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Date Submitted: 09/18/2012 04:33 PM
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