Geometry: A Very Short Introduction

Very Short Introductions #695

by Maciej Dunajski

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

This Very Short Introduction 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.

Genres: Mathematics, Nonfiction, Science

176 pages, Paperback

Published April 27, 2022

Reviews

[Wing · Rating 4 out of 5]

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.

[Semih · Rating 5 out of 5]

Bu kitap sayesinde "Very Short Introduction" Serisinin kitaplarını okumaya başladım. İlk sayfadan itibaren sizin hem temel bilgiye sahip olduğunuzu varsayıyor ve basit konuları atlıyor, hem yeterince bilgi sahibi olmadığınızı düşünerek çok derinleşmiyor fakat ele aldığı konuları asla basitleştirmeden kolay çiğnenmeyecek şekilde size sunuyor. En sonda ise akademik anlamda faydalı ve nokta atışı kürate edilmiş kitap önerilerinde bulunuyor. Kitabı bitireli çok olmadı fakat en kısa zamanda dönüp tekrar okumak, bahsettiği konular üzerine daha derin düşünmek istiyorum.
Sıradaki okumalarım Hilbert'in 'Geometry and the Imagination' ve Penrose'un 'Road to Reality'si olacak.

[Lydia · Rating 5 out of 5]

Maciej Dunajski's Geometry, VSI offers a fascinating and comprehensive survey of the field, ranging from the antique foundations (Pythagoras, Euclid), to spheres and hyperbolical surfaces, curvature and manifolds. In further chapters, projective geometry (which relates, for example, to the visual arts via perspective in painting) is discussed, as well as newer geometrical theories, such as the Erlangen programme. In the last chapter, the reader gains an insight into the flat and curved four-dimensional space-times of Einstein's theories of relativity.
All in all, I found this little book to be a challenging and thorough excursion into the intriguing world of geometrical thought and concepts. A worthwhile endeavour!

[Jack · Rating 4 out of 5]

A very short and good introduction to geometry.

[Andy · Rating 2 out of 5]

First half was a good re-intro to geometry. The second half won't make sense if you haven't taken geometry in a while.

I guess the first half counts as "a very short introduction" lol.

[kelly · Rating 3 out of 5]

I only understood one word in twenty but I made it!