Problem #8
It is relatively easy to see that the largest regular tetrahedron which
will fit inside a cube whose edges have length 1 is the tetrahedron shown
in the figure below. The length of an edge of this tetrahedron is Sqrt[2].
This month there are two questions:
- What is the length of an edge of the largest regular tetrahedron which
will fit inside a regular octahedron whose edges have length 1?"
- What is the length of an edge of the largest cube which will fit
inside a regular tetrahedron whose edges have length 1?"
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| tetrahedron |
octahedron |
(GIF's © 1998,
R. Mäder)