math_week4_assignment

math_week4_assignment - Let us check (20, 21, 29) is a...

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Project # 4 Pythagorean triples are triples of the form (a, b, c) for which a^2 + b^2 = c^2. A formula that can be used to generate infinite number of generating Pythagorean triples is: a = (2mn); b= (m^2 - n^2); c= (m^2 + n^2) where m and n are positive integers and m > n. Let us develop five Pythagorean triples: For m = 4, n = 3 a = 2mn = 2*4*3 = 24 b= m^2 - n^2 = 4^2 – 3^2 = 7 c= m^2 + n^2 = 4^2 + 3^2 = 25 Let us check (24, 7, 25) is a Pythagorean triple or not by using Pythagorean Theorem a^2 + b^2 = 24^2 + 7^2 = 625 c^2 = 25^2 = 625 Since a^2 + b^2 = c^2 so (24, 7, 25) is a Pythagorean triple. For m = 4, n = 1 a = 2mn = 2*4*1 = 8 b= m^2 - n^2 = 4^2 – 1^2 = 15 c= m^2 + n^2 = 4^2 + 1^2 = 17 Let us check (8, 15, 17) is a Pythagorean triple or not by using Pythagorean Theorem a^2 + b^2 = 8^2 + 15^2 = 289 c^2 = 17^2 = 289 Since a^2 + b^2 = c^2 so (8, 15, 17) is a Pythagorean triple. If we take m = 5, n = 2 a = 2mn = 2*5*2 = 20 b= m^2 - n^2 = 5^2 – 2^2 = 25 - 4 = 21 c= m^2 + n^2 = 5^2 + 2^2 = 25 + 4 = 29
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Unformatted text preview: Let us check (20, 21, 29) is a Pythagorean triple or not by using Pythagorean Theorem a^2 + b^2 = 20^2 + 21^2 = 841 c^2 = 29^2 = 841 Since a^2 + b^2 = c^2 so (20, 21, 29) is a Pythagorean triple. If we take m = 5, n = 3 a = 2mn = 2*5*3 = 30 b= m^2 - n^2 = 5^2 3^2 = 16 c= m^2 + n^2 = 5^2 + 3^2 = 34 Let us check (30, 16, 34) is a Pythagorean triple or not by using Pythagorean Theorem a^2 + b^2 = 30^2 + 16^2 = 1156 c^2 = 34^2 = 1156 Since a^2 + b^2 = c^2 so (30, 16, 34) is a Pythagorean triple. If we take m = 6, n = 2 a = 2mn = 24 b= m^2 - n^2 = 6^2 2^2 = 32 c= m^2 + n^2 = 6^2 + 2^2 = 40 Let us check (24, 32, 40) is a Pythagorean triple or not by using Pythagorean Theorem a^2 + b^2 = 24^2 + 32^2 = 1600 c^2 = 40^2 = 1600 Since a^2 + b^2 = c^2 so (24, 32, 40) is a Pythagorean triple. Reference: Bluman, A. G. (2005). Mathematics in our world (Ashford University Custom Edition). United States: McGraw-Hill....
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This note was uploaded on 07/27/2011 for the course SCI 207 taught by Professor Blume during the Spring '10 term at Ashford University.

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math_week4_assignment - Let us check (20, 21, 29) is a...

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