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. “The 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)
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:
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....