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Ingenuity in Mathematics (Anneli Lax New Mathematical Library)

5 out of 5 stars 3 customer reviews
ISBN-13: 978-0883856239
ISBN-10: 0883856239
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Editorial Reviews

Book Description

The nineteen essays here illustrate many different aspects of mathematical thinking. The author is very well-known for his best-selling books of problems; in this volume he seeks to share his appreciation of the elegant and ingenious approaches used in thinking about even elementary mathematics.
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Product Details

  • Series: Anneli Lax New Mathematical Library (Book 23)
  • Paperback: 216 pages
  • Publisher: The Mathematical Association of America (June 1975)
  • Language: English
  • ISBN-10: 0883856239
  • ISBN-13: 978-0883856239
  • Product Dimensions: 6 x 0.5 x 9 inches
  • Shipping Weight: 9.6 ounces (View shipping rates and policies)
  • Average Customer Review: 5.0 out of 5 stars  See all reviews (3 customer reviews)
  • Amazon Best Sellers Rank: #1,008,660 in Books (See Top 100 in Books)

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Format: Paperback
This is a marvellous volume for math enthusiasts of all ages and levels. It's accessible to an inquisitive high school student with little background in the subject; and it doesn't duplicate the sort of material found in high school and university courses, so it's still got plenty to offer the graduate student or math teacher. The author's enthusiasm for the subject leaps out from every paragraph, and it's contagious. Honsberger carefully and thoroughly explains the proofs he presents; very little of import is left to the reader. Among the results:
- If x and y are positive numbers less than 1, chosen at random, the probability that x, y, and 1 form the sides of an obtuse triangle is (pi-2)/4
- For any string of digits S=a_1a_2...a_m, and integer n not a power of 10, there is a power of n that begins with the string S
- On average, the probability that two randomly chosen integers are coprime is 6/pi^2.
At the end of each section are practice problems that make use of the material just presented, and these offer additional insight into the scope of the proofs.
In short, it's a great book, and it's particularly helpful for high school students looking for practice on contest-type problems, and for teachers looking for material for gifted students.
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Format: Paperback
As the Note to the reader recites, this book was written in order to make important mathematical ideas "interesting and understandable" to a larger audience than mere professionals. Inspired by Rademacher and Toplitz's masterpiece "the enjoyment of mathematics" and by the publications appeared in the memorable journal "Scripta Mathematica", Honsberger aims to provide examples that show the "incisiveness" and "ingenuity" of first-rate or less known mathematical results, that have all astounded him. This is not an easy task, especially if one wants to achieve all this without excessive technicalities. The result is however satisfactory. Honsberger collects 19 essays on miscellaneous topics loosely related one to other except for the fact of giving the reader an insight into incisive and ingenious mathematical work.
In order to have a better grasp of these qualities, I shall briefly survey the essay 15 on Mascheroni's and Steiner's results on geometric constructions. A first issue discussed by Honsberger is a beautiful question of elementary geometry: What problems can we solve if we use only the compass and we dispose of the ruler? Before answering this question, that was the subject of a book published by Mascheroni in 1797, Honsberger enters an instructive discussion on the equivalence of geometric instruments. For instance, we learn in the book that it can be proved in an elementary way that the collapsible compass (namely the compass which collapses when either arms are lifted from the paper) can effectuate the same constructions as the divider, i.e. the compass which can mark distances.
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Format: Paperback Verified Purchase
Great book! Had some ideas that were very clever and original to me.
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