King of Infinite Space: Euclid and His Elements

This is a short book with almost nothing to say. The technical content is fine, nothing that is said is wrong. The problem is that very of little of interest is said, and the manner of saying it is long winded and unclear.In any popular book on mathematics, the main job of the author is to clearly an unobtrusively explain the mathematical ideas; they are the stars of the show, not the words. Berlinski, unfortunately is too taken with his purple prose mongering, and the words get in the way of the mathematical ideas. Everything that is said in this book could be said, and said more clearly, in about one tenth the number of words. Here is just one example, where Berlinski attempts to describe the Poincaré disk model of the hyperbolic plane:"The Poincaré disk divides the Euclidean plane into three distinct regions of space. There are those points lying beyond the disk, those on its circumference, and those in its interior. ... Outside the circle, everything is Euclidean, and inside, everything hyperbolic. Outside and inside are Euclidean from the outside, but hyperbolic from the inside. The inside is accessible from the outside - step right in - but not the outside from the inside - no exit."The paragraph that I extracted the above quote from is about 100 words long, and only the first sentence of thirteen words contains any real content at all, and that content is frankly pretty basic. The rest of the book is the same.If you know anything at all about Euclid or geometry, you're unlikely to learn anything from this book, if you know nothing about Euclid or geometry I think you're likely to be confused about what is essential, and unlikely to come away with any appreciation of the mathematics that Berlinski is trying to write about.

What should have been an accessible and edifying introduction to Euclid and his geometry is ruined by being written in the style of a first year philosophy of science undergraduate trying to impress people in a Paris cafe. The writing leaves little room for Euclid or his geometry in between pointless references to various unrelated works of art and literature. If you are looking for an introduction to Euclidean geometry and its history look elsewhere.

I love David Berlinski, but with this one I bit off a bit more than I could chew. I enjoy him most in his philosopher mode. This a very good book but - obviously - it is about Euclid, and for most people Euclid is a bit dry. Buy it, but be prepared to make a biggish intellectual effort in a pretty rarified atmosphere.

Reading Berlinski is like dining at a buffet of delicious ideas. The courses go quickly, but frequently one must pause in order to savor a particularly juicy bite--then perhaps go back for another helping before proceeding to the next course.I teach mathematics at a school for some of the most intellectually advanced students in the world. I am always looking for ways to help my students discover the world beyond their curriculum...to understand the *why* and the wonder of a particular subject. To ask the big questions. To inspire and nurture their love of mathematics. Berlinski's book fits the bill.Geometry is particularly useful for nurturing critical thinking and logic, and Euclid is its patriarch. In a Geometry class many years ago, I challenged my students with the notion that "there are no circles in the material universe." This intrigued one of my students in particular, and for weeks she was asking follow-up questions as the notions wrought her intellect. One profound notion, and she became a critical thinker. Now, she is an astrophysicist. Never underestimate the life-changing power of a big idea. And Geometry...particularly a la Euclid...is teeming with big morsels.Berlinski really gets this, and his own joy glows in his prose. Berlinski communicates about mathematics like Feynman communicates about physics. Both of them see the big picture, but relish in the details. In one portion Berlinski notes the connection between Platonic forms and Euclid's geometry:"Mathematicians often draw a distinction between concrete and abstract models of Euclidean geometry. In the abstract models of Euclidean geometry, shapes enjoy a pure Platonic existence. The concrete models are in the physical world. Freeways masquerade as straight lines, ink drops as points, amphitheaters as circles, and planetary orbits as ellipses."Berlinski also notes that Euclid not only systematized several key ideas...he also recognized that the ideas themselves *could* be organized. This has had a profound and foundational effect on the history of Western civilization. Of course, Berlinski is not the first to recognize this. But how refreshing and what a pleasure to read the prose of someone who thinks in big ideas and *also* write so wryly and skillfully about them.I agree with Berlinski that when it comes to geometry, no one does it better than Euclid. After all, the elements has remained vivid and relevant for over two millenia, with a profound effect on the Western world. Every literate thinker should spend some quality time in Euclid's classroom. From a modern classroom pedagogical point of view, I think Jacob's "Geometry" (ISBN-13: 978-0716717454) is also quite practical, basically following Euclid's methods. This year, my students will experience all three books. It's gonna be fun.Well done, Dr. Berlinski!

This is not the book to learn Euclidean Geometry. It requires some basic knowledge of Mathematics; it is not a fast read. It is a good discussion of some of the assumptions and limitations of Euclidean Geometry. One of the points it makes is to show how, for all the reputation for being a logically rigorous system in which all assumptions are defined and justified; Euclidean Geometry includes a good dose of plain "common sense" and "self-evident truths" baked into its foundations. The book also moves on to discussing other geometries, of which one gets a flavor, but not much more. The style is a bit quirky, the author often doesn't tell you where he is going; lets things be revealed. I am not a mathematician, so who knows whether I got the right message or not; I enjoyed it and consider it time well spent.