内接矩形重合

IF 0.5 4区数学 Q3 MATHEMATICS

Advances in Geometry Pub Date : 2021-07-01 DOI:10.1515/advgeom-2021-0012

R. Schwartz

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引用次数: 2

摘要

摘要我们证明了一个关于矩形连续路径的积分公式。我们用这个积分公式证明了不等式M（γ）≥Δ（γ）/2–1，其中M（γ。

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Inscribed rectangle coincidences

Abstract We prove an integral formula for continuous paths of rectangles inscribed in a piecewise smooth loop. We use this integral formula to prove the inequality M(γ) ≥ Δ(γ)/2 – 1, where M(γ) denotes the total multiplicity of rectangle coincidences, i.e. pairs, triples, etc. of isometric rectangles inscribed in γ, and Δ(γ) denotes the number of stable diameters of γ, i.e. critical points of the distance function on γ.

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来源期刊

Advances in Geometry 数学-数学

CiteScore

1.00

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： Advances in Geometry is a mathematical journal for the publication of original research articles of excellent quality in the area of geometry. Geometry is a field of long standing-tradition and eminent importance. The study of space and spatial patterns is a major mathematical activity; geometric ideas and geometric language permeate all of mathematics.