Wild About Math! Making Math fun and accessible

Is it a triangle or a square?

Purdue Professor of Computer Science Greg N. Fredrickson is an absolute master of geometric dissections, the art and science of cutting up one or more geometric shapes and rearranging the pieces to form other shapes.

One example from Fredrickson’s web-site for his first book, Dissections: Plane & Fancy, is the dissection of a regular octagon to a square using only five pieces! This is quite a feat.

Creating these dissections is closely related to the field of tessellations which studies how planes (flat surfaces) can be tiled with geometric shapes.

Fredrickson’s second book, Hinged Dissections: Swinging & Twisting, explores dissections in which the pieces of the figure being dissected are held together with imaginary hinges. When parts of the figure are rotated about the hinges another figure is formed. An extremely elegant dissection is that of an equilateral triangle to a square with only four pieces!

If you want to build your own triangle-to-square hinged model using foamed rubber check out these directions. Be sure to watch the fun animation at the bottom of the page.