Dissection Puzzle

 

Dissection of an equilateral triangle into four pieces which can be rearranged into a square (Dudeney)

Introduction

A geometric dissection is like cutting a shape into a few smaller pieces, and then you can put them back together to make something completely different, but still the same size!  For instance, in the 2D example above, an equilateral triangle is split into four pieces, which you can then rearrange to form a square.  There are several wonderful books discussing this topic, and this book is a great place to start.  Geometric dissections have been around for over two thousand years, used by Greek and Arabic-Islamic mathematicians to prove things and show off their skills in visual geometry, like proving the Pythagorean theorem. Plus, they are super popular in fun math games like Tangram and dissection puzzles (also called transformation puzzle) where you try to put a set of pieces together into two or more different shapes. This post is all about dissection puzzles.

There are lots of dissection puzzles out there,  like letter puzzle E,  letter puzzle Z, squaring 2 crosses, square to decagon. But I wanted to dive into geometric dissection techniques and see if I could come up with some new and exciting puzzles. Let me know how I’m doing!

What puzzles are you offering?

• TW (Triangle-W) puzzle - a seven-piece puzzle that requires you to fill a triangle and a W pentomino shape
• HL (Hexagon-L) puzzle - a seven-piece puzzle that requires you to fill a hexagon and a L pentomo shape
• P&P puzzle - also a seven-piece puzzle with a pentagon frame and a P pentomino frame.