On the area formulas of inscribed polygons in classical geometry

Yohei Komori; Runa Umezawa; Takuro Yasui

doi:10.4310/PAMQ.2020.v16.n3.a8

On the area formulas of inscribed polygons in classical geometry

Yohei Komori, Runa Umezawa, Takuro Yasui

School of Education

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

Abstract

We show that there is no area formula of the general inscribed n-gon for n ≥ 5 only by using arithmetic operations and k-th roots of its side lengths in classical geometry.

Original language	English
Pages (from-to)	557-572
Number of pages	16
Journal	Pure and Applied Mathematics Quarterly
Volume	16
Issue number	3
DOIs	https://doi.org/10.4310/PAMQ.2020.v16.n3.a8
Publication status	Published - 2020

Keywords

Euclidean geometry
Hyperbolic geometry
Spherical geometry

ASJC Scopus subject areas

Mathematics(all)

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10.4310/PAMQ.2020.v16.n3.a8

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title = "On the area formulas of inscribed polygons in classical geometry",

abstract = "We show that there is no area formula of the general inscribed n-gon for n ≥ 5 only by using arithmetic operations and k-th roots of its side lengths in classical geometry.",

keywords = "Euclidean geometry, Hyperbolic geometry, Spherical geometry",

author = "Yohei Komori and Runa Umezawa and Takuro Yasui",

year = "2020",

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AU - Umezawa, Runa

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KW - Spherical geometry

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On the area formulas of inscribed polygons in classical geometry

Abstract

Keywords

ASJC Scopus subject areas

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