Planar Sections
Friday, May 28th, 2010 by lucasHere’s another one that we never solved.
Does a polyhedron exist with all of its plane sections triangular?
[Engel, Problem Solving Strategies 12.3.2 #60]
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Here’s another one that we never solved.
Does a polyhedron exist with all of its plane sections triangular?
[Engel, Problem Solving Strategies 12.3.2 #60]
Tags: Geometry, Unsolved
Posted in Problem of the Week | 1 Comment »
“Associated with each face of a solid convex polyhedron is a bug which crawls along the perimeter of the face, at varying speed, but only in the clockwise direction. Prove that no schedule will permit all the bugs to circumnavigate their faces and return to their initial positions without incurring a collision.” [Peter Winkler, Mathematical Puzzles, p. 82.]
Tags: Unsolved
Posted in Problem of the Week | 7 Comments »