# Week 4 Written Assignment Mat 126

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Kathryn McGuiness

Week 4 Assignment

MAT 126

Instructor Hammoud

September 10, 2012

The Pythagorean theorem was invented by Pythagoras. He was a Greek mathematician and philosopher, who lived in the 6th century BCE.

The formula for the Pythagorean theorem is: c^ = a^ + b^. The sum of the squares of length in a right triangle equals the sum of the hypotenuse, or opposite side of the right angle.

In this first example, here are the values of sides a, b and c:

a= 6

b= 8

6^ + 8^ = C^

36 + 64 = C^

The square of 100 = 10

C = 10.

Many other formulas for generating Pythagorean triples:

One method is: Choose any two positive integers. Let’s say they are s & t. Here is the triple:

{ 2st, s^-t^, s^ + t^ }

s = 5, t = 1.

2st = 10

s^ - t^ = 25. 1 = 24 and s^ + y^ = 25 + 1 = 26. The Pythagorean Triple is (10, 24, 26)

The answer is: 10^ + 24^ = 26^

100+576 = 676.

Another formula is: m & n need to be positive integers, and m >n.

A = m^ - n^

B = 2mn

C = m^ + n^

M = 8

N = 4

A = 8^ - 4^ = 64-16 = 48

B = 2 x 32 = 64

C = 64 + 16 = 80

Another formula is:

A = d *(m^-n^)

B= 2 * d * m * n

C = d * (m^2 + n^2)

D needs to be a positive integer, m > n, and the both have to be greater than 0.

Let m = 2, n = 1 and d = 1.

A = 1 * (4-1) = 3

B = 2 * 1 * 2 * 1 = 4

C = 1 * ( 8 + 2) = 10

References

http://www.emathemathics.net/trangrectangulo.php?

Bluman, Allan G. Mathematics in our World, McGraw-Hill