May 2002

## Mathematical Misfits

### Two-dimensional

Which fits best - a square peg in a round hole, or a round peg in a square hole? To be more precise, if you take a circle and fit inside it the largest possible square, and then take a square and fit inside it the largest possible circle, which leaves*proportionally*least space?

Which fits best?

### Three-dimensional

Which fits best in a sphere - a dodecahedron or an icosahedron? That is, if you fit the largest possible dodecahedron and icosahedron inside a given sphere, which leaves least space?
Dodecahedron |
Icosahedron |

(Both images copyright by Rüdiger Appel)

You can send your solution by e-mail to plus@maths.cam.ac.uk.

If you are stumped by last issue's puzzle, here is the solution.

For some challenging mathematical puzzles, see the NRICH puzzles from this month or last month.

Solution link