different between apeirogon vs monogon

English

Etymology

apeiro- +? -gon

Pronunciation

• IPA^(key): /??pi?????n/, /??pe??????n/
• Hyphenation: apei?ro?gon

Noun

apeirogon (plural apeirogons)

1. (mathematics, geometry) A polygon having an infinite number of sides and vertices.

Synonyms

• zerogon

Related terms

• apeirohedron

Further reading

• apeirogon on Wikipedia.Wikipedia

English

Etymology

mono- +? -gon.

Pronunciation

• Hyphenation: mon?o?gon

Noun

monogon (plural monogons)

1. (geometry) A one-dimensional object comprising one vertex and one (not necessarily straight) edge both of whose ends are that vertex.
   • 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) 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 Dover Publications edition, ?ISBN, page 231,

     According to Theorem 4.1.1, such a derived imbedding could be obtained from an imbedded voltage graph with one vertex, ${\displaystyle 6s+2}$ edges, and ${\displaystyle 4s+2}$ faces. Of these faces, ${\displaystyle 4s+1}$ 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", Geometry & Topology 6, page 158,

     There is no monogon in ${\displaystyle M-int(N(B))}$, ie, no disk ${\displaystyle D\subset M-int(N(B))}$ with ${\displaystyle \partial D=D\cap N(B)=\alpha \cup \beta }$, where ${\displaystyle \alpha \subset \partial _{v}N(B)}$ is in an interval fiber of ${\displaystyle \partial _{v}N(B)}$ and ${\displaystyle \beta \subset \partial _{h}N(B)}$.

   • a. 2006, Thilo Kuessner, "A survey on simplicial volume and invariants of foliations and laminations", in, Pawe? Walczak, et al., editors, Foliations 2005, ?ISBN, 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 ${\displaystyle \partial C}$.

3. (optics) A single-faceted reflector.
   • 1999, William L. Wolfe, Infrared Design Examples,^[4] 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.

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

Coordinate terms

• digon
• trigon
• polygon
• apeirogon

Derived terms

• monogonal

See also

• monogonic
• monogon on Wikipedia.Wikipedia