MAT126: Survey of Mathematical Methods

Pythagorean Triples

Pythagorean Triples has centuries of history according to the many web sites I have viewed. Pythagorean Triples and can be understood easily if you have the right web site for explanation. To my understanding (3) whole numbers, as in 3-4-5 make up “the sum of the squares of the legs (the two shortest sides) of a right triangle is equal to the square of the hypotenuse (the longest side),” Ryan, M. (n.d.). The two smaller numbers are the 'a' and 'b' (doesn't matter which one is which, 3, 4 or 4, 3) and the biggest number (5) is the 'c'. I will examine two different ways to think about Pythagorean Triples and show examples of each.

First we have the basic first three eligible numbers which are {3, 4, 5} that qualify to be a Pythagorean Triple. From these numbers I can create a new Pythagorean Triple by just doubling the three numbers which gives us:

102 = 62 + 82

The second way we can obtain Pythagorean Triples uses three little simple formulas:

a = 2xy b = x2 - y2 c = x2 + y2

Choose any value for x and y that you like -- only let the x be larger than the y, to avoid a negative in the b formula. Observe:

Let x = 5 and y = 2. This produces

a = 2×5×2 b = 52 - 22 c = 52 + 22

= 20 = 25 - 4 = 25 + 4

= 21 = 29

For breakfast, cereal whether hot or cold, is usually an excellent high-quality selection. I chose Kellogg’s Rice Krispies, which is a good fat free choice. The mathematical formula I am using goes as follows:

Serving size is 1 ¼ cups (33g) of Kellogg’s Rice Krispies w/ ½ cup skim milk. Going by the nutrition facts on the box of Kellogg’s Rice Krispies there is zero grams of fat in the above measurements of the cereal w/the skim milk.

To figure out the fat content, the formula used is:

A serving contains 4 grams of fat; 33g of cereal is 1 and 4/29 of an oz. + ½ cup milk is 4oz.

Approx....