Geometry by Its Transformations: Lessons Centered on the History from 1800-1855

Baltus, Christopher

Geometry by Its Transformations: Lessons Centered on the History from 1800-1855
  • 出版商: Birkhauser Boston
  • 出版日期: 2025-01-16
  • 售價: $2,190
  • 貴賓價: 9.5 折 $2,081
  • 語言: 英文
  • 頁數: 185
  • 裝訂: Quality Paper - also called trade paper
  • ISBN: 3031722809
  • ISBN-13: 9783031722806

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商品描述

This textbook combines the history of synthetic geometry, centered on the years 1800-1855, with a theorem-proof exposition of the geometry developed in those years. The book starts with the background needed from Euclid's Elements, followed by chapters on transformations, including dilation (similitude), homology, homogeneous coordinates, projective geometry, inversion, the Möbius transformation, and transformation geometry as in French schoolbooks of 1910. Projective geometry is presented by tracing its path through the work of J. V. Poncelet, J. Steiner, and K. G. C. von Staudt. Extensive exercises are included, many from the period studied. The prerequisites for approaching this course are knowledge of high school geometry and enthusiasm for mathematical demonstration.

This textbook is ideal for a college geometry course, for self-study, or as preparation for the study of modern geometry.

商品描述(中文翻譯)

這本教科書結合了合成幾何的歷史，重點在1800年至1855年間，並以定理證明的方式闡述了在這些年份發展的幾何學。書中首先介紹了從歐幾里得的《幾何原本》所需的背景知識，接著是有關變換的章節，包括擴張（相似）、同源、齊次座標、射影幾何、反演、莫比烏斯變換，以及1910年法國教科書中的變換幾何。射影幾何的介紹追溯了J. V. Poncelet、J. Steiner和K. G. C. von Staudt的研究成果。書中包含了大量的練習題，許多來自於所研究的時期。學習這門課程的先決條件是具備高中幾何的知識以及對數學證明的熱情。

這本教科書非常適合用於大學幾何課程、自學，或作為學習現代幾何的準備。

作者簡介

Christopher Baltus has degrees in history (BA), mathematics education (MAT), and mathematics (PhD). After three years of secondary mathematics teaching and two years in the Peace Corps, he taught college mathematics for 36 years. His article "Poncelet's discovery of homology" appeared in Historia Mathematica, May 2023. In retirement, in Poughkeepsie, NY, he and his wife volunteer in an elementary school, he as an in-the-classroom mathematics aide.

作者簡介(中文翻譯)

克里斯多福·巴爾圖斯（Christopher Baltus）擁有歷史（學士）、數學教育（碩士）和數學（博士）學位。在從事三年的中學數學教學和兩年的和平隊服務後，他在大學教授數學達36年。他的文章《龐塞萊的同調發現》於2023年5月刊登在《數學史》（Historia Mathematica）上。退休後，他和妻子在紐約州波基普西的一所小學擔任志工，他在課堂中擔任數學助理。

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