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CTK Exchange
itineracy
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Apr-30-09, 07:06 AM (EST) |
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"Cutting a torus (2nd attempt)"
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In a well-known puzzle, Martin Gardner asked for the maximum number of pieces into which a torus could be sliced by three planes. Based on the formula X(n)=(n^3+3n^2+8n)/6 for n planes, the answer is given as 13.
The formula however, assumes the torus to be a solid, where I thought a torus was supposed to be a surface.
Now, when slicing the torus in such a way that it would produce 13 pieces if it were a donut, it actually produces 14 pieces if it were an inner tube.
Q: Does anyone know the inner tube formula? Or how to obtain it through mathematical rigor?
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