The Sensual (Quadratic) Form (Carus Mathematical Monographs) [Hardcover]

John Horton Conway (Author), Francis Y. C. Fung (Author)

Book Description

Series: Carus Mathematical Monographs | Publication Date: November 1, 1997

The distinguished mathematician John Conway presents quadratic forms in a pictorial way that enables the reader to understand them mathematically without proving theorems in the traditional fashion. One learns to sense their properties. In his customary enthusiastic style, Conway uses his theme to cast light on all manner of mathematical topics from algebra, number theory and geometry, including many new ideas and features.

Editorial Reviews

Review

'Absolutely fascinating from beginning to end.' New Scientist

Book Description

Quadratic forms are here presented in a pictorial way that enables readers to understand them mathematically without proving theorems in the traditional fashion. In his customary enthusiastic style, Conway uses his theme to cast light on all manner of topics from algebra, number theory and geometry, including many new ideas and features.

See all Editorial Reviews

Product Details

• Hardcover: 228 pages
• Publisher: The Mathematical Association of America (November 1, 1997)
• Language: English
• ISBN-10: 0883850303
• ISBN-13: 978-0883850305
• Product Dimensions: 8.3 x 5.4 x 0.8 inches
• Shipping Weight: 12 ounces
• Average Customer Review: 5.0 out of 5 stars  See all reviews (2 customer reviews)
• Amazon Best Sellers Rank: #1,791,245 in Books (See Top 100 in Books)

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Most Helpful Customer Reviews

9 of 9 people found the following review helpful:

5.0 out of 5 stars If it's written by John Horton Conway, buy it., November 12, 2003

By 

D. Taylor (Colorado, USA) - See all my reviews
(REAL NAME)   

This review is from: The Sensual (Quadratic) Form (Carus Mathematical Monographs) (Hardcover)

The book doesn't need a review. It's written by John Horton Conway. Enough said. But if you insist on a review, the book (actually a series of three lectures) is a radical new "look" at quadratic forms through visual topographs. The lectures progress with even more ways of sensing quadratic forms (eg "hearing the shape of a drum"), and that's where the title comes from. "The Sensual Form" -- get it? It will change the way you look at QFs. If you need more information on Conway, he's the inventor of the mathematical game "life" and the author of the sublimest, rockingest math books on the planet, dude: Winning Ways, Numbers and Games, etc. He's one of the rarest of birds -- a contributor to the highest echelons of mathematical knowledge who's also great at putting it into readable, learnable text.

3 of 3 people found the following review helpful:

5.0 out of 5 stars Four of the five senses (hence the sensual) are related to basic quadratic equations, January 13, 2007

By 

Charles Ashbacher (Marion, Iowa United States) - See all my reviews
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This review is from: The Sensual (Quadratic) Form (Carus Mathematical Monographs) (Hardcover)

This book, a compilation of the lectures Conway presented at the Joint Meetings of the American Mathematical Society and Mathematical Association of America in 1991, is a bit overstated in the title. In particular, the inclusion of the word "sensual." While some mathematicians no doubt get a significant buzz over the quadratic form, (polynomials in several variables where every term has degree two), I doubt if it reaches the point of sexual stimulation. In the first lecture he considers only equations of the form a*x^2 + b*x*y + c*y^2, where a, b and c are integers. While at first glance this may appear to be a severe restriction, that is not the case. For example, by rewriting the quadratic into the matrix form,

| a b |
( x y ) | | (x y )
| c d |

it is possible to work with matrices, determinants, bases, superbases, equivalence of forms, primitive vectors, and norms of the vectors. Tree diagrams are used to represent the bases of the forms, this leads to a large number of successive descriptive operations. By the time you reach the end of the book, Conway has gone through several of the human senses, considering the following questions.

*) Can you see the values of 3x^2 + 6xy - 5y^2?
*) Can you hear the shape of a lattice?
*) ... and can you feel its form?

The title of the fourth lecture is "The Primary Fragrances" so he "covers" four of the five senses.
I found the difficulty to be rather high, there were many times when I had to slow way down and process the material in small chunks. One of the primary reasons for this is that Conway introduces a lot of notations and terminology and it was not always immediately clear to me what he meant. However, I did manage to understand nearly all of it, which made reading it very worthwhile. Once I finished, I found myself surprised that such a "simple" equation led me down so many different mathematical paths.

Published in Journal of Recreational Mathematics, reprinted with permission