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The Pythagorean Thereom and THe life of Pythagoras

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1: The Pythagorean Theorem and The Life of Pythagoras | By: Michaela Bloom

2: The Pythagorean Theorem states that in a right triangle, the square of th length of the hypotenuse is equal to the sum of the squares of the lengths of the legs. | The Pythagorean Theorem

3: Formula: c= a + b | 2 | 2 | 2

4: Explanation: | The Pythagorean Theorem is used to find the hypotenuse of a right triangle. First, you have to find the length of the legs and square them. | EX: Legs: a- 5 cm b- 6 cm | Squared: a- 25 cm b- 36cm

5: Add the two squared measurements together and find the squared root of this number. This new number is the measurement of the hypotenuse. | EX: 25 cm +36 cm ----------- 61 cm | 61 squared is about 7.8. c = 7.8 cm

6: Real World Examples | 1. A scuba diver dove 14 feet below the surface. Then, he swam 16 feet toward a coral formation. How far is the diver form his boat? | 2. A softball diamond is a square measuring 60 feet on each side. How far does a player on second base throw when they throw from second to home.

7: 3. A company designed a public play area in the shape of the square. A path runs diagonal through the park. What is the measurement of the hypotenuse of the right triangle that is formed if the legs measure 14 feet and 12 feet. | Answers on next page.....

8: 1. The hypotenuse is 21.3 feet. 14 feet squared is 196, and 16 feet squared is 256 feet. Those, added together equals 452 feet squared, and the square root of 452 is about 21.3 feet. | 2. The hypotenuse is 84.9 feet. 60 feet squared is 3600 and, since both legs are 60, 3600 + 3600 is 7200. The square root of 7200 is about 84.9 feet. | 3. The hypotenuse is about 18.4 feet. 14 feet squared is 196, and 12 feet squared is 144 feet. 196 and 144 feet added together equals 340. the square root of 340 is about 18.4 feet.

9: Born: about 569 BC Died: about 475 BC As a young boy Pythagoras traveled with his father, Mnesarchus, who was a merchant from Tyre, He was well educated and was taught by three philosophers. Their names were Thales, Anaximander, and Pherekydes. In about 535 BC Pythagoras traveled to Egypt, as Thales had encouraged him to. He was accepted into the priesthood in Egypt. Soon after, Egypt was taken over by the Persians. He was taken as a prisoner to Babylon, but was set free. He stayed for a while and was: "Instructed in their sacred rites and learnt about a very mystical worship of the gods. He also reached the acme of perfection in arithmetic and music and the other mathematical taught by the Babylonians..." (Iamblichus) | A Short Biography of Pythagoras

10: Biography Continued... | He then returned to Samos, founded a school, then went to Italy and: "Tried to use his symbolic method of teaching which was similar in all respects to the lessons he had learnt in Egypt." (Iamblichus) He founded a philosophical and religious school in Croton. It became a Society with different beliefs and teachings. Some of the members went on to be philosophers. Most of his work is not known. But we do know that he had a great fascination for geometry. Although the Babylonians had known the Theorem over a thousand years before, but he was the first to prove it. He died in about 475 BC.

11: Test Yourself!

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