BC: The End | Thank you for reading about Pythagoras and Pythagorean | http://0.tqn.com/d/space/1/0/G/i/pythagoras_7.jpg http://www.mathguide.com/lessons/pic-pythagorasT.gif http://www.frontiernet.net/~imaging/pythag_triangle.gif http://upload.wikimedia.org/wikipedia/commons/thumb/9/91/Illustration_to_Euclid's_proof_of_the_Pythagorean_theorem3.PNG/220px-Illustration_to_Euclid's_proof_of_the_Pythagorean_theorem3.PNG http://jwilson.coe.uga.edu/emt669/student.folders/morris.stephanie/emt.669/essay.1/image10.gif
FC: By Erica Kohr | Pythagoras and the Pythagorean Theorem
1: Pythagoras Biography: - Greek Mathematician -Learned in Egypt and Babylon -Many mythical legends about him | - Known for his religious practice -Not necessarily an active mathematician -Had a following of people called Pythagorean Brotherhood
2: Pythagorean Theorem -The formula is: a^2 + b^2 = c^2 a and b are the two shorter sides of a right triangle while c is the longest side (called the hypotenuse) Example: when a= 3 b=4 and c=5 a^2 + b^2= 3^2 + 4^2= 9 + 16= 25+ 5^2
3: Avoid using algebra: Rearrange the four triangles to get the same square of side a+b but now the triangles have been moved together into two rectangles. The remaining area is two squares, one of side a and one of b. In the first figure it is c^2 plus the triangles and in the second figure is a^2 + b^2 plus the four triangles.
4: This is an example of Euclid's proof of the Pythagorean Theorem | He dropped a perpendicular from the upper vertex of the right triangle, splitting the bottom into two pieces. Using basic facts about triangles and parallelograms, each piece of the bottom square is equal to the corresponding smaller square.
5: Conclusion: - Greek Mathematician -Learned in Egypt and Babylon -a^2 + b^2 = c^2 -Using geometry proofs to use the theorum -Euclid proofs