monogon
nounEtymology From mono- + -gon.
1
Geometry, Mathematics, Sciences A 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:
- 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:
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- 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, Mathematics, Sciences 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.
- 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:
- 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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- 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:
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Engineering, Natural sciences, Optics, Physical sciences, Physics A single-faceted reflector.
- 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:
- 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.