Nice book on geometry to gift an undergraduate in mathematics

Question

I would like some suggestions on a nice book on geometry to gift an undergraduate. I'm not searching for something that is common: I need something new and exciting. Suggestions?

Answer 1

I love this one. It is one of the most stimulating books on geometry that I have ever read: it is strikingly innovative and really enjoyable (also, it does not require a particularly advanced background).

From the book description:

New Horizons in Geometry represents the fruits of 15 years of work in geometry by a remarkable team of prize-winning authors—Tom Apostol and Mamikon Mnatsakanian. It serves as a capstone to an amazing collaboration. Apostol and Mamikon provide fresh and powerful insights into geometry that requires only a modest background in mathematics. Using new and intuitively rich methods, they give beautifully illustrated proofs of results, the majority of which are new, and frequently develop extensions of familiar theorems that are often surprising and sometimes astounding. It is mathematical exposition of the highest order.

The hundreds of full color illustrations by Mamikon are visually enticing and provide great motivation to read further and savor the wonderful results. Lengths, areas, and volumes of curves, surfaces, and solids are explored from a visually captivating perspective. It is an understatement to say that Apostol and Mamikon have breathed new life into geometry.

Answer 2

Green Lion Press's:

• Euclid's Elements: All Thirteen Books in One Volume

or

• The Bones: A handy where-to-find-it pocket reference companion to Euclid's Elements

The latter is very unique; it's all the propositions and diagrams, but without the detailed proofs.

Answer 3

Another very nice book is Indra's pearls The vision of Felix Klein with a preview at google.

Answer 4

I'll recommend Geometry Revisited by H. S. M. Coxeter and S. L. Greitzer.