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Odd Numbers

Herbert McKay
Cambridge University Press
Publication Date: 
Number of Pages: 
Cambridge Library Collection
[Reviewed by
Tom Schulte
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I recall being about ten years old at a summertime family picnic. My dear great aunt came up to as I was huddled in the only available shade, away from the group. She began lecturing me on the antisocial evils of the then-new hand-held electronic games. When I turned the device to show her it was my LED display calculator her expression of confusion and sadness needed the Steven Wright punch line “you’re a strange child, aren’t you?” If am ever the adult in that exchange, I’ll put Odd Numbers into the number-obsessed youngster’s hands.

Simple grade school arithmetic is the starting point here. Using wit and a fair number of anti-establishment attacks, McKay will make even the jaded young number-cruncher can see him as “cool.” For instance, he ridicules the venerable H. G. Wells for unsound Brobdingnagian proportionality in his re-imagination of Gulliver’s Travels. How enjoyable it would be to read McKay’s analysis of the Jack Black version! The metric system gets a personal attack in two different chapters. (McKay is dead on in using Wells’ mistake as an illustration, but his personal distaste for a decimal unit system makes him sound like an inflexible codger.)

Anyone looking for a numbers exploration starting from pre-high school and moving toward deeper insight can find it here, and have fun getting there. Since the book was published in the 1940s, those comfortable only with current American English will find obstacles in “groats,” the pre-1974 British definition of “billion,” and old-style UK units for currency and measurement. Add to this obsolete notation, such as decimal points that hover up to near superscript level and repeating decimal values indicated with a centered overline dot.

Among the pleasures here are the familiar pre-calculator accountants’ tricks for finding factors and the least significant digit of products. A chapter on proportion gets to the verge of proofs. The author’s outdoor vision of applying the Pythagorean Theorem recalls similar parts of The Dangerous Book for Boys. Triangulation and surveying lays the groundwork for trigonometry. On the other hand, one of the best story problem analysis sections, on the division among thieves of stolen apples, will be soured to many readers by the injudicious use of the same n-word that regularly gets Huckleberry Finn taken off the shelves.

Largely an old historical curiosity, this book still might hold its charm for the young and mathematically curious. Any reader who can get through the thicket of archaisms will be challenged to check assumptions and find fun in math.

Tom Schulte still plays with calculators in Waterford, Michigan.

1. Millions and billions and trillions
2. Great powers and little powers
3. How we got logarithms
4. Proportion
5. Comparisons
6. Proportion in triangles
7. Weights and measures
8. The delusive average
9. Approximations
10. Multiplication and division
11. Tables
12. Units
13. Oddities of numbers
14. The construction and solution of problems
15. Scales of notation.