Lectures on Euclidean Geometry - Volume 2: Circle Measurement, Transformations, Space Geometry, Conics
Pamfilos, Paris
- 出版商: Springer
- 出版日期: 2024-02-06
- 售價: $3,780
- 貴賓價: 9.5 折 $3,591
- 語言: 英文
- 頁數: 441
- 裝訂: Hardcover - also called cloth, retail trade, or trade
- ISBN: 3031489098
- ISBN-13: 9783031489099
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商品描述
This is a comprehensive two-volumes text on plane and space geometry, transformations and conics, using a synthetic approach. The first volume focuses on Euclidean Geometry of the plane, and the second volume on Circle measurement, Transformations, Space geometry, Conics.
The book is based on lecture notes from more than 30 courses which have been taught over the last 25 years. Using a synthetic approach, it discusses topics in Euclidean geometry ranging from the elementary (axioms and their first consequences), to the complex (the famous theorems of Pappus, Ptolemy, Euler, Steiner, Fermat, Morley, etc.). Through its coverage of a wealth of general and specialized subjects, it provides a comprehensive account of the theory, with chapters devoted to basic properties of simple planar and spatial shapes, transformations of the plane and space, and conic sections. As a result of repeated exposure of the material to students, it answers many frequently asked questions. Particularattention has been given to the didactic method; the text is accompanied by a plethora of figures (more than 2000) and exercises (more than 1400), most of them with solutions or expanded hints. Each chapter also includes numerous references to alternative approaches and specialized literature.
The book is mainly addressed to students in mathematics, physics, engineering, school teachers in these areas, as well as, amateurs and lovers of geometry. Offering a sound and self-sufficient basis for the study of any possible problem in Euclidean geometry, the book can be used to support lectures to the most advanced level, or for self-study.
商品描述(中文翻譯)
這是一本關於平面和空間幾何、變換和圓錐曲線的綜合性兩卷本教材，採用綜合方法。第一卷主要著重於平面的歐幾里得幾何，第二卷則關注圓的測量、變換、空間幾何和圓錐曲線。
本書基於過去25年中教授的30多門課程的講義。採用綜合方法，討論了從基礎（公理及其首要結果）到複雜（帕普斯、托勒密、歐拉、斯坦納、費馬、莫利等著名定理）的歐幾里得幾何主題。通過對各種一般和專門主題的全面涵蓋，提供了該理論的全面介紹，其中包括對簡單平面和空間形狀的基本性質、平面和空間的變換以及圓錐曲線的章節。由於學生多次接觸這些材料，本書回答了許多常見問題。特別重視教學方法，本文配有大量圖片（超過2000張）和練習題（超過1400道），其中大部分都有解答或詳細提示。每章還包括對其他方法和專門文獻的大量參考。
本書主要針對數學、物理、工程的學生，以及這些領域的學校教師、業餘愛好者和愛好幾何的人。本書提供了研究歐幾里得幾何中任何可能問題的堅實和自給自足的基礎，可用於支持最高級別的講座或自學。
作者簡介
Paris Pamfilos was born in Athens, Greece, and studied in Athens, Bonn and Cologne. His Ph.D. (in Differential Geometry) was obtained in Cologne under the supervision of Prof. Peter Dombrowski. He has held various assistant, researcher and visiting-professor positions at the Universities of Bonn, Essen, and Nicosia, and was an associate professor in the Department of Mathematics, University of Crete. He enjoys teaching, programming, and (in the infrequent remaining free time) doing his philosophical parerga. He speaks Greek, German, French, English, Italian and Russian. His main interest is in Geometry, especially Euclidean Geometry, a subject that he has lectured on for more than 25 years, and on which he continues to publish original articles.
作者簡介(中文翻譯)
Paris Pamfilos出生於希臘雅典，並在雅典、波恩和科隆學習。他在科隆獲得了博士學位（在微分幾何學方面），並在Peter Dombrowski教授的指導下完成。他曾在波恩大學、埃森大學和尼科西亞大學擔任助理、研究員和訪問教授職位，並曾是克里特大學數學系的副教授。他喜歡教學、編程，並在極少數的空閒時間裡從事他的哲學副業。他會說希臘語、德語、法語、英語、意大利語和俄語。他的主要興趣是幾何學，特別是歐幾里得幾何學，這是他已經講授了25多年的科目，並且他繼續發表原創文章。
