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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...

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...

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