Pythagoras
History of Pythagoras <ul><li>Pythagoras  was born in Samos, Greece around 570 BCE (it is difficult to pinpoint the exact ...
History of Pythagoras (cont.)  <ul><li>Pythagoras founded a philosophical and religious school/society in Croton (now spel...
History of Pythagoras (cont.)  <ul><li>There is not much evidence of Pythagoras and his society’s work because they were s...
Pythagoras and Music <ul><li>Pythagoras made important developments in music and astronomy </li></ul><ul><li>Observing tha...
Pythagoras and Math <ul><li>Pythagoras made many contributions to the world of math including: </li></ul><ul><ul><li>Studi...
The Theorem: <ul><li>The square of the hypotenuse of a right triangle is equal to the sum of the squares of the other 2 si...
Pythagorean Theorem
It’s Uses <ul><li>Determine side length of triangles </li></ul><ul><li>Height, distance of objects </li></ul><ul><ul><li>T...
Real World Uses <ul><li>Architecture, Engineering, Surveying </li></ul><ul><li>CAD (Computer Aided Drafting) </li></ul><ul...
Example Problems (1 of 2) <ul><li>Find the measure of C in the triangle above: </li></ul><ul><ul><li>a 2  + b 2  = c 2 </l...
Example Problems (2 of 2) <ul><li>Find the measure of C in the triangle above: </li></ul><ul><ul><li>a 2  + b 2  = c 2 </l...
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Pythagoras And The Pythagorean Theorem

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Pythagoras And The Pythagorean Theorem

  1. 1. Pythagoras
  2. 2. History of Pythagoras <ul><li>Pythagoras was born in Samos, Greece around 570 BCE (it is difficult to pinpoint the exact year) </li></ul><ul><li>He is often described as the first pure mathematician. </li></ul><ul><li>Around 535 BCE, Pythagoras journeyed to Egypt to learn more about mathematics and astronomy </li></ul>
  3. 3. History of Pythagoras (cont.) <ul><li>Pythagoras founded a philosophical and religious school/society in Croton (now spelled Crotone, in southern Italy) </li></ul><ul><li>His followers were commonly referred to as Pythagoreans. </li></ul><ul><li>The members of the inner circle of the society were called the “mathematikoi” </li></ul><ul><li>The members of the society followed a strict code which held them to being vegetarians and have no personal possessions </li></ul>
  4. 4. History of Pythagoras (cont.) <ul><li>There is not much evidence of Pythagoras and his society’s work because they were so secretive and kept no records </li></ul><ul><li>One major belief was that all things in nature and all relations could be reduced to number relations </li></ul>
  5. 5. Pythagoras and Music <ul><li>Pythagoras made important developments in music and astronomy </li></ul><ul><li>Observing that plucked strings of different lengths gave off different tones, he came up with the musical scale still used today. </li></ul><ul><li>Was an accomplished musician at playing the lyre </li></ul>
  6. 6. Pythagoras and Math <ul><li>Pythagoras made many contributions to the world of math including: </li></ul><ul><ul><li>Studies with even/odd numbers </li></ul></ul><ul><ul><li>Studies involving Perfect and Prime Numbers </li></ul></ul><ul><ul><li>Irrational Numbers </li></ul></ul><ul><ul><li>Various theorems/ideas about triangles, parallel lines, circles, etc. </li></ul></ul><ul><ul><li>Of course THE PYTHAGOREAN THEOREM </li></ul></ul>
  7. 7. The Theorem: <ul><li>The square of the hypotenuse of a right triangle is equal to the sum of the squares of the other 2 sides (legs) </li></ul><ul><li>a 2 + b 2 = c 2 </li></ul><ul><li>But what does it mean??? </li></ul>
  8. 8. Pythagorean Theorem
  9. 9. It’s Uses <ul><li>Determine side length of triangles </li></ul><ul><li>Height, distance of objects </li></ul><ul><ul><li>The Distance Formula </li></ul></ul><ul><li>Range finding </li></ul>
  10. 10. Real World Uses <ul><li>Architecture, Engineering, Surveying </li></ul><ul><li>CAD (Computer Aided Drafting) </li></ul><ul><li>Military Applications </li></ul><ul><li>Cartography (Map-Making/Directions) </li></ul>
  11. 11. Example Problems (1 of 2) <ul><li>Find the measure of C in the triangle above: </li></ul><ul><ul><li>a 2 + b 2 = c 2 </li></ul></ul><ul><ul><li>6 2 + 8 2 = C 2 </li></ul></ul><ul><ul><li>36 + 64 = C 2 </li></ul></ul><ul><ul><li>100 = C 2 </li></ul></ul><ul><ul><li> 100 =  C 2 so 10 = C </li></ul></ul>
  12. 12. Example Problems (2 of 2) <ul><li>Find the measure of C in the triangle above: </li></ul><ul><ul><li>a 2 + b 2 = c 2 </li></ul></ul><ul><ul><li>5 2 + 12 2 = C 2 </li></ul></ul><ul><ul><li>* 25 + 144 = C 2 </li></ul></ul>* 169 = C 2 *  169 =  C 2 so 13 = C

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