View source for Monogon

==English==

===Etymology===
From {{confix|en|mono|gon}}.

===Pronunciation===
* {{audio|en|LL-Q1860 (eng)-Rho9998-monogon.wav|a=UK}}
* {{hyphenation|en|mon|o|gon}}

===Noun===
{{en-noun}}

# {{lb|en|geometry}} A [[one]]-[[dimensional]] object comprising one [[vertex]] and one (not necessarily [[straight]]) [[edge]] both of whose [[end]]s are that vertex.
#* {{quote-book|en|year=1955|author=Herbert Busemann|title=The Geometry of Geodesics|url=http://books.google.com/books?id=NQFRAAAAMAAJ|page=295
|passage=A geodesic with multiple points contains at least one simple '''monogon'''.}}
#* {{quote-book|en|year=1981|author=Harold Abelson; Andrea A. DiSessa|title=Turtle Geometry: The Computer As a Medium for Exploring Mathematics|url=http://books.google.com/books?id=3geYp44hJVcC|isbn=0262510375|page=262
|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, [[w:Ludwig Wittgenstein|Ludwig Wittgenstein]] and [[w:Friedrich Waismann|Friedrich Waismann]], ''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'''?
# {{lb|en|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.
#* {{quote-book|en|year=1987|author=Jonathan L. Gross; Thomas W. Tucker|title=Topological Graph Theory|page=231|publisher=w:Dover Publications|year_published=2001|isbn=0486417417
|passage=According to Theorem 4.1.1, such a derived imbedding could be obtained from an imbedded voltage graph with one vertex, <math>6s+2</math> edges, and <math>4s+2</math> faces. Of these faces, <math>4s+1</math> 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", [[w:Geometry and Topology|''Geometry & Topology'']] 6, page 158,
#*: There is no monogon in <math>M-int(N(B))</math>, ie, no disk <math>D\subset M-int(N(B))</math> with <math>\partial D=D\cap N(B)=\alpha\cup\beta</math>, where <math>\alpha\subset\partial_vN(B)</math> is in an interval fiber of <math>\partial_vN(B)</math> and <math>\beta\subset\partial_hN(B)</math>.
#* {{ante|2006}}, Thilo Kuessner, "A survey on simplicial volume and invariants of foliations and laminations", in, Paweł 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 <math>\partial C</math>.
# {{lb|en|optics}} A single-faceted reflector.
#* {{quote-book|en|year=1991|author=Beam Deflection; Scanning Technologies|title=Leo Beiser|editor=Gerald F. Marshall|url=http://books.google.com/books?id=6ulRAAAAMAAJ|isbn=0819405531|page=33
|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'',<sup >[http://books.google.com/books?id=jXKjVmqYBYEC ]</sup> 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
* {{quote-journal|en|year=2008|author=Baris Coskunuzer|journal=Proceedings of the American Mathematical Society|volume=136|issue=4|pages=1427–1432
|passage=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]]

====Coordinate terms====
* [[digon]]
* [[trigon]]
* [[polygon]]
* [[apeirogon]]

====Derived terms====
* [[monogonal]]

====Translations====
{{trans-top|geometry}}
* Dutch: {{t+|nl|eenhoek|m}}
* Finnish: {{t|fi|yksikulmio}}
* German: {{t|de|Eineck|n}}
* Polish: {{t|pl|[[kształt]] [[o]] [[jeden|jednym]] [[wierzchołek|wierzchołku]]|m}}
* Russian: {{t+|ru|одноугольник|m}}
{{trans-bottom}}

====See also====
* [[monogonic]]
* {{pedia}}

{{C|en|Polygons|Shapes in non-Euclidean geometry|Sphere}}