Icons of Mathematics by Claudi Alsina and Roger Nelsen
This book can be enjoyed by amateurs and professionals alike.
This unusual work is a welcome addition to any library; all readers will find something to inform and even delight them. -- CHOICE
-- Mathematical Reviews
It is an excellent study item to prepare high school teachers of geometry. People currently teaching high school geometry will find it a valuable resource for more challenging problems to present to the students. Others with just an interest in geometry will find it worthy of an in-depth look.
---Charles Ashbacher, Journal of Recreational Mathematics
The authors present 20 icons of mathematics--that is, geometrical shapes such as the right triangle, the Venn diagram, and the yang and yin symbol--and explore mathematical results associated with them. As with their previous books (Charming Proofs, When Less is More, Math Made Visual
) proofs are visual whenever possible. The results require no more than high-school mathematics to appreciate and many of them will be new even to experienced readers. For example, I never knew the inverse Pythagorean theorem, that (1/a)^2 + (1/b)^2 = (1/h)^2 where a, b, and h are the lengths, respectively, of the legs and the altitude to the hypotenuse of a right triangle. If asked to prove it, I might have used something crass like trigonometry, but there is a better visual proof. Besides theorems and proofs, the book contains many illustrations and it gives connections of the icons to the world outside of mathematics. There are also problems at the end of each chapter, with solutions provided in an appendix. The book could be used by students in courses in problem solving, mathematical reasoning, or mathematics for the liberal arts.