What Triangles Are in the Triangle?
What Triangles Are in the Triangle?
Consider the triangular grid formed by dividing one equilateral triangle into a grid of equilateral subtriangles in such a way that there are in the base. We want to know which and how many subtriangles there are within this grid. It is a very interesting exercise, involving discrete mathematics tools, to derive the formula for the total number, which is .
n
4+10+4n-1+16
3
n
2
n
n
(-1)