Pythagorean triples Essay Example | Topics and Well Written Essays - 500 words

Pythagorean three-base hits - act ExampleThe most popular example of which is the 3-4-5 triangle, the triple which, according to Knott (2009), was known to the Babylonians since way back 5,000 old age and was possibly used as a basis in making true right angles in ancient building construction.Then again, the 3-4-5 triangle is just one of the infinitely mevery Pythagorean Triples, and approximation you, there argon various ways of generating such triples. One is, given two integers n and m, where n m, then sides a, b and c are define as n2- m2, 2nm and n2+ m2, respectively, following a simple confirmation (Bogomolny 2009)Taking for instance the triple 8-15-17, which is generated by taking n = 4 and m = 1, then a = n2- m2 = 42 - 12 = 16 - 1 = 15 b = 2mn = 2(1)(4) = 8, and c = n2+ m2 = 42 + 12 = 16 + 1 = 17. Another example is 7-24-25, which can be verified employ n = 4 and m = 3. Such triples are examples of Primitive Pythagorean Triples, or those triples that are not multiples of some other and are found using the n-m formula (Knott 2009). Other Pythagorean Triples can be found using a variety of methods as presented by Bogomolny (2009) and Knott (2009), some of which arec) by Two-fractions methodchoose any two fractions whose product is 2, add 2 to each fraction, then cross multiply, getting the two shorter sides of the triple 4/2, 2/2 8/2, 6/2 16, 12 162 + 122 = 202, andTo sum it up, there are infinitely many Pythagorean Triples existing. But one thing is for sure, a variety of techniques are purchasable that will serve useful in generating patterns among such triples. Hence, if you cannot list them all, be familiar of their patterns at least.Knott, R. (2009). Pythagorean Triangles and Triples. Retrieved November 20, 2009, from The University of Surrey, Mathematics Web site