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Pythagorean Triples And Theorem Equation Essay

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Pythagorean Triples and Theorem Equation
Constance Hall Lindemann
Survey of Mathematical Methods
Instructor: David Gualco
January 20, 2012

The Pythagorean Theorem comprises a right triangle, its hypotenuse c and other two sides a   and b. within this paper I will provide several examples of and describe the steps taken to find Pythagorean Triples and using the examples found in the text on page 559 item 10-9. To understand Pythagorean Triples you must first recognize that this is expressed as a^2 + b^2 = c^2 within math circle.
What is the Pythagorean Theorem?
The Pythagorean Theorem comprises a right triangle, its hypotenuse c and other two sides a   and b.   It then has a right triangle, an triangle which has a one 90-degree angle. An example of an right angle could be seen as the corner of a piece of paper. The hypotenuse will be the longest side of the triangle. β€œThe Pythagorean Theorem states that the square of the hypotenuse in right triangle is equal to the sum of the squares of the other two sides. This is expressed as a^2 + b^2 = c^2.” (Weisstien, 2011)
13
40
Pythagorean triangles are right triangles in which all three sides are integers. A Pythagorean triple is a triple of positive integers a, b and c such that a right triangle exists with legs a, b and c hypotenuse. An example would be:
95
5
5

41
12

5, 12, 13 9, 40, 41
52 + 122 = 132 92 + 402 = 412
25 + 144 = 169 81 + 1600 = 1681

By using the Pythagorean Theorem, you need to find the equivalent for finding positive integers a, b and c satisfying a2 + b2 = c2.
The smallest and best-known Pythagorean triple is (a, b, c) = (3, 4, 5). The right triangle having these side lengths is sometimes called the 3, 4, 5 triangle.
Who was Pythagoras?
Pythagoras was a Greek mathematician and philosopher, in the sixth century B.C.,   Pythagoras created the Pythagorean Theorem, which is used in geometry, this theorem is important when working with right triangles....

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