六边形平行对边定理的初等证明

IF 0.7 Q3 EDUCATION & EDUCATIONAL RESEARCH

International Journal of Mathematical Education in Science and Technology Pub Date : 2023-10-19 DOI:10.1080/0020739x.2023.2243944

Rolfdieter Frank, Heinz Schumann

{"title":"六边形平行对边定理的初等证明","authors":"Rolfdieter Frank, Heinz Schumann","doi":"10.1080/0020739x.2023.2243944","DOIUrl":null,"url":null,"abstract":"AbstractThe perpendicular bisectors of the sides of a hexagon, whose opposite sides are parallel, produce a point symmetric hexagon. Michael de Villiers already gave two proofs of this theorem, firstly an elaborate one with the aid of dynamic geometry and secondly a merely verifying one with the help of coordinates and computer algebra. In this note, we present a short elementary proof. Our proof uses the fact, that the three altitudes of a triangle intersect in a common point, and it also covers degenerate cases.KEYWORDS: Hexagonperpendicular bisectorpoint symmetry Disclosure statementNo potential conflict of interest was reported by the authors.","PeriodicalId":14026,"journal":{"name":"International Journal of Mathematical Education in Science and Technology","volume":"69 1","pages":"0"},"PeriodicalIF":0.7000,"publicationDate":"2023-10-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":"{\"title\":\"Elementary proof of a theorem about hexagons with parallel opposite sides\",\"authors\":\"Rolfdieter Frank, Heinz Schumann\",\"doi\":\"10.1080/0020739x.2023.2243944\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"AbstractThe perpendicular bisectors of the sides of a hexagon, whose opposite sides are parallel, produce a point symmetric hexagon. Michael de Villiers already gave two proofs of this theorem, firstly an elaborate one with the aid of dynamic geometry and secondly a merely verifying one with the help of coordinates and computer algebra. In this note, we present a short elementary proof. Our proof uses the fact, that the three altitudes of a triangle intersect in a common point, and it also covers degenerate cases.KEYWORDS: Hexagonperpendicular bisectorpoint symmetry Disclosure statementNo potential conflict of interest was reported by the authors.\",\"PeriodicalId\":14026,\"journal\":{\"name\":\"International Journal of Mathematical Education in Science and Technology\",\"volume\":\"69 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.7000,\"publicationDate\":\"2023-10-19\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"1\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"International Journal of Mathematical Education in Science and Technology\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1080/0020739x.2023.2243944\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"EDUCATION & EDUCATIONAL RESEARCH\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"International Journal of Mathematical Education in Science and Technology","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1080/0020739x.2023.2243944","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"EDUCATION & EDUCATIONAL RESEARCH","Score":null,"Total":0}

引用次数: 1

摘要

摘要对边平行的六边形各边的垂直平分线构成点对称六边形。米迦勒·德维利耶已经给出了这个定理的两个证明，第一个是借助动态几何的详细证明，第二个是借助坐标和计算机代数的简单验证。在这篇笔记中，我们给出一个简短的初等证明。我们的证明使用了一个事实，三角形的三个高度相交于一个公点，它也涵盖了简并的情况。关键词:六角形垂直平分点对称披露声明作者未报道潜在利益冲突。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文本刊更多论文

Elementary proof of a theorem about hexagons with parallel opposite sides

AbstractThe perpendicular bisectors of the sides of a hexagon, whose opposite sides are parallel, produce a point symmetric hexagon. Michael de Villiers already gave two proofs of this theorem, firstly an elaborate one with the aid of dynamic geometry and secondly a merely verifying one with the help of coordinates and computer algebra. In this note, we present a short elementary proof. Our proof uses the fact, that the three altitudes of a triangle intersect in a common point, and it also covers degenerate cases.KEYWORDS: Hexagonperpendicular bisectorpoint symmetry Disclosure statementNo potential conflict of interest was reported by the authors.

求助全文

通过发布文献求助，成功后即可免费获取论文全文。去求助

来源期刊

International Journal of Mathematical Education in Science and Technology EDUCATION & EDUCATIONAL RESEARCH-

CiteScore

3.30

自引率

11.10%

发文量

123

期刊介绍： Mathematics is pervading every study and technique in our modern world, bringing ever more sharply into focus the responsibilities laid upon those whose task it is to teach it. Most prominent among these is the difficulty of presenting an interdisciplinary approach so that one professional group may benefit from the experience of others. The International Journal of Mathematical Education in Science and Technology provides a medium by which a wide range of experience in mathematical education can be presented, assimilated and eventually adapted to everyday needs in schools, colleges, polytechnics, universities, industry and commerce. Contributions will be welcomed from lecturers, teachers and users of mathematics at all levels on the contents of syllabuses and methods of presentation.