Number Treasury 3: Investigations, Facts and Conjectures about More than 100 Number Families

This is a book that can serve as a resource for math classes from the later elementary grades all the way through college. It contains a set of descriptions and exercises involving over 100 number families. Some, such as the Fibonacci numbers, are well known. Yet, others are very obscure. For example, the last two are the “tautonymic” and “Lagado” numbers. Great fodder for people that are on the lookout for new number categories to explore.

With few exceptions, all of the numbers are integers and the exercises require only arithmetic operations on them. If the size of the numbers is kept low, then students in elementary grades can perform the investigations on their own. Many of the exercises involve looking for the presence and absence of patterns in the numbers. Solutions to all of the exercises are given in one of the last sections. But instructors of college classes in number theory can also find material for use in exercises where proofs are expected.

It is indeed an extremely rare occasion when a book can be used as a reference through such a broad level of math classes. This one is an existence proof. 

Charles Ashbacher splits his time between consulting with industry in projects involving math and computers, and teaching college classes. In his spare time, he reads about these things and helps his daughter in her lawn care business.