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Polygon vs Monogon - What's the difference?

polygon | monogon |

Polygon is a coordinate term of monogon.


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

is that polygon is (geometry) such a figure and its interior, taken as a whole while monogon is (geometry) a one-dimensional object comprising one vertex and one (not necessarily straight) edge both of whose ends are that vertex.

As nouns the difference between polygon and monogon

is that polygon is (geometry) a plane figure bounded by straight edges while monogon is (geometry) a one-dimensional object comprising one vertex and one (not necessarily straight) edge both of whose ends are that vertex.

polygon

English

Noun

(wikipedia polygon) (en noun)
  • (geometry) A plane figure bounded by straight edges.
  • (geometry) The boundary of such a figure.
  • (geometry, more generally) A figure comprising vertices and (not necessarily straight) edges, alternatingly.
  • (geometry) Such a figure and its interior, taken as a whole.

    • Hypernyms

    * See

    Hyponyms

    * See

    Meronyms

    * See

    Derived terms

    * cumulative frequency polygon * frequency polygon * funicular polygon * polygon of forces

    Related terms

    * polygonal * polygonality * polygonhood * polygonness

    See also

    * polyhedron ----

    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")