Torus - Cutting A Torus

Cutting A Torus

A standard torus (specifically, a ring torus) can be cut with n planes into at most


\frac16
(n^3 + 3n^2 + 8n)
parts.

The initial terms of this sequence for n starting from 1 are:

2, 6, 13, 24, 40, … (sequence A003600 in OEIS).

Read more about this topic:  Torus

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    This man was very clever and quick to learn anything in his line. Our tent was of a kind new to him; but when he had once seen it pitched, it was surprising how quickly he would find and prepare the pole and forked stakes to pitch it with, cutting and placing them right the first time, though I am sure that the majority of white men would have blundered several times.
    Henry David Thoreau (1817–1862)