Mathematical Reflections [Hardcover]

Peter Hilton (Author), Derek Holton (Author), Jean Pedersen (Author)

Book Description

ISBN-10: 0387947701 | ISBN-13: 978-0387947709 | Publication Date: December 13, 1996 | Edition: Corrected

A relaxed and informal presentation conveying the joy of mathematical discovery and insight. Frequent questions lead readers to see mathematics as an accessible world of thought, where understanding can turn opaque formulae into beautiful and meaningful ideas. The text presents eight topics that illustrate the unity of mathematical thought as well as the diversity of mathematical ideas. Drawn from both "pure" and "applied" mathematics, they include: spirals in nature and in mathematics; the modern topic of fractals and the ancient topic of Fibonacci numbers; Pascals Triangle and paper folding; modular arithmetic and the arithmetic of the infinite. The final chapter presents some ideas about how mathematics should be done, and hence, how it should be taught. Presenting many recent discoveries that lead to interesting open questions, the book can serve as the main text in courses dealing with contemporary mathematical topics or as enrichment for other courses. It can also be read with pleasure by anyone interested in the intellectually intriguing aspects of mathematics.

Product Details

• Hardcover: 351 pages
• Publisher: Springer; Corrected edition (December 13, 1996)
• Language: English
• ISBN-10: 0387947701
• ISBN-13: 978-0387947709
• Product Dimensions: 10 x 6.9 x 1 inches
• Shipping Weight: 1.8 pounds (View shipping rates and policies)
• Average Customer Review: 5.0 out of 5 stars  See all reviews (2 customer reviews)
• Amazon Best Sellers Rank: #951,904 in Books (See Top 100 in Books)

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Customer Reviews

Most Helpful Customer Reviews

6 of 6 people found the following review helpful:

5.0 out of 5 stars Two thumbs up for this book., August 17, 1997

By A Customer

This review is from: Mathematical Reflections (Hardcover)

"Mathematical Reflections" can be enjoyed by anyone with a high school level of mathematical education but will also interst the more advanced reader. Topics from tiling of the plane to paper folding to Fibonacci numbers are presented in a clear and interesting manner along with problems and solutions. If you ever wondered why the ratio of consecutive Fibonacci numbers converges to the "golden ratio", this book is worth the purchase price

5 of 5 people found the following review helpful:

5.0 out of 5 stars Visual Thinkers Paradise, August 16, 2000

By 

"thirteenthfairy" (, N.S.W. Australia) - See all my reviews

This review is from: Mathematical Reflections (Hardcover)

If you have trouble understanding and particularly visualizing what mathematical formulae mean. If you have a belief that all mathematical concepts CAN be visualized if only mathematicians tried hard enough. If you like math books but wish there were more pictures. If you wish there were instructions on things to do in Math books other than write out formulae and solutions. If you want hope that there's new and exciting stuff out there that you can find by doing things with paper other than writing on it. THIS IS THE BOOK FOR YOU. A particularly interesting section on how to generate the Cantor Set by Geometric iteration using the tent map and a good explanation of sets related to the Cantor set and the general relationship of things like the Cantor Set to more complicated fractals. One of the most interesting books I have eever read vastly increased my understanding and provided me with valuable ideas to furthur my own creative efforts. Well done HHandP I look forward to the new book.