December 11, 2017

Mathematical Curiosities by Alfred S. Posamentier and Ingmar Lehmann

On sale now.

Today, we’ll delve into the exciting and exhilarating world of mathematics. Wait, wait, come back…

This week we’ll be looking at Mathematical Curiosities: A Treasure Trove of Unexpected Entertainments out from Prometheus Books by Alfred S. Posamentier and Ingmar Lehmann.

Fans of this space will also remember our reviews of The Glorious Golden Ratio, The Secrets of Triangles and Magnificent Mistakes also by Lehmann and Posamentier.

Mathematical Curiosities aptly demonstrates that math doesn’t have to journey into its higher dimensions to be bizarre. The authors start with some great examples straight out of elementary school math class and assume no prior knowledge of algebra and higher mathematics. There’s lots to delve into here, and the authors take the reader on an exciting (yes, math can be exciting!) journey through alternate counting systems, mathematical curiosities and peculiarities, and much more.

Some of our faves:

-      Did you know that you can (sometimes) arrive at the right answer… using the wrong method? These “howlers” come straight out of math class, one of which is depicted in Bogdanov-Belski’s 1895 painting entitled “A Difficult Assignment.”

-      The number eight is the only cube number smaller than a square number by one. The Chinese consider this to be a “lucky” number for this reason. Further wackiness ensues with much larger numbers along the decimal scale, and one must remember that in some cases, it took centuries to prove that such things were true through an infinite series of numbers.

-      The reverse of the prime number 193,939 – 939,391 – is also prime. Four other variations of the same number – 919,393, 391,939, 939,193 and 393,919 are also prime. Then there’s the world of mersene primes, perfect numbers and much more…

And speaking of alternate counting systems, some of the ancient systems of mathematics, such as the Babylonian system of long division and multiplication are also addressed in the book.

Some mysteries are recently solved or remain open, and examples abound in everyday life. One great example addressed in the book is Kepler’s Conjecture, only recently solved in 1998. Kepler’s Conjecture addresses the most efficient use of space when stacking spherical objects, be it oranges or cannon balls. A seemingly straight forward dilemma, problems such as these can prove to be devilishly difficult!

The last half of the book is dedicated to a rapid fire selection of mathematical teasers that would make a great addition to a classroom test for extra credit.

Three math examples from the book;

-What are the probabilities that particular calendars dates land on the same day of the week? Anyone who follows our musings about various world calendars, Friday the 13ths and other vagaries of astronomical timekeeping knows how wacky this can be.

-Where on Earth can you walk one mile south, one mile west and one mile north and end up back where you began?

-What’s the smallest number with exactly 28 divisors?

And yes, solutions are provided, just in case some of these keep you awake at night… yeah, it happened to us too!

Be sure to give Mathematical Curiosities a read for some rip-roaring good puzzles!

 

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