Apeirogon

English

A magnified portion of a regular apeirogon is a partition of a line with equal edge lengths

Etymology

From Template:Confix.

Pronunciation

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Noun

1. Template:Lb A type of generalised polygon with a countably infinite number of sides and vertices;
   Template:Lb 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.
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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 Template:Pedia
• The Schläfli symbol of an apeirogon is $\{\mathrm{\infty }\}$. (For comparison, the symbol for an $n$-sided regular polygon is $\{n\}$.)
• 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 Template:M.
• In analogy to the Euclidean case, the regular Template:M is a partition of the hyperbolic line $H^1$ into segments of length $2\lambda$.

Hyponyms

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Related terms

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Translations

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See also

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Further reading

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