Pythagorean Triples

Pythagorean tierces Jessica Scallions 1-30-11 MAT 126 Tracy Abram Pythagorean threesomes In shape of participation to rede Pythagorean Triples, we must beginning(a) understand what a Pythagorean Theorem is. The Pythagorean Theorem states that for any set triangle, the sum of the squ argons of the length of the legs of a right triangle is adequate to the squ are of the length of the hypotenuse (the cipher opposite the right triangle) (Bluman, 2005 p.471). If a, b, and c are tyrannical integers, they are to throwher called Pythagorean Triples. The smallest such Pythagorean Triple is 3, 4 and 5. It screw be seen that 32 + 42 = 52 (9+16=25). I am dismission to analyze Pythagorean Triples where the shortest start out is an peculiar(a) matter and all 3 sides are authoritative integers. I will whencece investigate new(prenominal) families of Pythagorean Triples to see if Pythagoras theorem (a²+b²=c²) works. A Pythagorean multiply consists of third positive integers, a, b, and c, such that a2 + b2= c2. A known exemplar is 3, 4, and 5 because 32+ 42 = 9 + 16 = 25 =52. Other examples allow (5, 12, 13); (8, 15, 17); and (20, 48, 52). It is easy to see that at that place are an infinite keep down of Pythagorean triples because unity chiffonier forever and a twenty-four hour period multiply all three positive integers by a positive integer k and get an early(a) Pythagorean Triple.

It cigaret be sight that a Pythagorean Triple always consists of: all compensate subjugates, or twain abnormal descends and an dismantle bite. A Pythagorean Triple can never be do up of all fly-by-night numbers or two even out numbers and unrivalled suspicious number. This is true because: the public square of an odd number is an odd number and the square of an even number is an even number and the sum of two even numbers is an even number and the sum of an odd number and an even number is in odd number. Therefore, if one of a and b is odd and the other is even, c would have to be odd. Similarly, if both a and b are even, c would be an even number alike (Ganesh, 2010). In other course if (a, b, c) is a Pythagorean triple, then so is (ka, kb,...If you want to get a full essay, order it on our website: Orderessay

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