New Dilemma: Universal Book vs. the Internet
An old song claimed: "The times they are a changing...." When a beginning math teacher, I always had at hand certain "comprehensive" dictionaries or encyclopeadias. These tomes helped me respond to student questions, do a quick study on new ideas, and browse at random through paths of neat ideas. Now, these books are replaced by the Internet; it is easy to do a "google" before reaching for a reference book.
Nonetheless, this week's review focuses on such a reference book...primarily because I still like bookstheir feel, their organization, and their supposed validity. If you are looking for a comprehensive resource, I recommend David Darling's The Universal Book of Mathematics: From Abracadabra to Zeno's Paradoxes (2004). Though a noted astronomer, Darling wrote this book on mathematics because of the "wonderful and weird possibilities" of mathematical topics. In fact, he describes the book as a "collection of mathematical oddities, delights, whimsies, and profundities."
The book is a fun "browse," to borrow the term from the Internet world. It contains 1800 interesting explorations of mathematical ideas, alphabetically ranging from historical notes to understandable explanations to problems for exploration to biographies.
Consider these random examples...do you know what they are?
 ABC Conjecture
 Aristotle's wheel
 Champernowne's number
 Dupin cyclide
 Gilbreath's conjecture
 Mascheroni construction
 Perrin sequence
 Reuleaux triangle
 Sperner's lemma
 Vinculum
How many of these did you know? Sure, you could look them up on the Internet now that you know the names, but how would you know the names if not for this book? Ergo, fun books like these will always have a place (and use) in my life as a mathematics teacher....and hopefully yours as well.
NOTE: This book can be picked up for less than $10 online...what a bargain, about $0.0055 per neat idea.
