Counting Parallel Segments: New Variants of Pick’s Area Theorem

Alexander Belyaev; Pierre-Alain Fayolle

doi:10.1007/s00283-019-09921-8

Counting Parallel Segments: New Variants of Pick’s Area Theorem

Alexander Belyaev^*, Pierre-Alain Fayolle

^*Corresponding author for this work

School of Engineering & Physical Sciences

Research output: Contribution to journal › Article › peer-review

2 Citations (Scopus)

120 Downloads (Pure)

Abstract

New variants of Pick's Area Formula for lattice polygons are proposed. They are based on a proper counting of parallel lattice segments contained in and intersecting a given lattice polygon. An extension to 3D lattice polyhedra is also considered.

Original language	English
Pages (from-to)	1-7
Number of pages	7
Journal	The Mathematical Intelligencer
Volume	41
Issue number	4
Early online date	8 Aug 2019
DOIs	https://doi.org/10.1007/s00283-019-09921-8
Publication status	Published - Dec 2019

ASJC Scopus subject areas

General Mathematics
History and Philosophy of Science

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title = "Counting Parallel Segments: New Variants of Pick{\textquoteright}s Area Theorem",

abstract = "New variants of Pick's Area Formula for lattice polygons are proposed. They are based on a proper counting of parallel lattice segments contained in and intersecting a given lattice polygon. An extension to 3D lattice polyhedra is also considered.",

author = "Alexander Belyaev and Pierre-Alain Fayolle",

year = "2019",

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AU - Fayolle, Pierre-Alain

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AB - New variants of Pick's Area Formula for lattice polygons are proposed. They are based on a proper counting of parallel lattice segments contained in and intersecting a given lattice polygon. An extension to 3D lattice polyhedra is also considered.

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Counting Parallel Segments: New Variants of Pick’s Area Theorem

Abstract

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