# Integer Triangles

It’s a sample chapter from MATHEMATICS GALORE!, published by the MAA in 2012.
( Check out the book here!)

Enjoy the mathematics of triangles with integer side-lengths and see the proof developed by high-school students establishing that the number of integer triangles with perimeter N is N*N/48 rounded to the its nearest integer if N even, and (N+3)(N+3)/48, again rounded, if N is odd.

For example: How many different triangles can you make with 20 toothpicks?
Answer: round(400/48) = round(8.333…) = 8. (This is the same count as the number you can make with just 17 toothpicks.)

• ## ON-LINE SHORT COURSES!

QUADRATICS, Permutations and Combinations, EXPLODING DOTS, and more!

Written for educators - and their students too! - this website, slowly growing, takes all the content Tanton has developed in his books, videos, and workshops, and organizes it into short, self-contained, and complete, curriculum units proving that mathematics, at all points of the school curriculum, can be joyous, fresh, innovative, rich, deep-thinking, and devoid of any rote doing! Let's teach generations of students to be self-reliant thinkers, willing to flail and to use their common sense to "nut their way" through challenges, to assess and judge results, and to adjust actions to find success. (Great life skills!)

CHECK OUT: www.gdaymath.com