Doi:10.1515/JAA.2011

Richter, Wolf-Dieter; Schicker, Kay

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Circle numbers of regular convex polygons. (English) ?Zbl 1380.52002 ?

Result. Math. 69, No. 3-4, 521-538 (2016).

Authors' abstract: The circle number function is extended here to regular convex polygons. To this end, the radius of the polygonal circle is defined as the Minkowski functional of the circumscribed polygonal disc, and the arc-length of the polygonal circle is measured in a generalized Minkowski space having the rotated polar body as the unit disc.

Reviewer: Mowaffaq Hajja (Amman)

MSC:

52A10 26B15 28A50 28A75 51M25 51F99 52A38 52C05

Convex sets in 2 dimensions (including convex curves) Integration of real functions of several variables: length, area, volume Integration and disintegration of measures Length, area, volume, other geometric measure theory Length, area and volume in real or complex geometry Metric geometry Length, area, volume and convex sets (aspects of convex geometry) Lattices and convex bodies in 2 dimensions (aspects of discrete geometry)

Cited in 2 Documents

Keywords:

polygonal radius; polygonally generalized circumference; rotated polar body geometry; disintegration of Lebesgue measure; polygonally generalized uniform distribution; regular convex polygons

Full Text: DOI

References:

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This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.

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