monogon

plural monogons

1. geometryA one-dimensional object comprising one vertex and one (not necessarily straight) edge both of whose ends are that vertex.

   A geodesic with multiple points contains at least one simple monogon.

   1955, Herbert Busemann, The Geometry of Geodesics, page 295

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   There are no one-sided closed polygons on a plane. On the cube, however, monogons are a diverse and interesting class of figures.

   1981, Harold Abelson, Andrea A. DiSessa, Turtle Geometry: The Computer As a Medium for Exploring Mathematics, →ISBN, page 262

   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. geometryA 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.

   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⊂M-int(N(B)) with ∂D=D∩N(B)=α∪β, where α⊂∂_(vN)(B) is in an interval fiber of ∂_(vN)(B) and β⊂∂_(hN)(B).

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   According to Theorem 4.1.1, such a derived imbedding could be obtained from an imbedded voltage graph with one vertex, 6s#43;2 edges, and 4s#43;2 faces. Of these faces, 4s#43;1 should be 3-sided and satisfy KVL. The other face should be a monogon whose net voltage has order two.

   1987, Jonathan L. Gross, Thomas W. Tucker, Topological Graph Theory, Dover Publications, published 2001, →ISBN, page 231

   An end-compressing monogon for F is a monogon properly embedded in the complimentary^([sic]) region C which is not homotopic (rel. boundary) into #92;partialC.

   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

3. engineeringA single-faceted reflector.

   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.

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   A new optical scanner is described which serves as a monogon or single-facet device, providing one scan per shaft rotation.

   1991, Beam Deflection, Scanning Technologies, edited by Gerald F. Marshall, Leo Beiser, →ISBN, page 33