You are here

Knots and Borromean Rings, Rep-Tiles, and Eight Queens

Martin Gardner
Cambridge University Press/Mathematical Association of America
Publication Date: 
Number of Pages: 
The New Martin Gardner Mathematical Library
BLL Rating: 

The Basic Library List Committee considers this book essential for undergraduate mathematics libraries.

[Reviewed by
Tom Schulte
, on

This is the fourth entry in the first complete collection of Martin Gardner's Mathematical Library, covering the entire twenty-five-year run of his Scientific American columns. Oddly, the cover and spine have no indication of this ordinal or the count of volumes. It is not immediately obvious this is part of a set.

The back cover does cite Don Knuth as saying that this material is “…always worth reading and rereading.” I agree. This edition contains extensively updated material from Gardner, so that the detailed afterwords and extensive bibliographies are often longer than the original columns. Gardner’s contributions are from as late as 2005, meaning we can read Gardner citing Web sites and considering 3D printing applications. This gives this compendium a different voice from any other Gardner collection I have perused.

Strict completists should be made aware that some material has been redacted. “Thirty-Seven Catch Questions” is now “Thirty-Six Catch Questions”. Since this collection was published in 1968 (and 1991) as The Unexpected Hanging and other Mathematical Diversions, readers are no longer to be confronted with a quandary beginning “The third woman, who weighs 300 pounds, is sitting on a hippopotamus skin…”

“The Unexpected Hanging” is a favorite riddle of mine and while pushed off the cover by topological flash, the hangman’s paradox is still here with enigmas around the cat’s cradle, the fourth dimension, gambling, peg solitaire, the transcendental and popular e, and more. Gardner’s engaging explorations telegraph an awe of the beauty of mathematics making this collection a treat and a challenge for any mathematics enthusiast.

Tom Schulte enthusiastically teaches mathematics at Oakland Community College and first fell in love with Martin Gardner’s writings through the Aha volumes. 

1. The paradox of the unexpected hanging
2. Knots and Borromean rings
3. The transcendental number e
4. Geometric dissections
5. Scarne on gambling
6. The church of the fourth dimension
7. Eight problems
8. A matchbox game-learning machine
9. Spirals
10. Rotations and reflections
11. Peg solitaire
12. Flatlands
13. Chicago magic convention
14. Tests of divisibility
15. Nine problems
16. The eight queens and other chessboard diversions
17. A loop of string
18. Curves of constant width
19. Rep-tiles: replicating figures in the plane
20. Thirty-seven catch questions.