Pythagorean Triples

To begin you must understand the Pythagoras theorem is an equation of a2 + b2 = c2. This simply means that the sum of the areas of the two squares formed along the two small sides of a right-angled triangle equals the area of the square formed along the longest. Let a, b, and c be the three sides of a right-angled triangle. To define, a right-angled triangle is a triangle in which any one of the angles is equal to 90 degrees. The longest side of the right-angled triangle is called the ‘hypotenuse’.

Once you have this basic understanding you can apply the understanding that if a, b, and c are positive integers, they are called Pythagorean Triples. Our textbook explains that “the numbers 3, 4, and 5 are called Pythagorean triples since 32 + 42 = 52” (Bluman, pg. 522) and that there is a set of formulas that will generate an infinite number of Pythagorean triples.  The set of Pythagorean Triples is endless.

Let n be any integer greater than 1 as in this example which is a set of Pythagorean triple, is true because: (3n)2 + (4n)2 = (5n)2

Some other Pythagorean Triples are (5,12,13); (7,24,25); (8,15,17); (9,40,41); (17,144,145); and (25,312,313).

To summarize, it is fairly easy to show that no matter what numbers you use for n you can use this method to show that there are infinitely many Pythagorean Triples. Since the Pythagorean Theorem states that every right triangle has side lengths satisfying the formula a2 + b2 = c2; the Pythagorean triples describe the three integer side lengths of a right triangle.

References:

  1. Bluman, A. G. (2005). Mathematics in Our World (1st Ed. ) Ashford University, Custom Edition. New York: McGraw-Hill.
  2. Ganesh, J. (2010). Pythagorean Triples –Advanced. Retrieved on June 27, 2010 from http://www. mathsisfun. com/numbers/pythagorean-triples. html

Examples and Calculations:

  1. Protein Formula x/y * 100% = zx/y * 100% = z
  2. Dannon Greek Blueberry Yogurt 0*9=012*4=48 0/120 * 100% = 0%48/120*100% = 40%
  3. Kashi Wheat Cereal 1*9=96*4=24 9/190*100%= 4. 74%24/190*100%= 12. 6%
  4. Tostitos 7*9=632*4=8 63/140*100%= 45%8/140*100%= 5. 7%

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