Following completion of your readings, complete the exercise 4 in the “Projects”
ID: 2942007 • Letter: F
Question
Following completion of your readings, complete the exercise 4 in the “Projects” section on page 522 of Mathematics in Our World.Make sure you build or generate at least five more Pythagorean Triples using one of the many formulas available online for doing this.
After building your triples, verify each of them in the Pythagorean Theorem equation.
The assignment must include (a) all math work required to answer the problems as well as (b) introduction and conclusion paragraphs.
Your introduction should include three to five sentences of general information about the topic at hand.
The body must contain a restatement of the problems and all math work, including the steps and formulas used to solve the problems.
Your conclusion must comprise a summary of the problems and the reason you selected a particular method to solve them. It would also be appropriate to include a statement as to what you learned and how you will apply the knowledge gained in this exercise to real-world situations.
Explanation / Answer
I remember in 10th grade hearing that integer right triangles were pretty rare, but then more recently, I played with them a little and found out that every integer greater than two is the short leg of an integer right triangle, albeit a very skinny one. Needless to say, I was pretty mad at Mr. Emmons for keeping this from us. Of course, I was not one of the first people to discover this. This method misses triplets, but each shape is different and there are an infinite number of them. long leg n, hypotenuse (n+1) gives all odd integers > 1 as short legs n^2 + 2n + 1 is hypotenuse squared, n^2 is long side squared. Difference is 2n +1. So, say 11 is the short leg, 121 = 2n +1, n = 60 11, 60, 61 is a right triangle next odd triangle 13 is short leg. 169 = 2n +1, n = 168 13, 84, 85 is a right triangle (3, 4, 5; 5, 12, 13; 7, 24, 25 9, 40, 41 . . . )