Depends on the shape of the rock --- if it has a "neck" somewhere, the lower bound is the circumference of the neck. The worst case must be a sphere --- the edges of a blown-up regular tetrahedron probably gives a lower bound on the total length in that case, though it doesn't allow a single piece of string --- a blown-up regular octahedron does, giving you an upper bound. WFL On 2/8/11, Hilarie Orman <ho@alum.mit.edu> wrote:
The rubber band shapes reminded me of a problem that I have been wondering about since last summer. If I have a smooth rock, what is the minimum length of string that I need to tie the string around the rock so that the rock can't slip out of the knot? How many knots are needed?
Hilarie
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