## The King of Infinite Space: Euclid and His ElementsGeometry defines the world around us, helping us make sense of everything from architecture to military science to fashion. And for over two thousand years, geometry has been equated with Euclid’s Elements, arguably the most influential book in the history of mathematics In The King of Infinite Space, renowned mathematics writer David Berlinski provides a concise homage to this elusive mathematician and his staggering achievements. Berlinski shows that, for centuries, scientists and thinkers from Copernicus to Newton to Einstein have relied on Euclid’s axiomatic system, a method of proof still taught in classrooms around the world. Euclid’s use of elemental logic—and the mathematical statements he and others built from it—have dramatically expanded the frontiers of human knowledge.The King of Infinite Space presents a rich, accessible treatment of Euclid and his beautifully simple geometric system, which continues to shape the way we see the world. |

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#### LibraryThing Review

User Review - jimocracy - LibraryThingI liked this book but I need to relearn mathematics (particularly the geometry) to really appreciate this book. Also, the print or ebook format would be more suitable to digest the information. That being said, I am now motivated to reinvigorate my math skills and reread this book! Read full review

#### LibraryThing Review

User Review - GlennBell - LibraryThingI listened to this book as a CD while driving to/from work. This did not work well as some of the book refers to diagrams and equations. In spite of that it was an interesting discussion, which bordered on philosophy at times. The author also has an entertaining sense of humor. Read full review

### Contents

Signs of Men | 1 |

An Abstraction from the Gabble | 11 |

Common Beliefs | 19 |

Darker by Definition | 33 |

The Axioms | 45 |

The Greater Euclid | 57 |

Visible and Invisible Proof | 77 |

The Devils Offer | 91 |

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### Common terms and phrases

abstract AEF and EFD affirms algebra analytic geometry argument Aristotle arithmetic assumptions axiomatic system base their proofs bers blackboard century circle circumference clid’s clidean coincide common notions congruent contrapositive curvature curved David Hilbert definition demonstrated diagram dimensions distinction equal equation equilateral Erlangen program Ernst Steinitz Euclid’s axioms Euclid’s Elements Euclid’s fourth Euclid’s parallel postulate Euclid’s proof Euclidean geometry Euclidean group Euclidean plane Euclidean points false Figure VII.1 flat Gauss geodesics geome Greek hyperbolic plane idea identity illustrations inference infinite integers interior angles isosceles triangle lies evenly logical logicians M’lud mathe mathematician mathematics matician means models of Euclidean moved natural numbers neutral geometry never nineteenth non-Euclidean geometry Omar Khayyám once pair of numbers parallel to CD Poincaré disk pseudosphere Pythagorean theorem real numbers remarked René Thom right angles sense shapes sides space sphere square root straight line suggest surface theory things tion triangle ABC true