monogon

English

Etymology

From mono- +‎ -gon.

Pronunciation

• Audio (UK):

  (file)

• 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, 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.

   • 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?

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, Thomas W. Tucker, Topological Graph Theory, Dover Publications, published 2001, →ISBN, page 231:

     According to Theorem 4.1.1, such a derived imbedding could be obtained from an imbedded voltage graph with one vertex, $6s+2$ edges, and $4s+2$ faces. Of these faces, $4s+1$ 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 $M-int(N(B))$, ie, no disk $D\subset M-int(N(B))$ with $\partial D=D\cap N(B)=\alpha \cup \beta$, where $\alpha \subset \partial _{v}N(B)$ is in an interval fiber of $\partial _{v}N(B)$ and $\beta \subset \partial _{h}N(B)$.

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

3. (optics) A single-faceted reflector.
   • 1991, Beam Deflection, Scanning Technologies, edited by Gerald F. Marshall, 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.

   • 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.

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].

Synonyms

• henagon

Coordinate terms

• digon
• trigon
• polygon
• apeirogon

Derived terms

• monogonal

Translations

geometry

• Dutch: eenhoek (nl) m
• Finnish: yksikulmio
• German: Eineck n
• Polish: kształt o jednym wierzchołku m
• Russian: одноугольник (ru) m (odnougolʹnik)

See also

• monogonic
• monogon on Wikipedia.Wikipedia