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Mathematical Amazements and Surprises: Fascinating Figures and Noteworthy Numbers

Alfred S. Posamentier and Ingmar Lehmann
Prometheus Books
Publication Date: 
Number of Pages: 
[Reviewed by
Charles Ashbacher
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The joy of mathematics is the knowledge of discovery: endless, continuous and often difficult discovery of new knowledge. New areas, new truths and new points of bafflement are what make mathematics a challenge that can never be overcome. This book contains no new outstanding and baffling challenge, the few unsolved problems presented are well known. For example there is a description of the Collatz conjecture.

What it contains is a set of mathematical realities that the mathematical layperson can understand yet can occasionally surprise the professional mathematician that has never ventured into that territory. Some examples of this are in chapter 4: “Geometry Surprises.” If you have never ventured deep into geometry, the sections on Napoleon’s triangle, Morley’s triangle, Desargues’ relationship and Simon’s relationship will describe conclusions that can have you reach a level of at least modest astonishment.

The main parts of the book cover unusual properties of numbers. For example, on page 34 there is the relationship 25 × 92 = 2592. To most followers of the field, nearly all of this material will be familiar. Nevertheless, this is a book that can educate the masses and is an excellent book that the professional can read and ponder at their leisure. It is also an excellent answer to the question, “What do math people read for fun?”

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

The table of contents is not available.