Problem: Divide a polygon (other than a right triangle) into similar triangles that are not congruent and not right triangles. How can this be done?
Some triangles have sides . In terms of a value , they have power sides . If all sides are multiplied by , one gets the similar triangle . This is called a powered triangle (not to be confused with a power triangle, used for AC circuits). For the given problem, powered triangles can simplify the solution process.
When powered triangles fit perfectly around a vertex, they make a wheel graph. Sometimes these wheels can lead to solutions when more triangles are added. For example, wheel 5 based on with powers and additions gives a solution when is also added. If the original figure is a triangle, it cannot be similar to the component triangles.
Wheel 1 based on with powers and additions can have added to make a triangle, originally found by Andrzej Zak .