Pythagoras was a Greek mathematician born around 570 BCE in Samos, Greece. He founded a school in Croton, Italy where he studied mathematics and developed the Pythagorean theorem, which states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides. Pythagoras made many contributions to mathematics and music. He discovered that the musical scale is based on string length ratios and ratios of whole numbers.

1. Pythagoras

2. History of Pythagoras Pythagoras was born in Samos, Greece around 570 BCE (it is difficult to pinpoint the exact year) He is often described as the first pure mathematician. Around 535 BCE, Pythagoras journeyed to Egypt to learn more about mathematics and astronomy

3. History of Pythagoras (cont.) Pythagoras founded a philosophical and religious school/society in Croton (now spelled Crotone, in southern Italy) His followers were commonly referred to as Pythagoreans. The members of the inner circle of the society were called the “mathematikoi” The members of the society followed a strict code which held them to being vegetarians and have no personal possessions

4. History of Pythagoras (cont.) There is not much evidence of Pythagoras and his society’s work because they were so secretive and kept no records One major belief was that all things in nature and all relations could be reduced to number relations

5. Pythagoras and Music Pythagoras made important developments in music and astronomy Observing that plucked strings of different lengths gave off different tones, he came up with the musical scale still used today. Was an accomplished musician at playing the lyre

6. Pythagoras and Math Pythagoras made many contributions to the world of math including: Studies with even/odd numbers Studies involving Perfect and Prime Numbers Irrational Numbers Various theorems/ideas about triangles, parallel lines, circles, etc. Of course THE PYTHAGOREAN THEOREM

7. The Theorem: The square of the hypotenuse of a right triangle is equal to the sum of the squares of the other 2 sides (legs) a 2 + b 2 = c 2 But what does it mean???

8. Pythagorean Theorem

9. It’s Uses Determine side length of triangles Height, distance of objects The Distance Formula Range finding

10. Real World Uses Architecture, Engineering, Surveying CAD (Computer Aided Drafting) Military Applications Cartography (Map-Making/Directions)

11. Example Problems (1 of 2) Find the measure of C in the triangle above: a 2 + b 2 = c 2 6 2 + 8 2 = C 2 36 + 64 = C 2 100 = C 2  100 =  C 2 so 10 = C

12. Example Problems (2 of 2) Find the measure of C in the triangle above: a 2 + b 2 = c 2 5 2 + 12 2 = C 2 * 25 + 144 = C 2 * 169 = C 2 *  169 =  C 2 so 13 = C