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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The 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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In 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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Pythagorean 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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A 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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THE 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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mathematics 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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In 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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4.14 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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Pythagorean 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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Farhrenheit = 1.8 x (Celsius) + 32 8. The Pythagorean Theorem states that the sum of the squares of the sides of a right triangle is equal to the square of the hypotenuse. For example‚ if two sides of a right triangle have lengths 3 and 4‚ then the hypotenuse must have a length of 5. The integers 3‚ 4‚ and 5 together form a Pythagorean triple. There is an infinite number of such triples. Given two positive integers‚ m and n‚ where m > n‚ a Pythagorean triple can be generated by the following formulas:
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How We Use the Pythagorean Theorem in Everyday Life First‚ let’s discuss the inventor of the theorem before how we use it. Pythagoras of Samos is a very odd fellow but is very well known despite not have written anything in his lifetime so what we know about him comes from Historians and Philosophers. Though we know he was a Greek philosopher and mathematician mainly known for the Pythagorean Theorem that we all learned in 6th grade. (a2 + b2 = c2). His theorem states that that the square of
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Pythagorean Triples To begin you must understand the Pythagoras theorem is an equation of a2 + b2 = c2. This simply means that the sum of the areas of the two squares formed along the two small sides of a right angled triangle equals the area of the square formed along the longest. Let a‚ b‚ and c be the three sides of a right angled triangle. To define‚ a right angled triangle is a triangle in which any one of the angles is equal to 90 degrees. The longest side of the right angled triangle
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Pythagorean Triples Tammie Strohl MAT 126 David Gualco November 9‚ 2009 Pythagorean Triples Pythagorean Theorem states that the sum of the areas of the two squares formed along the two small sides of a right angled triangle equals the area of the square formed along the longest. ￼ If a‚ b‚ and c are positive integers‚ they are together called Pythagorean Triples. The smallest such Pythagorean Triple is 3‚ 4 and 5. It can be seen that 32 + 42 = 52 (9+16=25). Here are some examples:
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Pythagorean Quadratic Member MAT 222 Introduction to Algebra Instructor Yvette Gonzalez-Smith August 04‚ 2013 Pythagorean Quadratic The Pythagorean Theorem is an equation that allows a person to find the length of a side of a right triangle‚ as long as the length of the other two sides is known. The theorem basically relates the lengths of three sides of any right triangle. The theorem states that the square of the hypotenuse is the sum of the squares of the legs
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Pythagorean Quadratic MAT 221: Introduction to Algebra Pythagorean Quadratic The Pythagorean Theorem was termed after Pythagoras‚ who was a well-known Greek philosopher and mathematician‚ and the Pythagorean Theorem is one of the first theorems identified in ancient civilizations. “The Pythagorean theorem says that in any right triangle the sum of the squares of the lengths of the legs is equal to the square of the length of the hypotenuse” (Dugopolski‚ 2012‚ p. 366 para. 8). For this reason
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Pythagorean Triples Ashley Walker MAT126 Bridget Simmons November 28‚ 2011 A Pythagorean triple is a triple of positive integers a‚ b‚ and c such that a right triangle exists with legs a‚ b‚ and hypotenuse c (Bluman‚ 2005). A Pythagorean triple is a triple of positive integers (a‚ b‚ c) where a2 + b2 = c2. A triple is simply a right triangle whose sides are positive integers. An easy way to generate Pythagorean triples is to multiply any known Pythagorean triple by an integer (any integer)
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Fermat’s last theorem Currently holding the world record for longest standing math problem ever‚ Fermat’s last theorem went unsolved for 365 years. Fermat’s last theorem was one of the largest white whales in the study of math. Over the centuries‚ thousands were puzzled by the impossible problem. From its conception to its solution‚ Fermat’s last theorem was one of the most difficult to solve yet easy to understand problems in mathematics. First‚ I will discuss the theorem and how it was introduced
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Print 2.7.4 Practice: Modeling: Similarity Theorems Practice Assignment Geometry Sem 1 (S2758702) Points possible: 20 Date: ____________ YOUR ASSIGNMENT: About Face! Your Peak of Choice Your friend Tyler is preparing to climb a rock face and wants to figure out how far he will need to climb to reach one of three different peaks. You remember a trick you can use to help him out. You realize that if you place a small mirror on the ground and move it to where Tyler
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LAST THEOREM I am going to do my project in the field of number theory. Number theory‚ a subject with a long and rich history‚ has become increasingly important because of its application to computer science and cryptography. The core topics of number theory are such as divisibility‚ highest common factor‚ primes‚ factorization‚ Diophantine equations and so on‚ among which I chose Diophantine equations as the specific topic I would like to go deep into. Fermat ’s Last Theorem states
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