Ingenuity in mathematics (New mathematical library) [Paperback]

Ross Honsberger (Author)

Book Description

Series: New mathematical library | Publication Date: 1970

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. Standard high school courses in algebra and geometry furnish a sufficient basis for understanding each essay. Topics include number theory, geometry, combinatorics, logic and probability, and the methods used often involve an interaction between these disciplines. Some of the essays are easy to read, others more challenging; some of the exercises are routine, others lead the reader deeper into the subject.

--This text refers to an alternate Paperback edition.

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. --This text refers to an alternate Paperback edition.

Product Details

• Paperback: 204 pages
• Publisher: Random House/Singer School Division (1970)
• Language: English
• ISBN-10: 0394709233
• ISBN-13: 978-0394709239
• Average Customer Review: 5.0 out of 5 stars  See all reviews (1 customer review)
• Amazon Best Sellers Rank: #8,306,588 in Books (See Top 100 in Books)

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Customer Reviews

Most Helpful Customer Reviews

17 of 18 people found the following review helpful:

5.0 out of 5 stars A delightful, accessible book, December 15, 2001

By 

MS (British Columbia, Canada) - See all my reviews

This review is from: Ingenuity in Mathematics (Anneli Lax New Mathematical Library) (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.