Wednesday, February 16, 2011

The Triangle Dissection Fallacy

Take a look at the above picture, and agree with me that this is weird. We see two triangles, and based on the grid they are both the same size. A quick count of the grid boxes tells us that the surface of both triangles should be 13 × 5 ÷ 2. All the pieces are equal in size, yet by shuffling them around we suddenly have a spare grid box!

This does not make any sense. The act of rearranging the triangle pieces should not change the surface area. What's going on here?