Pretty good book. Contains proofs of some theorems and shows wonderfully illustrated images that demonstrate these ideas. ( )

Geometry books are the books where overleaf-placed figures are at their most reader-frustrating, and this volume is no exception. Otherwise, its high production quality and extensive color artwork do make it a thing of beauty. Besides (mostly Euclidean) geometry, it includes some number theory.

If you want to love, or even like, geometry again, then this book might just do it. Beautiful Geometry pairs Maor’s elegant proofs with Jost’s vivid illustrations to help the layman understand geometry. They start with the basics—point, lines, and shapes—and work their way to Euclid, then prime geometry, infinite series, the golden ratio, experimentation with pi, parabolic geometry, and even fractals and epicycloids. There’s a fair amount of history on famous geometers and how they arrived at their discoveries. At the very least, if the proofs bore you, you can always marvel at the visuals. They’re worth the cost of admission. A quick and pretty book. ( )

When I was a single digit prime number, I bought a ten cent comic book that was different from all the rest. It was called Donald Duck in Mathematics Land, and it was all about the absolute magic of numbers in geometry. It was a treasure and I still have it, carefully pressed flat and kept from the ravages of light.

Now just 50 years later, come a couple of number theory heavyweights, one in math and one in math-based art, one-upping Donald. Beautiful Geometry makes art of science and sense of math.

The science dates back to the golden age of Greece, that less-than-hundred year period where the Greeks ruled the intellectual world, spent their time racking up truckloads of discoveries, and elevating science to unheard of heights. Interestingly, there were no generalizations in the approach of the Greeks. Each time they discovered a variation or new instance, it became a new theorem, even though it might describe the same phenomenon as another theorem. Nothing was insignificant in the golden age. And though they did not have a real number system to work with (that had to wait till 1200 AD), and a lot of what they proposed was (ultimately) incorrect, they made remarkable contributions and remarkable progress.

There are 51 three page chapters, each illustrating magic of some sort in numbers and their geometric origin and/or display. The middle page of each chapter is a full page color work of art employing the topic of the chapter.

For those not mathematically inclined, it will be work to understand it all. But it is written as simply and basically as mathematics can be, and the overall effect is one of childlike fascination with the magic of it all. From equivalence to symmetry to infinity, it’s all here, updating and collecting facets of number theory that have occupied and obsessed the minds of mathematicians and philosophers for more than 2000 years. ( )

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