The Pythagorean theorem

1. The Pythagorean theorem

2. A Little History • Pythagoras (569-500 B.C.) was born on an island named Samos in Greece. • Pythagoras did a lot of traveling (mostly in Egypt) learning mathematics, among other things. • Founded The Brotherhood of Pythagoreans. A foundation for studying mathematics. Pythagorean History. (n.d.). The Geometry Center Welcome Page. Retrieved December 3, 2012, from http://www.geom.uiuc.edu/~demo5337/Group3/hist.html

3. History • Legend has it that after completing the theorem, Pythagoras sacrificed 100 oxen. • It is impossible to tell if Pythagoras is the actual author. • The Brotherhood of Pythagoreans wrote many other Geometric proofs, and it is impossible to know who wrote what. • The Pythagoreans kept their findings secret. • This lead to the discovery of irrational numbers being postponed by 200 years. The Pythagoreans had discovered irrational numbers, but they kept it secret.

4. Formula a^2 + b^2 = c^2

5. Parts of the Right Triangle The hypotenuse is the longest of the three sides and it is directly across from the 90-degree angle, which is shown in this picture by a square in the 90-degree angle.

6. Step 1: • Figure out what the missing piece of information is. In this picture one side length is equal to 15cm and another is equal to 12cm. The Hypotenuse is labeled as “c” and there is no value given. This means you have to solve for c. 15cm 12cm

7. Step 2: Plug in the information 15^2 + 12^2 = c^2 • This is where you take the information given and begin to solve for the missing variable.

8. Step 3:Combine like terms. 15^2 + 12^2 = c^2 225 + 144 = c^2 369 = c^2 • After you plug in the information you know you have to combine like terms and solve for the missing variable.

9. Step 4: Solve for the Variable 369 = c^2 √(369) = √(c^2) 19.2 = c • Once you have it down to a number equaling a variable squared, you have to take the square root of both sides.