Customer Reviews

Ingenuity in mathematics (New mathematical library)

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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.