Integer Triangles – and more! (Essay!)

With 11 matchsticks one can make four different triangles with integer sides: 5-5-1, 5-4-2, 5-3-3, 4-4-3. Surprisingly, this count goes down if you add one more matchstick to the mix. With 12 matchsticks one can only make THREE integer triangles: 5-5-2, 5-4-3 and 4-4-4.

In this essay we explore geometric figures with integer sidelengths and some of their curious properties, and also find an explicit formula for the number of different integer triangles one can make with N matchsticks.



    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!)


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