On Triangulations with Fixed Areas

We prove that the number of triangulations of a given polygon into triangles with fixed areas of faces is finite, and that an equidissection is algebraic as long as the vertices of the original polygon have algebraic coordinates.

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Publication Details

Journal
Functional Analysis and Its Applications
Published
2025-12-01
DOI
https://doi.org/10.1134/s1234567825040093
Primary Topic
Advanced Combinatorial Mathematics
Type
article
Field-Weighted Citation Impact
0.00
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article

On Triangulations with Fixed Areas

Ivan Il'ich Frolov
Functional Analysis and Its Applications
Advanced Combinatorial Mathematics
article

On Triangulations with Fixed Areas

Ivan Il'ich Frolov
article en

Abstract

We prove that the number of triangulations of a given polygon into triangles with fixed areas of faces is finite, and that an equidissection is algebraic as long as the vertices of the original polygon have algebraic coordinates.

Functional Analysis and Its ApplicationsVol. 59(4)
National Research University Higher School of Economics (RU), Instituto Nacional de Matemática Pura e Aplicada (BR)
Openalex Percentile: Top 15%
Advanced Combinatorial Mathematics
DOISourceOpenAlex
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On Triangulations with Fixed Areas — Ivan Il'ich Frolov · Functional Analysis and Its Applications (2025) | TGRS Research Map | TGRS