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Putting Two and Two Together

Burkard Polster and Marty Ross
Publication Date: 
Number of Pages: 
[Reviewed by
Fabio Mainardi
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Like the authors’ previous book (A Dingo Ate My Math Book), this volume is a collection of columns that appeared between 2007 and 2014 in Melbourne’s Age newspaper. Those columns were intended for a general reader, and no mathematical background is needed to enjoy the 64 short chapters (~4 pages each). Perhaps some background on the Australian society would be more useful to the reader, as the authors make plenty of references to Australian sports, cities, buildings, and education system.
What does this book talk about? Nearly everything. Just to cite two of my favorites: the optimal way to lace your shoes, and why pictures often refuse to hang straight. 
I also love Chapter 4, where they consider an infinite set of wooden blocks of dimensions 1 x 1 x 1, 1 x 1/2 x 1/2, 1 x 1/3 x 1/3, and so on. After reminding the reader of the convergence properties of the harmonic series, they conclude the chapter noting that it would take a finite amount of wood to make the blocks, but it would require an infinite amount of paint to paint them! Even stranger, if we hollow the blocks, “it would only require a finite amount of paint to fill them: wouldn’t that effectively paint that same infinite area?”. This is a nice puzzle to ponder. Speaking of which, each chapter closes with a puzzle to ponder, and all the solutions are given at the end of the book.
All the chapters are nicely illustrated, with pictures or drawings helping to visualize and understand the reasoning throughout. By the way, several chapters are about the shapes of buildings located in various places in Australia, so it’s definitely handy to have their pictures at the beginning of the chapter.
I think this is a book that is never boring, always entertaining and humorous, and often positively surprising. 
Fabio Mainardi ([email protected]) works as senior data scientist at Nestlé Research, Lausanne. After a PhD in number theory, he has been working as applied mathematician in R&D divisions of different companies. His mathematical interests include statistical models, probability, discrete mathematics and optimization theory.