# Dissecting a Regular Triangle into Three Similar Tiles

Dissecting a Regular Triangle into Three Similar Tiles

Two figures are called similar if they have the same shape; they may have different sizes.

This Demonstration presents solutions to three closely connected dissection problems, one of them trivial, one of them easy, and one of them difficult. The problem is to cut a regular triangle into three similar pieces.

If the tiles can all be the same size, then there are many solutions (challenge 1).

If the tiles must all be different sizes, then there is one solution (challenge 2).

If two of the three tiles must be the same size, the solution is a polyiamond (challenge 3).

There is also a fractal solution to the mixed case.