Scholarlink

Abstract <p> In the paper, we discuss a version of the classical problem of partitioning a figure into two congruent parts, which was posed in 1999. We consider the conjecture that when partitioning a convex centrally symmetric figure into two congruent parts, the center of symmetry always lies on the common boundary of the two parts. The main result of the paper consists in proving the conjecture for simple but not necessarily convex figures on the plane under the condition that the figure is partitioned into two parts by a curve that is not self-intersecting. There is a certain advance in classifying the types of motions in the general case on the plane. </p>

错误：搜索内容不能为空，请输入英文关键词
错误：关键词超出字数限制，请精简
高级检索

Problem of Cutting a Polygon into Two Congruent Parts

  • 期刊论文

  • 发表日期：

    2025年4月1日

查看全文
  • A. Yu. Sadovnichii

摘要

Abstract

In the paper, we discuss a version of the classical problem of partitioning a figure into two congruent parts, which was posed in 1999. We consider the conjecture that when partitioning a convex centrally symmetric figure into two congruent parts, the center of symmetry always lies on the common boundary of the two parts. The main result of the paper consists in proving the conjecture for simple but not necessarily convex figures on the plane under the condition that the figure is partitioned into two parts by a curve that is not self-intersecting. There is a certain advance in classifying the types of motions in the general case on the plane.