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Vertex vs Monogon - What's the difference?

vertex | monogon |

In context|geometry|lang=en terms the difference between vertex and monogon

is that vertex is (geometry) the common point of the two rays of the angle, or its equivalent structure in polyhedra (meeting of edges) and higher order polytopes while monogon is (geometry) a one-dimensional object comprising one vertex and one (not necessarily straight) edge both of whose ends are that vertex.

In context|optics|lang=en terms the difference between vertex and monogon

is that vertex is (optics) the point where the surface of a lens crosses the optical axis while monogon is (optics) a single-faceted reflector.

As nouns the difference between vertex and monogon

is that vertex is the highest point of something while monogon is (geometry) a one-dimensional object comprising one vertex and one (not necessarily straight) edge both of whose ends are that vertex.

vertex

English

(wikipedia vertex)

Noun

(en-noun)
  • The highest point of something.
  • (anatomy) The highest surface on the skull.
  • (geometry) The common point of the two rays of the angle, or its equivalent structure in polyhedra (meeting of edges) and higher order polytopes.
  • (mathematics) A point on the curve with a local minimum or maximum of curvature.
  • (graph theory) One of the elements of a graph joined or not by edges to other vertices.
  • (computer graphics) A point in space, usually given in terms of its Cartesian coordinates.
  • (optics) The point where the surface of a lens crosses the optical axis.
  • (nuclear, or, particle physics) An interaction point.
  • (astrology) The point where the prime vertical meets the ecliptic in the western hemisphere of a natal chart.

    • Synonyms

    * (highest point) acme, apex, peak, top * (part of a graph) node

    Derived terms

    * vertexal, vertexial

    See also

    * Mathworld article on vertices of polyhedra * Mathworld article on verticies of polygons ----

    monogon

    English

    Noun

    (en noun)
  • (geometry) A one-dimensional object comprising one vertex and one (not necessarily straight) edge both of whose ends are that vertex.
  • *{{quote-book, 1955, Herbert Busemann, The Geometry of Geodesics citation
    • , passage=A geodesic with multiple points contains at least one simple monogon . }}
  • *{{quote-book, 1981, Harold Abelson and Andrea A. DiSessa, Turtle Geometry: The Computer As a Medium for Exploring Mathematics citation
    • , passage=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, , 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 ?
  • (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 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, 6s+2 edges, and 4s+2 faces. Of these faces, 4s+1 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", 6, page 158,
  • *:There is no monogon in M-int(N(B)), ie, no disk D\subset M-int(N(B)) with \partial D=D\cap N(B)=\alpha\cup\beta, where \alpha\subset\partial_vN(B) is in an interval fiber of \partial_vN(B) and \beta\subset\partial_hN(B).
  • * Thilo Kuessner, "A survery on simplicial volume and invariants of foliations and laminations", in, Pawe? 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 \partial C.
  • (optics) A single-faceted reflector.
  • *{{quote-book, 1991, Beam Deflection and Scanning Technologies, Leo Beiser, editor=Gerald F. Marshall citation
    • , passage=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 *(wikipedia "monogon")