apeirogon

Noun

apeirogon (plural apeirogons)

1. A type of generalised polygon with a countably infinite number of sides and vertices;
   • Hence the regular polygon ABCD ... can either be a convex n-gon, a star n-gon, a horocylic^([sic – meaning horocyclic]) apeirogon or a hypercyclic apeirogon.1984, Coxeter-Festschrift [Mitteilungen aus dem Mathem[atisches] Seminar Giessen], Giessen: Gießen Mathematischen Institut, Justus Liebig-Universität Gießen, page 247
   • In geometry, an apeirogon is a limiting case of a regular polygon. The number of sides in an apeirogon is becoming infinite, so the apeirogon as a whole approaches a circle. A magnified view of a small piece of the apeirogon looks like a straight line.1994, Steven Schwartzman, The Words of Mathematics: An Etymological Dictionary of Mathematical Terms Used in English, Washington, D.C.: Mathematical Association of America, →ISBN, page 27
2. 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.