PYTHAGOREAN THEOREM More than 4000 years ago‚ the Babyloneans and the Chinese already knew that a triangle with the sides of 3‚ 4 and 5 must be a right triangle. They used this knowledge to construct right angles. By dividing a string into twelve equal pieces and then laying it into a triangle so that one side is three‚ the second side four and the last side five sections long‚ they could easily construct a right angle. A Greek scholar named Pythagoras‚ who lived around 500 BC‚ was also fascinated
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Open DocumentThe assignment for the week is on page 371 number 98. We will be using Pythagorean Theorem‚ quadratic‚ zero factor‚ and compound equation‚ to solve this equation. We will explain step by step to solve how many paces to reach Castle Rock for Ahmed and Vanessa had to accomplish to meet there goal. Ahmed has half of a treasure map‚ which indicates that the treasure is buried in the desert 2x + 6 paces from Castle Rock. Vanessa has the other half of the map. Her half indicates that to find the treasure
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Open DocumentIn mathematics‚ the Pythagorean theorem — or Pythagoras’ theorem — is a relation in Euclidean geometry among the three sides of a right triangle (right-angled triangle). In terms of areas‚ it states: In any right-angled triangle‚ the area of the square whose side is the hypotenuse (the side opposite the right angle) is equal to the sum of the areas of the squares whose sides are the two legs (the two sides that meet at a right angle). The theorem can be written as an equation relating the lengths
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Open DocumentPythagorean Theorem Diana Lorance MAT126 Dan Urbanski March 3‚ 2013 Pythagorean Theorem In this paper we are going to look at a problem that can be seen in the “Projects” section on page 620 of the Math in our World text. The problem discusses Pythagorean triples and asks if you can find more Pythagorean triples than the two that are listed which are (3‚4‚ and 5) and (5‚12‚ and 13) (Bluman‚ 2012). The Pythagorean theorem states that for any right triangle‚ the sum of the squares of the length
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Open DocumentA Brief History of the Pythagorean Theorem Just Who Was This Pythagoras‚ Anyway? Pythagoras (569-500 B.C.E.) was born on the island of Samos in Greece‚ and did much traveling through Egypt‚ learning‚ among other things‚ mathematics. Not much more is known of his early years. Pythagoras gained his famous status by founding a group‚ the Brotherhood of Pythagoreans‚ which was devoted to the study of mathematics. The group was almost cult-like in that it had symbols‚ rituals and prayers. In addition
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Open DocumentTHE WIZARD OF OZ 2 The Wizard of Oz Scarecrow’s Speech on Pythagorean Theorem The Pythagorean theorem is one of the earliest theorems known to ancient civilization. The well-known theorem is named after the Greek mathematician and philosopher‚ Pythagoras. In the Wizard of Oz‚ after the Scarecrow gets a brain‚ he states the Pythagorean theorem. However‚ he mistakenly says it applies to an isosceles triangle when it applies to a right triangle. He not only says the wrong triangle
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Open Documentmathematics that developed from simple measurements. A theorem is the most important result in all of elementary mathematics. It was the motivation for a wealth of advanced mathematics‚ such as Fermat’s Last Theorem and the theory of Hilbert space. The Pythagorean Theorem asserts that for a right triangle‚ the square of the hypotenuse is equal to the sum of the squares of the other two sides. There are many ways to prove the Pythagorean Theorem. A particularly simple one is the scaling relationship
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Open DocumentIn mathematics‚ the Pythagorean Theorem — or Pythagoras’ theorem — is a relation in Euclidean geometry among the three sides of a right triangle (right-angled triangle). In terms of areas‚ it states: In any right-angled triangle‚ the area of the square whose side is the hypotenuse (the side opposite the right angle) is equal to the sum of the areas of the squares whose sides are the two legs (the two sides that meet at a right angle). The theorem can be written as an equation relating the lengths
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Open Document4.14 TRIANGLES Triangles are three-sided shapes that lie in one plane. Triangles are a type of polygons. The sum of all the angles in any triangle is 180º. Triangles can be classified according to the size of its angles. Some examples are : Acute Triangles An acute triangle is a triangle whose angles are all acute (i.e. less than 90°). In the acute triangle shown below‚ a‚ b and c are all acute angles. Sample Problem 1: A triangle has angles 46º‚ 63º and 71º. What type of triangle is this? Answer:
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Open DocumentPythagorean Theorem: Some False Proofs Even smart people make mistakes. Some mistakes are getting published and thus live for posterity to learn from. I ’ll list below some fallacious proofs of the Pythagorean theorem that I came across. Some times the errors are subtle and involve circular reasoning or fact misinterpretation. On occasion‚ a glaring error is committed in logic and leaves one wondering how it could have avoided being noticed by the authors and editors. Proof 1 One such error appears
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