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Fractal Music, Hypercards and More Mathematical Recreations from "Scientific American"

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This book is another pillar holding up the banner that proclaims the author to be `the most ubiquitous man in the most ubiquitous of fields." He seems to have no mathematical weaknesses, attacking and explaining every topic with charm, wit, grace and thoroughness. It there is such a thing as mathematical savoir-faire, Martin Gardner possesses it.
In this work, Dr. Gardner explains fractal music, the Bell numbers and their uses, Egyptian fractions, packing circles and squares, mathematical chess problems, imaginary numbers, and tangent circles. He also discusses the career of Charles Saunders Pierce and the book Godel, Escher, Bach: An Eternal Golden Braid, by Douglas Hofstadter. Negative comments on minimal sculpture and psychic research methods are also included.
Informative as well as entertaining, the works of this author should be part of every liberal education.

Published in Journal of Recreational Mathematics, reprinted with permission.

Martin Garner is a genius, no doubt. However, he left no contact information for readers to report math errors.
On page 156, Figure 68, I hold the proof that 10 circles can be packed to a 3.81 density. In a clever disclaimer, at least Martin admits on the same page, that proofs exist for 1-9, but not 10. Martin, if you want my solution for 10 circles, circlepacker.afm@OrdinaryAmerican.net is my contact info.