{"title":"如何计算旋转双曲固体的体积","authors":"Robert L. Lamphere","doi":"10.1080/07468342.2023.2276651","DOIUrl":null,"url":null,"abstract":"SummaryWe give two formulas for finding the volumes of solids of revolution in hyperbolic geometry. We also prove each formula. These formulas and their proofs are analogous to the ones in Euclidean geometry. We also provide several examples of their use. These formulas may be useful in college geometry courses that include a section on hyperbolic geometry. Additional informationNotes on contributorsRobert L. Lamphere Robert L. Lamphere (robert.Lamphere@kctcs.edu) received his Masters in mathematics from University of Illinois and his Masters in computer science from Northern Illinois University. He is an emeritus professor at the Elizabethtown Community and Technical College. His research interests are Non-Euclidean geometry and Newton’s Principia.","PeriodicalId":38710,"journal":{"name":"College Mathematics Journal","volume":null,"pages":null},"PeriodicalIF":0.0000,"publicationDate":"2023-11-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"How to Compute the Volumes of Hyperbolic Solids of Revolution\",\"authors\":\"Robert L. Lamphere\",\"doi\":\"10.1080/07468342.2023.2276651\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"SummaryWe give two formulas for finding the volumes of solids of revolution in hyperbolic geometry. We also prove each formula. These formulas and their proofs are analogous to the ones in Euclidean geometry. We also provide several examples of their use. These formulas may be useful in college geometry courses that include a section on hyperbolic geometry. Additional informationNotes on contributorsRobert L. Lamphere Robert L. Lamphere (robert.Lamphere@kctcs.edu) received his Masters in mathematics from University of Illinois and his Masters in computer science from Northern Illinois University. He is an emeritus professor at the Elizabethtown Community and Technical College. His research interests are Non-Euclidean geometry and Newton’s Principia.\",\"PeriodicalId\":38710,\"journal\":{\"name\":\"College Mathematics Journal\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2023-11-10\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"College Mathematics Journal\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1080/07468342.2023.2276651\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q4\",\"JCRName\":\"Social Sciences\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"College Mathematics Journal","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1080/07468342.2023.2276651","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"Social Sciences","Score":null,"Total":0}
引用次数: 0
摘要
摘要给出了双曲几何中求旋转立体体积的两个公式。我们还证明了每个公式。这些公式及其证明类似于欧几里得几何中的公式。我们还提供了几个使用它们的例子。这些公式在包含双曲几何部分的大学几何课程中可能很有用。Robert L. Lamphere (robert.Lamphere@kctcs.edu)获得伊利诺伊大学数学硕士学位和北伊利诺伊大学计算机科学硕士学位。他是伊丽莎白镇社区和技术学院的名誉教授。他的研究兴趣是非欧几里得几何和牛顿原理。
How to Compute the Volumes of Hyperbolic Solids of Revolution
SummaryWe give two formulas for finding the volumes of solids of revolution in hyperbolic geometry. We also prove each formula. These formulas and their proofs are analogous to the ones in Euclidean geometry. We also provide several examples of their use. These formulas may be useful in college geometry courses that include a section on hyperbolic geometry. Additional informationNotes on contributorsRobert L. Lamphere Robert L. Lamphere (robert.Lamphere@kctcs.edu) received his Masters in mathematics from University of Illinois and his Masters in computer science from Northern Illinois University. He is an emeritus professor at the Elizabethtown Community and Technical College. His research interests are Non-Euclidean geometry and Newton’s Principia.
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