# monogon

## Contents

## English[edit]

### Etymology[edit]

### Pronunciation[edit]

- Hyphenation: mon‧o‧gon

### Noun[edit]

**monogon** (*plural* **monogons**)

- (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**.

- A geodesic with multiple points contains at least one simple
**1981**, Harold Abelson and Andrea A. DiSessa, Turtle Geometry: The Computer As a Medium for Exploring Mathematics^{[2]}, →ISBN, 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.

- There are no one-sided closed polygons on a plane. On the cube, however,
**2003**, Gordon Baker, translator and editor, Ludwig Wittgenstein and Friedrich Waismann,*The Voices of Wittgenstein: The Vienna Circle*, Routledge, →ISBN, 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**?

- 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

- (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, page 231,- According to Theorem 4.1.1, such a derived imbedding could be obtained from an imbedded voltage graph with one vertex, edges, and faces. Of these faces, should be 3-sided and satisfy
*KVL*. The other face should be a**monogon**whose net voltage has order two.

- According to Theorem 4.1.1, such a derived imbedding could be obtained from an imbedded voltage graph with one vertex, edges, and faces. Of these faces, should be 3-sided and satisfy
**2002**, Tao Li, "Laminar Branched Surfaces in 3–manifolds",*Geometry & Topology*6, page 158,- There is no monogon in , ie, no disk with , where is in an interval fiber of and .

*a.***2006**, Thilo Kuessner, "A survey on simplicial volume and invariants of foliations and laminations", in, Paweł Walczak, et al., editors,*Foliations 2005*, →ISBN, 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 .

- An end-compressing

- (optics) A single-faceted reflector.
**1991**, Beam Deflection and Scanning Technologies, Gerald F. Marshall, editor, Leo Beiser^{[3]}, →ISBN, page 33:- A new optical scanner is described which serves as a
**monogon**or single-facet device, providing one scan per shaft rotation.

- A new optical scanner is described which serves as a
**1999**, William L. Wolfe,*Infrared Design Examples*,^{[4]}Tutorial Texts in Optical Engineering Volume TT36, SPIE Press, →ISBN, 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.

- These devices also start with the

#### Quotations[edit]

- 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].

- As nonproper embeddedness must produce