Surfaces32 of 113
Möbius band
Möbius and Listing, 1858
A strip given a half-twist before its ends are joined. It has one side and one edge: an ant walking the centre line comes back upside down. An odd number of half-twists keeps it one-sided; an even number gives an ordinary twisted ring.
((1 + v cos(ku/2)) cos u, (1 + v cos(ku/2)) sin u, v sin(ku/2))
On mathcurve.com as Ruban de Möbius
Drawn as
Elsewhere
1Work the library cites and does not hold: in copyright, never released as a file, or not a file at all. The cited shelf
- 1963
Ants walk the band in single file. Each one passes over both faces of the strip and comes back to its start, because the strip has only one face.
Not yet checkedSuggested by an AI model, 2026-10-08
An AI reviewer agreed, 2026-10-09: Escher's own words, quoted in the Wikipedia article, say "on this strip nine red ants crawl after each other and travel the front side as well as the reverse side", which matches ants in single file crossing both faces of a one-sided strip. The library's Möbius band entry (one side, one edge) confirms the shape, and the article's "marching forever" covers the return to the start.