An Assignment on Pythagorean Triple

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An Assignment on Pythagorean Triple
Tamika Mays
MAT126: Survey of Mathematical Methods
Instructor Jody Tate
September 10, 2012

An Assignment on Pythagorean Triple
Anybody that has taken a Geometry class should know or remember the Pythagorean Theorem. Pythagorean Theorem is the statement that the sum of the area of the two small squares equals the area of the big one. In algebraic terms a2 + b2 = c2, where c is the hypotenuse and a and b are the legs of the triangle.
This week’s assignment required us to build or generate at least five Pythagorean Triples using one of the many formulas available online. In addition, after building the triples, we had to verify each of them in the Pythagorean Theorem equation.
A Pythagorean 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 any integer.
Sides of a known triple: 5, 12, 13
Multiply by 2 = 10, 24, 26
….verification: 10² + 24² = 26² = 676
100 + 576 = 676
676 = 676
Multiply by 3 = 15, 36, 39
….verification: 15² + 36² = 39² = 1521
225 + 1296 = 1521
1521 = 1521
Multiply by 4 = 20, 48, 52
….verification: 20² + 48² = 52² = 2704
400 + 2304 = 2704
2704 = 2704
Sides of a known triple: 7, 24, 25
Multiply by 2 = 14, 48, 50
….verification: 14² + 48² = 50² = 2500
196 + 2304 = 2500
2500 =2500
Multiply by 3 = 21, 72, 75
….verification: 21² + 72² = 75² = 5625
441 + 5184 = 5625
5625 = 5625
Multiply by 4 = 28, 96, 100
….verification: 28² + 96² = 100² = 10000
784 + 9216 = 10000
10000 = 10000
Sides of a known triple: 3, 4, 5
Multiply by 2 = 6,8,10
….verification: 6² + 8² = 10² = 100
36 + 64 = 100
100 = 100
Multiply by 3 = 9, 12, 15
….verification: 9² + 12² = 15² = 225
81 + 144 = 225
225 = 225
Multiply by 4 = 12, 16, 20
….verification: 12² + 16² = 20² = 400
144 + 256 = 400
400 =   400
To calculate all possible Pythagorean Triples, use the following...