Geometry: A Very Short Introduction – Maciej Dunajski – (geometry 中文) (geometry)

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Geometry A Very Short Introsrcction

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《Geometry: A Very Short Introsrcction》—— Maciej Dunajski

The study of geometry is at least 2500 years old, and it is within this field that the concept of mathematical proof – desrcctive reasoning from a set of axioms – first arose. To this day geometry remains a very active area of research in mathematics.

This Very Short Introsrcction covers the areas of mathematics falling under geometry, starting with topics such as Euclidean and non-Euclidean geometries, and ranging to curved spaces, projective geometry in Renaissance art, and geometry of space-time inside a black hole. Starting from the basics, Maciej Dunajski proceeds from concrete examples (of mathematical objects like Platonic solids, or theorems like the Pythagorean theorem) to general principles. Throughout, he outlines the role geometry plays in the broader context of science and art.

关键词：几何：非常简短的介绍;

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A very short and good introsrcction to geometry.

The strength of the book is that it gives the reader chances to think as Professor Dunajski keeps jumping steps and invites the reader to fill in the gaps. Most of the time I can do it but beginning from the section on projective geometry things become quite abstract. It then ventures into very difficult topics but the author quite clearly specifies those areas that are there just to give the reader a taste of what they are like. The last chapter on space-time is dense and seems rather rushed. I am a doctor by trade and my mathematics is only at high school level. I do agree with the author that this is all that is needed to understand what he wants the reader to appreciate. Many bits are quite illuminating (e.g. hyperbolic plane, parameterization, affine group). Four stars.