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

Famous quotes containing the word cutting:

    The sole work and deed of universal freedom is therefore death, a death too which has no inner significance or filling, for what is negated is the empty point of the absolutely free self. It is thus the coldest and meanest of all deaths, with no more significance than cutting off a head of cabbage or swallowing a mouthful of water.
    Georg Wilhelm Friedrich Hegel (1770–1831)