A classical puzzle in recreational math is to dissect a shape into pieces that can be rearranged into another shape. In this project you can turn an equilateral triangle into a square. If you cut out the pieces along the lines in the pattern you can rearrange them to form a square. In this case the rearrangement can be done by essentially turning the shape inside out. If you put hinges on three of the four places where the lines meet the edges of the triangle, the whole shape can be turned inside out while the hinges keep all the pieces connected.