# 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)