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Submitted by plusadmin on 1 May, 2002
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?

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

Dodecahedron
Icosahedron

Icosahedron
You can see rotating versions of these here (70k download each).

(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
Mathematical misfits two-dimensional solution
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