The Four Pillars of Geometry 2025 pdf epub mobi 电子书

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The Four Pillars of Geometry 2025 pdf epub mobi 电子书著者简介

John Stillwell is Professor of Mathematics at the University of San Francisco. He is the author of several highly regarded books published by Springer, including Elements of Number Theory (2003), Mathematics and Its History (Second Edition, 2002), Numbers and Geometry (1998) and Elements of Algebra (1994).

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发表于2025-03-04

The Four Pillars of Geometry 2025 pdf epub mobi 电子书

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一般而言，要想找到一本体现某些真正的几何思想精髓的书并不是很容易，但我还是有幸读到了John Stillwell的这本《Four Pillars of Geometry》，读完后至今仍令人荡气回肠！这本书不算太艰深，但真的不同于传统的介绍几何的读物，特别是展现了很多本科生并不熟悉的视角，使人...

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出版者:Springer

作者:John Stillwell

出品人:

页数:229

译者:

出版时间:2010-12-1

价格:USD 54.95

装帧:Paperback

isbn号码:9781441920638

丛书系列:Undergraduate Texts in Mathematics

图书标签: 数学几何 Geometry Stillwell Springer Mathematics 數學几何与拓扑

The Four Pillars of Geometry 2025 pdf epub mobi 电子书图书描述

For two millennia the right way to teach geometry was the Euclidean approach, and in many respects, this is still the case. But in the 1950s the cry "Down with triangles!" was heard in France and new geometry books appeared, packed with linear algebra but with no diagrams. Was this the new right approach? Or was the right approach still something else, perhaps transformation groups?

The Four Pillars of Geometry approaches geometry in four different ways, spending two chapters on each. This makes the subject accessible to readers of all mathematical tastes, from the visual to the algebraic. Not only does each approach offer a different view; the combination of viewpoints yields insights not available in most books at this level. For example, it is shown how algebra emerges from projective geometry, and how the hyperbolic plane emerges from the real projective line.

The author begins with Euclid-style construction and axiomatics, then proceeds to linear algebra when it becomes convenient to replace tortuous arguments with simple calculations. Next, he uses projective geometry to explain why objects look the way they do, as well as to explain why geometry is entangled with algebra. And lastly, the author introduces transformation groups---not only to clarify the differences between geometries, but also to exhibit geometries that are unexpectedly the same.

All readers are sure to find something new in this attractive text, which is abundantly supplemented with figures and exercises. This book will be useful for an undergraduate geometry course, a capstone course, or a course aimed at future high school teachers.

The Four Pillars of Geometry 2025 pdf epub mobi 电子书

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