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.