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Leonardo's Mirror and Other Puzzles

Ivan Moscovich
Dover Publications
Publication Date: 
Number of Pages: 
Mastermind Collection
[Reviewed by
Alex Bogomolny
, on

Dual review of:

Ivan Moscovich, the author of the two books under review, is a well known and much respected puzzlist and toy creator. The books — one of which first appeared in 1994, the other in 2004 — have been recently republished by Dover. Both books are lavishly and beautifully illustrated in full color and would make memorable presents.

Both books are more than mere collections. Most of the puzzles are presented with background information that sometimes is sufficiently comprehensive to occupy a page or two. The reader is treated to the shapes of planetary trajectories, a short biography of Leonardo da Vinci, and one of Leonardo of Pisa; the quadrature of lunes and geometric dissections; the ideas of mechanical linkages and sphere packing; the Golomb rulers; paper-and-pencil games; and Ramsey theory. The breadth of the collections and occasional depth are quite staggering.

What about the “puzzles” themselves? In what sense are Monge’s theorem of three circles or visual illusions puzzles? Some of the “puzzles” are in fact engaging mathematical problems, others are thought provoking or plain entertaining activities — these are combined into groups of 2 to 5. What makes them “puzzles” is their great diversity, which keeps the reader continuously involved, puzzled and puzzling.

Some of the puzzles are well known, but many appear to be original. E.g., I do not remember seeing a Hex-like game played on a square grid in which the moves are those of the chess knight.

The solutions at the end of the books are similarly well illustrated and provide visual clues accompanied by textual explanations.

The level of the puzzles varies but — on the whole — the books will be appreciated by a broad readership of puzzle lovers as well by the parents who would like to sprinkle the interaction with their kids with engaging mostly-mathematical activities. The books are so attractively made they could not fail but engross even young children’s minds.

Alex Bogomolny is a freelance mathematician and educational web developer. He regularly works on his website Interactive Mathematics Miscellany and Puzzles and blogs at Cut The Knot Math. Follow Alex on twitter

88 Mathematical Puzzles