## mat 126 week 4 rewritten

Name

Math 126 Survey of Mathematical Methods

Pythagorean Triple

Instructor

Date

When we began to deal with Pythagorean Triples it can be very hard and difficult in doing any kind of mathematics problems. When we first starting this class and saw that it involve doing Pythagorean Triples knew it was going to be a challenge. When we deal with using formula you must know how to use them in the proper order and make sure you are using the correct one as well. If we can do that then we can be good at doing the problems as well as use the formulas later on.

Name

Math 126 Survey of Mathematical Methods

Pythagorean Triple

Instructor

Date

When we began to deal with Pythagorean Triples it can be very hard and difficult in doing any kind of mathematics problems. When we first starting this class and saw that it involve doing Pythagorean Triples knew it was going to be a challenge. When we deal with using formula you must know how to use them in the proper order and make sure you are using the correct one as well. If we can do that then we can be good at doing the problems as well as use the formulas later on.

A Pythagorean triple is simply a right triangle whose sides are positive integers. After reviewing here’s the way to generate Pythagorean Triples is to multiply any known Pythagorean Triple by an integer (any integer). Sides of a known triple: 3,4,5 Multiply by 2 = 6,8,10

Verification: 6² + 8² = 10² = 100 Multiply by 3 = 9,12,15 verification: 9² + 12² = 15² = 225 Multiply by 4 = 12,16,20

verification: 12² + 16² = 20² = 400 Sides of a known triple: 5,12,13 Multiply by 2 = 10,24,26 verification: 10² + 24² = 26² = 676 Multiply by 3 = 15,36,39 verification: 15² + 36² = 39² = 1521 Multiply by 4 = 20,48,52 verification: 20² + 48² = 52² = 2704 Sides of a known triple: 7,24,25 Multiply by 2 = 14,48,50 verification: 14² + 48² = 50² = 2500 Multiply by 3 = 21,72,75 verification: 21² + 72² = 75² = 5625 Multiply by 4 = 28,96,100 verification: 28² + 96² = 100² = 10000 In addition, there are many formulas A Pythagorean Triple (a² + b² = c²) can be calculated using the following method: By choosing any tow integers: x and y. y must be greater than x. The sides of a new Pythagorean Triple are: a = 2*x*y, b = y² – x², and c = y² + x² for example, let x = 5 and y = 6 a = 2*x*y = 2*5*6 = 60 b = y² – x² = 6² – 5² = 36 – 25 = 11 c = y² + x² = 6² + 5² = 36 + 25 = 61 the sides of the new Pythagorean Triple are: 60,11,61 verification: 60² + 11² = 61² = 3721 Here’s how I calculate a possible Pythagorean…