## mat 126 rewritten by tonight

Pythagorean Triple by an integer (any integer).

Sides of a known triple: 3,4,5

Multiply by 2 = 6,8,10

Verification: 6 + 8 = 10 = 100

Multiply by 3 = 9,12,15

verification: 9 + 12 = 15 = 225

Multiply by 4 = 12,16,20

verification: 12 + 16 = 20 = 400

Sides of a known triple: 5,12,13

Multiply by 2 = 10,24,26

verification: 10 + 24 = 26 = 676

Multiply by 3 = 15,36,39

verification: 15 + 36 = 39 = 1521

Multiply by 4 = 20,48,52

verification: 20 + 48 = 52 = 2704

Sides of a known triple: 7,24,25

Multiply by 2 = 14,48,50

verification: 14 + 48 = 50 = 2500

Multiply by 3 = 21,72,75

verification: 21 + 72 = 75 = 5625

Multiply by 4 = 28,96,100

verification: 28 + 96 = 100 = 10000

In addition, there are many formulas

A Pythagorean Triple (a + b = c ) 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 = y – x , and c = y + x

for example, let x = 5 and y = 6

a = 2*x*y = 2*5*6 = 60

b = y – x = 6 – 5 = 36 25 = 11

c = y + x = 6 + 5 = 36 + 25 = 61

the sides of the new Pythagorean Triple are: 60,11,61

verification: 60 + 11 = 61 = 3721

Here s how I calculate a possible Pythagorean Triples, use the following formula:

a = 2*d*x*y

b = d*(y^2 – x^2)

c = d*(y^2 + x^2)

d = any positive integer

y > x > 0

x and y must be positive integers

x and y must be even, odd; or odd, even integers