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Pythagorean Theorem By Luis Arenas Arnold Gonzalez Jesus Morales
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What are we going to talk about? <ul><li>We are going to talk about the Pythagorean Theorem and some problems about it. The formulas that he used to figure out distance. We also going to talk about Pythagoras life. </li></ul><ul><li>Also to prove his innocents </li></ul>
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Pythagoras Life <ul><li>He was born on the island of Samos in 568BC. </li></ul><ul><li>He studied for 3 years temples of tyre Sidon and Byblos. </li></ul><ul><li>He study some time on Egypt where he learn geometric principles. </li></ul><ul><li>He died 475BC he was 99 years old when he died on Metapontus. </li></ul><ul><li>He lived 4 years on Metapontus before he died. </li></ul><ul><li>He discovered the Pythagorean theorem in 500B.C </li></ul>
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Problem <ul><li>When a 70foot ship tosses an anchor and the anchor lands 30ft away from the ship how long will the anchors chain be? </li></ul><ul><li>70^2+30^2=C^2 </li></ul><ul><li>4900+900=C^2 </li></ul><ul><li>5800=C^2 </li></ul><ul><li>Sqrt of 5800=C^2 </li></ul><ul><li>76.16=C </li></ul>70ft 30ft
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Problem 2 <ul><li>1. If a ramp that is 40 feet high is put up perpendicular to a tree, and the base length of the ramp is 10 feet. How high will the ramp be? </li></ul><ul><li>10^2 + h^2= 40^2 </li></ul><ul><li>100 + h^2= 1600 </li></ul><ul><li>h^2= 1600-100 </li></ul><ul><li>h^2= 1500 </li></ul><ul><li>Sqrt of 1500 </li></ul><ul><li>h= 38.72 </li></ul>40ft 10ft
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Our proof For our proof you start off with a Regular right angle then you get 3 more triangles and rotate them 90o, 180o, and 270o which looks like this. Each has area ab/2
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Our Proof Pythagorean theorem c^2=a^2+b^2 The square has a square hole with the side a – b, Summing up its area (a - b)2. The area of the four triangles ½ ab * 4 Which when you get to this step you foil an solve (a – b)(a – b) + 2ab Which gives you c^2=a^2 –ab –ab + b^2 + 2ab Then you combine like terms c^2=a^2 -2ab + b^2 + 2ab c^2=a^2 + b^2 Which proves that the Pythagorean theorem does work. C B A
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First Problem A A B C 15 15 Find the Hypotenuse of letter C To find the Hypotenuse you multiply 15 x Sqrt of 2 =21.21
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Second Problem <ul><li>In order to find the length of C you need to use the Pythagorean Theorem which is A^2 + B^2 = C^2. </li></ul><ul><li>First you multiply 15 x 15 = 225 and 20 x 20 = 400. </li></ul><ul><li>Then you add them up 225 + 400 = 625. </li></ul><ul><li>Finally you used the square root. </li></ul><ul><li>Sqrt of 625 = 25 </li></ul>20 15 A B C
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Conclusion Our conclusion is that Pythagoras should be innocent because he did a lot of great things in his life. He found a theorem that is named after his name. which is A^2 + B^2 =C^2 or the Pythagorean theorem. He opened three different schools in different countries. Which he helped a lot of people to learn. So young people could learn about his theorem. He’s work was great and a lot of people admired his work and thought it was a really great job. His work today is helping us learn about his theorem. He learned geometric principles in Egypt and that is how he got his theorem. He left to Metapontum because of a plot against him and his followers by a guy named Cylon. He died in Metapontum in the age of 90.
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