English

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, 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, 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, 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.

   • 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 survery 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 .

3. (optics) A single-faceted reflector.
   • 1991, Beam Deflection and Scanning Technologies, Gerald F. Marshall, editor, Leo Beiser, 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, 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].

Synonyms

• henagon

Derived terms

• monogonal

Coordinate terms

• digon
• trigon
• polygon
• apeirogon

See also

• monogonic
• monogon on Wikipedia.Wikipedia