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JOURNALS // Funktsional'nyi Analiz i ego Prilozheniya // Archive
Funktsional. Anal. i Prilozhen., 2025 Volume 59, Issue 4, Pages 101–105 (Mi faa4269)
Brief communications

On triangulations with fixed areas

Ivan Frolovab

a Instituto Nacional de Matemática Pura e Aplicada (IMPA), Rio de Janeiro, Brasil
b National Research University Higher School of Economics, Moscow, Russia

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.

Keywords: triangulation, area, configuration space.

MSC: 52C25, 51M25, 14N05, 52B45

Received: 06.11.2024
Revised: 26.02.2025
Accepted: 25.03.2025

DOI: 10.4213/faa4269


 English version: Functional Analysis and Its Applications, 2025, 59:4, 468–471

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© Steklov Math. Inst. of RAS, 2026