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On triangulations with fixed areas

Ivan Frolov

Abstract

We prove that the number of dissections 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.

On triangulations with fixed areas

Abstract

We prove that the number of dissections 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.
Paper Structure (2 sections, 6 theorems, 4 equations, 1 figure)

This paper contains 2 sections, 6 theorems, 4 equations, 1 figure.

Table of Contents

  1. Introduction
  2. Proofs

Key Result

Theorem 1

The number of triangulations of a polygon $P$ in $\mathbb R^2$ with fixed number of faces and fixed areas of faces is finite.

Figures (1)

  • Figure :

Theorems & Definitions (10)

  • Theorem 1
  • Theorem 2
  • Remark
  • Proposition 3
  • proof
  • Lemma 4
  • proof
  • Lemma 5
  • proof
  • Lemma 6