apeirogon

== English == === Etymology === From apeiro- +‎ -gon. === Pronunciation === IPA(key): /əˈpiːɹɵɡɑn/, /əˈpeɪ̯ɹɵɡɑn/, Southern England /əˈpɪəɹəɡən/ Hyphenation: apei‧ro‧gon === Noun === apeirogon (plural apeirogons) (mathematics, geometry) A type of generalised polygon with a countably infinite number of sides and vertices;(in the regular case) the limit case of an n-sided regular polygon as n increases to infinity and the edge length is fixed; typically imagined as a straight line partitioned into equal segments by an infinite number of equally-spaced points. ==== Usage notes ==== Some authors use the term only for the regular apeirogon. A regular apeirogon can be described as a partition (or tessellation) of the Euclidean line into infinitely many equal-length segments. For alternative definitions, see Apeirogon § Definitions on Wikipedia.Wikipedia The Schläfli symbol of an apeirogon is { ∞ } {\displaystyle \{\infty \}} . (For comparison, the symbol for an n {\displaystyle n} -sided regular polygon is { n } {\displaystyle \{n\}} .) The limit case of an n-sided regular polygon as n increases to infinity and the perimeter length is fixed (meaning the edge lengths decrease to zero) is a circle, which in this context is sometimes called a zerogon. In analogy to the Euclidean case, the regular pseudogon is a partition of the hyperbolic line H 1 {\displaystyle H^{1}} into segments of length 2 λ {\displaystyle 2\lambda } . ==== Hyponyms ==== zerogon (a specific non-regular case) ==== Derived terms ==== ==== Related terms ==== apeirohedron ==== Translations ==== === See also === infinigon pseudogon === Further reading === apeirogon on Wikipedia.Wikipedia