Proof Without Words: Estimating Generalized Pi

Euclidean geometry is a special case of the p-metric whose unit circle satisfies |x|p+|y|p=1, and we may use its area to define a generalized version of pi. We wordlessly deduce some simple bounds on the values of generalized pi from inscribed and exscribed octagons.

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Publication Details

Journal
College Mathematics Journal
Published
2024-08-19
DOI
https://doi.org/10.1080/07468342.2024.2388473
Primary Topic
Algorithms and Data Compression
Type
article
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article

Proof Without Words: Estimating Generalized Pi

William E. Wood
College Mathematics Journal
Algorithms and Data Compression
article

Proof Without Words: Estimating Generalized Pi

William E. Wood
article en

Abstract

Euclidean geometry is a special case of the p-metric whose unit circle satisfies |x|p+|y|p=1, and we may use its area to define a generalized version of pi. We wordlessly deduce some simple bounds on the values of generalized pi from inscribed and exscribed octagons.

College Mathematics JournalVol. 56(1)
University of Northern Iowa (US)
Openalex Percentile: Top 89%
Algorithms and Data Compression
DOISourceOpenAlex
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