monogon
Definition from Wiktionary, the free dictionary
Contents
English[edit]
Etymology[edit]
Noun[edit]
monogon (plural monogons)
 (geometry) A onedimensional 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 onesided 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 biangle. 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?

 (geometry) A twodimensional 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 3sided 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 endcompressing monogon for F is a monogon properly embedded in the complimentary^{[sic]} region C which is not homotopic (rel. boundary) into .
 1987, Jonathan L. Gross and Thomas W. Tucker Topological Graph Theory, 2001 Dover Publications edition, ISBN 0486417417, page 231,
 (optics) A singlefaceted 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 singlefacet 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 0819433195, page 133,
 These devices also start with the monogon, a plane mirror, and include the bigon, a twosided mirror, the trigon, quadrigon, and general ngons.

Quotations[edit]
 To be listed under the applicable sense
 2008, Baris Coskunuzer, Proceedings of the American Mathematical Society, Volume 136, Number 4, pages 14271432,
 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].