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English
Etymology
From mono- + -gon.
Pronunciation
Noun
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, 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, →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?
- (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, 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 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 region C which is not homotopic (rel. boundary) into .
- (optics) A single-faceted reflector.
1991, Beam Deflection, Scanning Technologies, edited by Gerald F. Marshall, Leo Beiser, →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, 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 .
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