Circles, Spheres and Spherical Geometry
Maehara, Hiroshi, Martini, Horst
- 出版商: Birkhauser Boston
- 出版日期: 2024-08-10
- 售價: $3,310
- 貴賓價: 9.5 折 $3,145
- 語言: 英文
- 頁數: 336
- 裝訂: Hardcover - also called cloth, retail trade, or trade
- ISBN: 303162775X
- ISBN-13: 9783031627750
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相關主題
商品描述
This textbook focuses on the geometry of circles, spheres, and spherical geometry. Various classic themes are used as introductory and motivating topics.
The book begins very simply for the reader in the first chapter discussing the notions of inversion and stereographic projection. Here, various classical topics and theorems such as Steiner cycles, inversion, Soddy's hexlet, stereographic projection and Poncelet's porism are discussed. The book then delves into Bend formulas and the relation of radii of circles, focusing on Steiner circles, mutually tangent four circles in the plane and other related notions. Next, some fundamental concepts of graph theory are explained. The book then proceeds to explore orthogonal-cycle representation of quadrangulations, giving detailed discussions of the Brightwell-Scheinerman theorem (an extension of the Koebe-Andreev-Thurston theorem), Newton's 13-balls-problem, Casey's theorem (an extension of Ptolemy's theorem) and its generalizations. The remainder of the book is devoted to spherical geometry including a chapter focusing on geometric probability on the sphere.
The book also contains new results of the authors and insightful notes on the existing literature, bringing the reader closer to the research front. Each chapter concludes with related exercises of varying levels of difficulty. Solutions to selected exercises are provided.
This book is suitable to be used as textbook for a geometry course or alternatively as basis for a seminar for both advanced undergraduate and graduate students alike.
商品描述(中文翻譯)
本教科書專注於圓、球體和球面幾何學。各種經典主題被用作入門和激勵性的話題。
該書在第一章非常簡單地討論了反演和立體投影的概念，為讀者提供了很好的起點。在這裡，討論了各種經典主題和定理，如斯坦納環、反演、索迪六角形、立體投影和庞斯莱定理。然後，書中深入探討了本德公式和圓的半徑關係，重點關注斯坦納圓、平面上互相相切的四個圓和其他相關概念。接下來，解釋了一些圖論的基本概念。然後，書中繼續探討四邊形的正交循環表示，詳細討論了布萊特威爾-謝因曼定理（是科比-安德烈夫-瑟斯頓定理的擴展）、牛頓的13球問題、凱西定理（是托勒密定理的擴展）及其推廣。書的其餘部分專注於球面幾何學，包括一章專注於球面上的幾何概率。
該書還包含作者的新成果和對現有文獻的深入註解，使讀者更接近研究前沿。每章結尾都有相關的練習題，難度各不相同。提供了部分練習題的解答。
本書適合作為幾何學課程的教科書，也可以作為高年級本科生和研究生研討會的基礎。
作者簡介
Hiroshi Maehara is an emeritus professor of mathematics at Ryukyu University in Japan. He obtained his Ph.D. in mathematics from Tokyo University in 1986. He was a guest professor at the Institute of Statistical Mathematics in Tokyo from 1994 to 2005. He also held professor position at the Research Institute of Education Development of Tokai University in Tokyo from 2009 to 2012. His main research interests lie in discrete geometry and combinatorics.
Horst Martini is a distinguished retired professor of mathematics from the Chemnitz University of Technology in Germany. He obtained his Ph.D. in mathematics from the University of Dresden 1988, followed by his Habilitation from the University of Jena in 1993. His research interests include convex geometry, discrete geometry, functional analysis, and classical subfields of geometry, as well as applications in optimization and related fields. His scholarly pursuits also extend to certain fields in history of mathematics. He previously served as editor in chief of the Springer journal Contributions to Algebra and Geometry. In 2015, he received an honorary professorship from the Harbin University for Science and Technology in China. His passions include travelling to interesting places of geographical and historical significance and studying different genres of good music.
作者簡介(中文翻譯)
廣島前原（Hiroshi Maehara）是日本琉球大學的名譽數學教授。他於1986年從東京大學獲得數學博士學位。他曾在東京的統計數學研究所擔任客座教授，任期從1994年到2005年。他還曾在東京的東海大學教育發展研究所擔任教授，任期從2009年到2012年。他的主要研究興趣包括離散幾何和組合數學。
Horst Martini是德國克姆尼茨科技大學的傑出退休數學教授。他於1988年從德累斯頓大學獲得數學博士學位，並於1993年在耶拿大學獲得博士後資格。他的研究興趣包括凸幾何、離散幾何、泛函分析和幾何的經典子領域，以及在優化和相關領域的應用。他的學術追求還延伸到數學歷史的某些領域。他曾擔任Springer期刊《Contributions to Algebra and Geometry》的主編。2015年，他獲得中國哈爾濱理工大學的名譽教授職位。他的興趣包括前往地理和歷史上有意義的有趣地方旅行，並研究不同類型的好音樂。
