Some Hexagon Area Ratios: Problem Solving by Related Example
Michael D. de Villiers · 2010
Have you seen it before? Or have you seen the same problem in a slightly different form? Do you know a related problem? Do you know a theorem that could be useful? Look at the unknown! And try to think of a familiar problem having the same or a similar unknown. Here is a problem related to yours and solved before. Could you use it? Could you use its result? Could you use its method? George Polya (1945) As starters, I would like to strongly encourage the reader to try to prove each of the three conjectures in this article before looking at my solutions as some readers may very well find even shorter, more elegant proofs than those give here. However, if the reader is not successful in finding a proof, s/he is likely to benefit far more from reading further than someone who hasn’t tried at all. Conjecture