Circles, Spheres and Spherical Geometry
暫譯: 圓、球與球面幾何學
Maehara, Hiroshi, Martini, Horst
- 出版商: Birkhauser Boston
- 出版日期: 2024-08-10
- 售價: $3,370
- 貴賓價: 9.5 折 $3,202
- 語言: 英文
- 頁數: 336
- 裝訂: Hardcover - also called cloth, retail trade, or trade
- ISBN: 303162775X
- ISBN-13: 9783031627750
海外代購書籍(需單獨結帳)
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)
這本教科書專注於圓、球體及球面幾何的幾何學。書中使用了各種經典主題作為引言和激勵話題。
本書在第一章以非常簡單的方式開始，討論了反演和立體投影的概念。在這裡，討論了各種經典主題和定理，如斯坦納循環、反演、索迪六邊形、立體投影和龐塞萊的定理。接著，書中深入探討了彎曲公式和圓的半徑之間的關係，重點關注斯坦納圓、平面上互相切觸的四個圓及其他相關概念。接下來，解釋了一些圖論的基本概念。然後，書中探討了四邊形劃分的正交循環表示，詳細討論了布萊特威爾-謝因曼定理（科貝-安德烈耶夫-瑟斯頓定理的擴展）、牛頓的13球問題、凱西定理（托勒密定理的擴展）及其一般化。書的其餘部分專注於球面幾何，包括一章專注於球面上的幾何概率。
本書還包含了作者的新結果和對現有文獻的深刻註解，使讀者更接近研究前沿。每一章結尾都有相關的練習題，難度各異。提供了部分練習題的解答。
這本書適合作為幾何課程的教科書，或作為高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)
前原宏是日本琉球大學的名譽數學教授。他於1986年在東京大學獲得數學博士學位。從1994年到2005年，他擔任東京統計數學研究所的客座教授。2009年至2012年，他在東京的東海大學教育發展研究所擔任教授。他的主要研究興趣在於離散幾何和組合數學。
霍斯特·馬丁尼是德國開姆尼茨科技大學的傑出退休數學教授。他於1988年在德累斯頓大學獲得數學博士學位，並於1993年在耶拿大學獲得資格認證（Habilitation）。他的研究興趣包括凸幾何、離散幾何、泛函分析以及幾何的古典子領域，並應用於優化及相關領域。他的學術追求還延伸至數學史的某些領域。他曾擔任施普林格期刊《代數與幾何貢獻》的主編。2015年，他獲得中國哈爾濱科技大學的榮譽教授職稱。他的興趣包括旅行到具有地理和歷史意義的有趣地方，以及研究不同類型的優秀音樂。
