of Mathematics. Second Edition. John Wiley & Sons, New York, Pg.43-61