{"title":"拿破仑四边形外向定理的发展","authors":"Mashadi, Chitra Valentika, S. Gemawati, Hasriati","doi":"10.11648/j.pamj.20170604.11","DOIUrl":null,"url":null,"abstract":"In this article we discuss Napoleon’s theorem on the rectangles having two pairs of parallel sides for the case of outside direction. The proof of Napoleon’s theorem is carried out using a congruence approach. In the last section we discuss the development of Napoleon’s theorem on a quadrilateral by drawing a square from the midpoint of a line connecting each of the angle points of each square, where each of the squares is constructed on any quadrilateral and forming a square by using the row line concept.","PeriodicalId":46057,"journal":{"name":"Italian Journal of Pure and Applied Mathematics","volume":null,"pages":null},"PeriodicalIF":0.2000,"publicationDate":"2017-07-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":"{\"title\":\"The Development of Napoleon’s Theorem on the Quadrilateral in Case of Outside Direction\",\"authors\":\"Mashadi, Chitra Valentika, S. Gemawati, Hasriati\",\"doi\":\"10.11648/j.pamj.20170604.11\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"In this article we discuss Napoleon’s theorem on the rectangles having two pairs of parallel sides for the case of outside direction. The proof of Napoleon’s theorem is carried out using a congruence approach. In the last section we discuss the development of Napoleon’s theorem on a quadrilateral by drawing a square from the midpoint of a line connecting each of the angle points of each square, where each of the squares is constructed on any quadrilateral and forming a square by using the row line concept.\",\"PeriodicalId\":46057,\"journal\":{\"name\":\"Italian Journal of Pure and Applied Mathematics\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.2000,\"publicationDate\":\"2017-07-18\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"1\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Italian Journal of Pure and Applied Mathematics\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.11648/j.pamj.20170604.11\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q4\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Italian Journal of Pure and Applied Mathematics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.11648/j.pamj.20170604.11","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"MATHEMATICS","Score":null,"Total":0}
The Development of Napoleon’s Theorem on the Quadrilateral in Case of Outside Direction
In this article we discuss Napoleon’s theorem on the rectangles having two pairs of parallel sides for the case of outside direction. The proof of Napoleon’s theorem is carried out using a congruence approach. In the last section we discuss the development of Napoleon’s theorem on a quadrilateral by drawing a square from the midpoint of a line connecting each of the angle points of each square, where each of the squares is constructed on any quadrilateral and forming a square by using the row line concept.
期刊介绍:
The “Italian Journal of Pure and Applied Mathematics” publishes original research works containing significant results in the field of pure and applied mathematics.