{"title":"关于Courant和Robbins的一个“互补问题”","authors":"Jakob Krarup","doi":"10.1016/S0966-8349(98)00043-6","DOIUrl":null,"url":null,"abstract":"<div><p>For a given triangle <em>ABC</em> with ∠<em>A</em>>120°, the Simpson variant of Torricelli’s geometrical construction for solving a problem, allegedly first formulated by Fermat in the early 1600s, will identify a point which incorrectly was claimed by Courant and Robbins (Courant, R., Robbins, H., 1941. <em>What is Mathematics?</em> Oxford University Press, Oxford.) to solve the so-called <em>Complementary problem</em>: <span><math><mtext>min</mtext><mtext>{BX+CX−AX:X∈</mtext><mtext>R</mtext><msup><mi></mi><mn>2</mn></msup><mtext>}</mtext></math></span>. The correct solution for <em>any</em> triangle is provided here.</p></div>","PeriodicalId":100880,"journal":{"name":"Location Science","volume":"6 1","pages":"Pages 337-354"},"PeriodicalIF":0.0000,"publicationDate":"1998-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/S0966-8349(98)00043-6","citationCount":"9","resultStr":"{\"title\":\"On a “Complementary Problem” of Courant and Robbins\",\"authors\":\"Jakob Krarup\",\"doi\":\"10.1016/S0966-8349(98)00043-6\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>For a given triangle <em>ABC</em> with ∠<em>A</em>>120°, the Simpson variant of Torricelli’s geometrical construction for solving a problem, allegedly first formulated by Fermat in the early 1600s, will identify a point which incorrectly was claimed by Courant and Robbins (Courant, R., Robbins, H., 1941. <em>What is Mathematics?</em> Oxford University Press, Oxford.) to solve the so-called <em>Complementary problem</em>: <span><math><mtext>min</mtext><mtext>{BX+CX−AX:X∈</mtext><mtext>R</mtext><msup><mi></mi><mn>2</mn></msup><mtext>}</mtext></math></span>. The correct solution for <em>any</em> triangle is provided here.</p></div>\",\"PeriodicalId\":100880,\"journal\":{\"name\":\"Location Science\",\"volume\":\"6 1\",\"pages\":\"Pages 337-354\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"1998-05-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://sci-hub-pdf.com/10.1016/S0966-8349(98)00043-6\",\"citationCount\":\"9\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Location Science\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S0966834998000436\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Location Science","FirstCategoryId":"1085","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0966834998000436","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
On a “Complementary Problem” of Courant and Robbins
For a given triangle ABC with ∠A>120°, the Simpson variant of Torricelli’s geometrical construction for solving a problem, allegedly first formulated by Fermat in the early 1600s, will identify a point which incorrectly was claimed by Courant and Robbins (Courant, R., Robbins, H., 1941. What is Mathematics? Oxford University Press, Oxford.) to solve the so-called Complementary problem: . The correct solution for any triangle is provided here.
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