{"title":"四面体度量不变量的一个开放问题","authors":"Lu Yang, Zhenbing Zeng","doi":"10.1145/1073884.1073934","DOIUrl":null,"url":null,"abstract":"In ISSAC 2000, P. Lisoněk and R.B. Israel [3] asked whether, for any given positive real constants V,R,A1,A2,A3,A4, there are always finitely many tetrahedra, all having these values as their respective volume, circumradius and four face areas. In this paper we present a negative solution to this problem by constructing a family of tetrahedra T(x,y) where $(x,y)$ varies over a component of a cubic curve such that all tetrahedra T(x,y) share the same volume, circumradius and face areas.","PeriodicalId":311546,"journal":{"name":"Proceedings of the 2005 international symposium on Symbolic and algebraic computation","volume":"23 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2005-07-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"7","resultStr":"{\"title\":\"An open problem on metric invariants of tetrahedra\",\"authors\":\"Lu Yang, Zhenbing Zeng\",\"doi\":\"10.1145/1073884.1073934\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"In ISSAC 2000, P. Lisoněk and R.B. Israel [3] asked whether, for any given positive real constants V,R,A1,A2,A3,A4, there are always finitely many tetrahedra, all having these values as their respective volume, circumradius and four face areas. In this paper we present a negative solution to this problem by constructing a family of tetrahedra T(x,y) where $(x,y)$ varies over a component of a cubic curve such that all tetrahedra T(x,y) share the same volume, circumradius and face areas.\",\"PeriodicalId\":311546,\"journal\":{\"name\":\"Proceedings of the 2005 international symposium on Symbolic and algebraic computation\",\"volume\":\"23 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2005-07-24\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"7\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Proceedings of the 2005 international symposium on Symbolic and algebraic computation\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1145/1073884.1073934\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Proceedings of the 2005 international symposium on Symbolic and algebraic computation","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1145/1073884.1073934","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 7
摘要
在ISSAC 2000中，P. lison k和R. b . Israel[3]问，对于任何给定的正实常数V,R,A1,A2,A3,A4，是否总是有有限多个四面体，它们的体积，周长和四个面面积都有这些值。在本文中，我们通过构造一个四面体族T(x,y)给出了这个问题的一个负解，其中$(x,y)$在三次曲线的一个分量上变化，使得所有的四面体T(x,y)具有相同的体积，圆周半径和面面积。
An open problem on metric invariants of tetrahedra
In ISSAC 2000, P. Lisoněk and R.B. Israel [3] asked whether, for any given positive real constants V,R,A1,A2,A3,A4, there are always finitely many tetrahedra, all having these values as their respective volume, circumradius and four face areas. In this paper we present a negative solution to this problem by constructing a family of tetrahedra T(x,y) where $(x,y)$ varies over a component of a cubic curve such that all tetrahedra T(x,y) share the same volume, circumradius and face areas.
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