Austria-Poland triangle decomposition
Source: Austria-Poland 2004, team competition, problem 8
February 15, 2005
geometrysimilar trianglescombinatorics unsolvedcombinatorics
Problem Statement
a.) Prove that for or each triangle can be decomposed in similar (not necessarily congruent) triangles.
b.) Show: An equilateral triangle can neither be composed in 3 nor 5 triangles.
c.) Is there a triangle which can be decomposed in 3 and 5 triangles, analogously to a.). Either give an example or prove that there is not such a triangle.