Billiard Circuits in Quadrilaterals

IF 0.4 4区数学 Q4 MATHEMATICS

American Mathematical Monthly Pub Date : 2023-08-02 DOI:10.1080/00029890.2023.2230860

K. Knox

引用次数: 0

Abstract

Abstract A quadrilateral contains a closed billiard circuit that bounces consecutively on the interiors of its sides each exactly once per cycle, if and only if it is cyclic and its interior contains the center of its circumscribed circle.

查看原文本刊更多论文

四边形台球回路

摘要一个四边形包含一个闭合的台球回路，该回路在其侧面的内部连续反弹，每个循环恰好反弹一次，当且仅当它是循环的，并且其内部包含其外切圆的中心。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

求助全文

约1分钟内获得全文求助全文

来源期刊

American Mathematical Monthly Mathematics-General Mathematics

CiteScore

0.80

自引率

20.00%

发文量

127

审稿时长

6-12 weeks

期刊介绍： The Monthly''s readers expect a high standard of exposition; they look for articles that inform, stimulate, challenge, enlighten, and even entertain. Monthly articles are meant to be read, enjoyed, and discussed, rather than just archived. Articles may be expositions of old or new results, historical or biographical essays, speculations or definitive treatments, broad developments, or explorations of a single application. Novelty and generality are far less important than clarity of exposition and broad appeal. Appropriate figures, diagrams, and photographs are encouraged. Notes are short, sharply focused, and possibly informal. They are often gems that provide a new proof of an old theorem, a novel presentation of a familiar theme, or a lively discussion of a single issue. Abstracts for articles or notes should entice the prospective reader into exploring the subject of the paper and should make it clear to the reader why this paper is interesting and important. The abstract should highlight the concepts of the paper rather than summarize the mechanics. The abstract is the first impression of the paper, not a technical summary of the paper. Excessive use of notation is discouraged as it can limit the interest of the broad readership of the MAA, and can limit search-ability of the article.