Geometry: A Very Short Introduction (Very Short Introductions)

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it is fascinating when, having thoughts of the debates of wether it was invented or discovered, and thinking about mathematics generally on very basic terms, how the phenomenas of the universe and nature (even in social and economic sciences) are translated from them to us through this language, how we preserve and receive that knowledge through mathematics.

Gowers has written a beautiful book that dabbles in the 'very mathematical', but never actually becomes mathematical.I enjoyed this book so much, and because of its length, I finished it in one "seating" :-) The most important idea that I learned is to think about what a mathematical object DOES rather what it IS. 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. Many of the examples used to introduce to the reader to mathematical thinking are explained more clearly (and in a more engaging fashion) in Fermat's Enigma by Simon Singh. The amount of equations is minimal, but still some maturity is required to fully appreciate the contents.

It takes readers from Euclidean and non-Euclidean geometries, to curved spaces, and the geometry of space-time inside a black hole, and outlines the role geometry plays in the broader context of science and art. Gradually they will get used to only half understanding what their mathemtics teachers say, and after a few more missed leaps they will find that even half is an overestimate. Maciej Dunajski, Professor of Mathematical Physics, University of Cambridge Maciej Dunajski is a Fellow of Clare College http: //www. The author views mathematics through a late-wittgensteinian lense, abstracting from semantics of mathematical terms while focusing on their use. Various geometries are presented, each with particularly engaging examples of problems that are formulated in that particular geometry.while reading the 6th part I remembered of the phrase that was engraved on the door of plato's academy which goes like this: "LET NO ONE IGNORANT OF GEOMETRY ENTER HERE", I wonder how many people were rejected. It is a lovely little book, to be recommended for sixth-formers or first year undergraduates: it will open their eyes to the amazing beauty and power of this ancient and modern subject. This book has vividly elaborated how the complex set of theorems or proofs arise from the basics axioms. For my whole life, I have been HORRIBLE at math (or, at least since the 3rd grade, when fractions were introduced to my life).