Geometric Transformations

Gelca, Răzvan, Onişor, Ionuţ, Shine, Carlos Yuzo

Geometric Transformations
  • 出版商: Springer
  • 出版日期: 2023-11-16
  • 售價: $2,740
  • 貴賓價: 9.5 折 $2,603
  • 語言: 英文
  • 頁數: 578
  • 裝訂: Quality Paper - also called trade paper
  • ISBN: 3030978486
  • ISBN-13: 9783030978488

    • 海外代購書籍(需單獨結帳)

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商品描述

This textbook teaches the transformations of plane Euclidean geometry through problems, offering a transformation-based perspective on problems that have appeared in recent years at mathematics competitions around the globe, as well as on some classical examples and theorems. It is based on the combined teaching experience of the authors (coaches of several Mathematical Olympiad teams in Brazil, Romania and the USA) and presents comprehensive theoretical discussions of isometries, homotheties and spiral similarities, and inversions, all illustrated by examples and followed by myriad problems left for the reader to solve. These problems were carefully selected and arranged to introduce students to the topics by gradually moving from basic to expert level. Most of them have appeared in competitions such as Mathematical Olympiads or in mathematical journals aimed at an audience interested in mathematics competitions, while some are fundamental facts of mathematics discussed in the framework of geometric transformations. The book offers a global view of the geometric content of today's mathematics competitions, bringing many new methods and ideas to the attention of the public.
Talented high school and middle school students seeking to improve their problem-solving skills can benefit from this book, as well as high school and college instructors who want to add nonstandard questions to their courses. People who enjoy solving elementary math problems as a hobby will also enjoy this work.

商品描述(中文翻譯)

這本教科書透過問題教授平面歐幾里得幾何的變換，提供了一種基於變換的視角，針對近年來在全球數學競賽中出現的問題，以及一些經典範例和定理。它基於作者的綜合教學經驗（巴西、羅馬尼亞和美國的數學奧林匹克隊教練），並對等距變換、相似變換、螺旋相似和反演進行了全面的理論討論，所有內容均以範例說明，並附有大量留給讀者解答的問題。這些問題經過精心挑選和安排，旨在通過逐步從基礎到專家的方式引導學生了解主題。大多數問題曾出現在數學奧林匹克等競賽中，或在針對對數學競賽感興趣的讀者的數學期刊中發表，而有些則是幾何變換框架下討論的數學基本事實。這本書提供了當今數學競賽幾何內容的全球視野，將許多新方法和想法帶入公眾視野。

有才華的高中和中學學生希望提高他們的解題能力，教師也可以從這本書中受益，特別是那些希望在課程中加入非標準問題的高中和大學講師。喜歡將解決基礎數學問題作為愛好的讀者也會喜歡這部作品。

作者簡介

Razvan Gelca is a Professor at Texas Tech University, USA, and holds a PhD in Mathematics from the University of Iowa, USA (1997). He coached the US International Mathematical Olympiad Team and co-authored, with Titu Andreescu, the books "Putnam and Beyond," published by Springer, and "Mathematical Olympiad Challenges" (Birkhäuser), both now in their 2nd edition.
Ionut Onisor is a Professor at the Colegiul National de Informatica Tudor Vianu, Romania.
Carlos Yuzo Shine teaches at the Colégio Etapa, Brazil. He studied Production Engineering at the University of São Paulo, Brazil, and holds a Master's degree (2018) from Texas A&M University, USA. He has been coordinating and coaching Mathematical Olympiad teams in Brazil since 2002.

作者簡介(中文翻譯)

Razvan Gelca 是美國德州科技大學的教授，並於美國愛荷華大學獲得數學博士學位（1997年）。他曾指導美國國際數學奧林匹克隊，並與 Titu Andreescu 共同撰寫了由 Springer 出版的《Putnam and Beyond》及由 Birkhäuser 出版的《Mathematical Olympiad Challenges》，這兩本書目前均已進入第二版。

Ionut Onisor 是羅馬尼亞圖多爾·維亞努國立資訊學院的教授。

Carlos Yuzo Shine 在巴西的 Colégio Etapa 教學。他在巴西聖保羅大學學習生產工程，並於美國德州農工大學獲得碩士學位（2018年）。自2002年以來，他一直在巴西協調和指導數學奧林匹克隊。

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