Mathematical Curiosities: A Treasure Trove Of Unexpected Entertainments by Alfred S. Posamentier and Ingmar Lehmann (book review).

I should say from the start that anyone picking up ‘Mathematical Curiosities’ is that you must have a love of numbers and certainly an aptitude towards mathematics. If you don’t recognise that a dot not on the baseline of a sentence but the centre ‘ˑ’ is an alternative for the ‘x’ or multiplication sign or the exclamation mark ‘!’ is used to indicate a factorial number, then this book might not be for you. I haven’t seen the first notation since college and that’s a while back.



It’s not as though this book is particularly complicated because authors Alfred S. Posamentier and Ingmar Lehmann lay out all their examples and proofs for you to peruse and test. They say it’s simple but I would also add a little knowledge of trigonometry and statistics would help you follow their formulas. They are also not beyond suggesting a computer or calculator to do the number-crunching from time to time but not to make a habit of it. I do think with the computer, a spreadsheet program might be handier than the regular calculator, especially if you’re going to rely on formulas.

Mathematicians are always seeking out patterns in numbers. A lot of the time it’s for creating prime numbers, mostly used for encryption in computers. What these authors point out is the properties of various numbers and how you can use this knowledge in calculations. We’ve covered the number 11 with another review  fairly recently but there is a lot more given to what you can do with it. There’s even some tricks with fractions that I was never taught at school for reducing large numbers to smaller fractions that I will certainly remember although I tried it on a couple numbers where I knew the answer, that it didn’t appear to work. According this book, with double number fractions, if you took away the top right and bottom left numbers you reduce to the smallest nominator. However, it doesn’t work with 25/50 because that becomes 2/0 which obviously isn’t half. It works well with big fractions but this came about after me thinking about it.

A lot of the mathematical curiosities do need a lot of thinking and working out. There’s an entire section devoted to working through 90 problems, although I wish they’d but the answers next to them or at least gave the page reference so it would serve the same purpose. I did do a few of them but I’d be here a year of Sundays if I had a go at all of them. I will use one as an example about the odds of 35 people together having the same birthday. They use the US presidents as an example of this, both for birthdays and deaths but let’s concentrate on the former. One thing they omitted that does improve the odds is the fact that the majority of people are born at certain times of the year. There are times when you do need to know a little more than maths theory, although I have to confess here it was something I remembered from elsewhere.

There are a lot of terms noted throughout this book that I wish the authors had given a glossary to for easy reference but it makes for an interesting learning curve.

This book would really suit those with a mathematical disposition and if your sprogs are and want something to challenge themselves or learn and pass the information to others then it will be well read.

GF Willmetts

September 2014

(pub: Prometheus Books. 338 page enlarged paperback. Price: $19.95 (US), $21.00 (CAN), £16.99 (UK). ISBN: 978-1-61614-931-4)

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