# monogon

## English

mono- +‎ -gon.

### Pronunciation

• Hyphenation: mon‧o‧gon

### Noun

monogon (plural monogons)

1. (geometry) A one-dimensional object comprising one vertex and one (not necessarily straight) edge both of whose ends are that vertex.
• 1955, Herbert Busemann, The Geometry of Geodesics[1], page 295:
A geodesic with multiple points contains at least one simple monogon.
• 1981, Harold Abelson and Andrea A. DiSessa, Turtle Geometry: The Computer As a Medium for Exploring Mathematics[2], ISBN 0262510375, page 262:
There are no one-sided closed polygons on a plane. On the cube, however, monogons are a diverse and interesting class of figures.
• 2003, Gordon Baker, translator and editor, Ludwig Wittgenstein and Friedrich Waismann, The Voices of Wittgenstein: The Vienna Circle, Routledge, ISBN 0415056446, page 409,
We explain to somebody what is a regular quadrilateral constructed within the circle; then a regular triangle and a regular bi-angle. Now we ask him to draw a regular monogon by analogy, and we probably think that he cannot do this. But what if he draws a point on the circle and says that it is a regular monogon?
2. (geometry) A two-dimensional object comprising one vertex, one edge both of whose ends are that vertex, and one face filling in the hollow formed by that edge.
• 1987, Jonathan L. Gross and Thomas W. Tucker Topological Graph Theory, 2001 Dover Publications edition, ISBN 0486417417, page 231,
According to Theorem 4.1.1, such a derived imbedding could be obtained from an imbedded voltage graph with one vertex, ${\displaystyle 6s+2}$ edges, and ${\displaystyle 4s+2}$ faces. Of these faces, ${\displaystyle 4s+1}$ should be 3-sided and satisfy KVL. The other face should be a monogon whose net voltage has order two.
• 2002, Tao Li, "Laminar Branched Surfaces in 3–manifolds", Geometry & Topology 6, page 158,
There is no monogon in ${\displaystyle M-int(N(B))}$, ie, no disk ${\displaystyle D\subset M-int(N(B))}$ with ${\displaystyle \partial D=D\cap N(B)=\alpha \cup \beta }$, where ${\displaystyle \alpha \subset \partial _{v}N(B)}$ is in an interval fiber of ${\displaystyle \partial _{v}N(B)}$ and ${\displaystyle \beta \subset \partial _{h}N(B)}$.
• a. 2006, Thilo Kuessner, "A survey on simplicial volume and invariants of foliations and laminations", in, Paweł Walczak, et al., editors, Foliations 2005, ISBN 9812700749, page 295,
An end-compressing monogon for F is a monogon properly embedded in the complimentary[sic] region C which is not homotopic (rel. boundary) into ${\displaystyle \partial C}$.
3. (optics) A single-faceted reflector.
• 1991, Beam Deflection and Scanning Technologies, Gerald F. Marshall, editor, Leo Beiser[3], ISBN 0819405531, page 33:
A new optical scanner is described which serves as a monogon or single-facet device, providing one scan per shaft rotation.
• 1999, William L. Wolfe, Infrared Design Examples,[4] Tutorial Texts in Optical Engineering Volume TT36, SPIE Press, ISBN 0-8194-3319-5, page 133,
These devices also start with the monogon, a plane mirror, and include the bigon, a two-sided mirror, the trigon, quadrigon, and general n-gons.

#### Quotations

To be listed under the applicable sense
• 2008, Baris Coskunuzer, Proceedings of the American Mathematical Society, Volume 136, Number 4, pages 1427-1432,
As nonproper embeddedness must produce monogons, one can get a contradiction by using Hass and Scott's surgery arguments for least area objects in [HS].