Product Description
This is a collection of informative extracts from Gardners' "Scientific American" column. Each brain-teasing article has been updated to include new mists, new ideas, and new solutions. Highlights include two new chapters-one on pi and poetry, one on minimal sculpture-and intriguing forays into time reversal, forms of fractions and magic, and an imaginary "Math Zoo" with its own publication, "ZOO-NOOZ". ... Read more

Customer Reviews (2)

profound masterpiece
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.

Another work from the master of explaining mathematics
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 everytopic with charm, wit, grace and thoroughness. It there is such a thing asmathematical 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 chessproblems, imaginary numbers, and tangent circles. He also discusses thecareer of Charles Saunders Pierce and the book Godel, Escher, Bach: AnEternal Golden Braid, by Douglas Hofstadter. Negative comments on minimalsculpture and psychic research methods are also included.
Informativeas well as entertaining, the works of this author should be part of everyliberal education.

Published in Journal of RecreationalMathematics, reprinted with permission. ... Read more

Product Description
Establishing a new genre of musical analysis, this book goes beyond the usual analysis of chord symbols and period forms to examine such topics as: Fibonacci number and golden mean proportions, Statistics for distinguishing among styles, Self-similarity in form. This second edition includes many new illustrations and concepts, including: Orbit drawings of attractors, Correlation coefficients, Melodic dimensions. It is intended for readers with little mathematical background and requires only algrebra and trigonometry. ... Read more

Product Description
From Ancient Greek times, music has been seen as a mathematical art, and the relationship between mathematics and music has fascinated generations.This collection of wide ranging, comprehensive and fully-illustrated papers, authorized by leading scholars, presents the link between these two subjects in a lucid manner that is suitable for students of both subjects, as well as the general reader with an interest in music.Physical, theoretical, physiological, acoustic, compositional and analytical relationships between mathematics and music are unfolded and explored with focus on tuning and temperament, the mathematics of sound, bell-ringing and modern compositional techniques. ... Read more

Customer Reviews (1)

Expendable collection of essays
Only two chapters address fundamental mathematical-musical issues, namely decent chapters on the Pythagorean principles of consonance and scales and Helmholtz's theory of consonance. The rest of the book treats various quirky side topics, many of them trying in more or less contrived ways to force mathematical ideas (magic squares, finite projective planes, fractals, the Erlanger Programm, etc.) into a musical setting. Personally, I was amused by chapter 7 on bell-ringing: a bell-tower has a few different bells and of course "an evening spent playing unchanging rounds might be considered uneventful", so we wish to change the ringing order of our bells, but "because bells are heavy and slow" we are limited to changing the order one adjacent pair at a time, and so eighteenth century bell-ringers developed a sophisticated understanding of symmetric groups generated by transpositions, which we can now illustrate with modern concepts and Cayley diagrams and so on, only to conclude that the ringers "had been doing 'group theory' and 'ringing the cosets' all along". That's about as good as it gets. The book as a whole suffers from many shortcomings including lack of depth (e.g., chapter 2 on Kepler's musical cosmology doesn't contain a single line of mathematics), lack of breadth (e.g., Fourier analysis is not even in the index), and lack of originality (e.g., chapter 4 consists of recycled Ian Stewart material which in turn was mostly recycled Barbour material, down to consistent misspelling of the main character's name). ... Read more

Product Description
1 videocassette. VHS. 30 min., 1987. An artistic study of over 20 different regions within a mathematically defined region known as the Mandelbrot Set. A unique perspective on the world of mathematics. Computer animation is used to demonstrate the nature of fractals, a peculiar shape discovered by Dr. Mandelbrot. ... Read more