Carly Ayers
MAT126: Survey of Mathematical Methods
Professor Colleen Radke
November 5, 2012
Pythagorean Triples
very much described as the first pure mathematician, Pythagoras of Samos was a pre-Socratic classical philosopher, who founded, perhaps, one of the most important mathematical theorems, although, he dual-lane no written historical documents. The Pythagorean Theorem, a congenator among the sides of a beneficial triangle, states: The area of the square built upon the hypotenuse of a right triangle is equal to the sum of the areas of the squares upon the remaining sides (Morris, 1997). The theorem uses the compare x2 + y2 = z2, where the exponent, z, represents the length of the hypotenuse, and the exponents, a and b, represent the lengths of the former(a) sides of a right triangle. A Pythagorean triple is an ordered triple (x, y, z) of trine positive integers such that x2 + y2 = z2. If x, y, and z are relatively prime, wherefore the triple is called primitive (Rowland, 2011, Theorem 1). As our assignment this week states (Bluman, 2011, p. 620, project 4), one ex ample of a Pythagorean triple is 3, 4, and 5, because 32 + 42 = 52 which reads 9 + 16 = 25 when solved. This is the same with the numbers 5, 12, and 13, because 52 + 122 = 132 which reads 25 + 144 = 169 when solved.
In this assignment, we go forth test one set of formulas which will generate an absolute number of Pythagorean triples, all the while showing examples of other Pythagorean triples.
One set of formulas is noted by Amar Kumar Mohapatra and Nupur Prakash, of the Guru Gobind Singh Indraprastha University of Delhi, India, in their written work, A generalized formula to determine Pythagorean triples. Pythagoras himself has provided a formula for infinitely many triples, namely, x = 2n + 1, y = 2n2 + 2n and z = 2n2 + 2n + 1, where n is an arbitrary positive integer (Mohapatra & Prakash, 2010). We can now test the formula using the sure three numbers listed in the instructions of...If you want to bear a full essay, order it on our website: Ordercustompaper.com
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