Which Way Did the Bicycle Go?: And Other Intriguing Mathematical Mysteries (Dolciani Mathematical Expositions) by Joseph D. E. Konhauser (PDF)

Description

This book contains the best problems selected from over 25 years of the Problem of the Week at Macalester College. This collection will give students, teachers, and university professors a chance to experience the pleasure of wrestling with some beautiful problems of elementary mathematics. Readers can compare their sleuthing talents with those of Sherlock Holmes, who made a bad mistake regarding the first problem in the collection: Determine the direction of travel of a bicycle that has left its tracks in a patch of mud. The collection contains a variety of other unusual and interesting problems in geometry, algebra, combinatorics, and number theory. For example, if a pizza is sliced into eight 45-degree wedges meeting at a point other than the center of the pizza, and two people eat alternating wedges, will they get equal amounts of pizza? Or: Is an advertiser’s claim that a certain unusual combination lock allows thousands of combinations justified? Complete solutions to the 191 problems are included with problem variations and topics for investigation.

User’s Reviews

Editorial Reviews: Review The problems are not brain-teaser types that have a “trick” to their solution: They all involve insightful mathematics. This text devotes 60 pages to the problems and 160 pages to their annotated solutions. The solutions are well written, make historical references, and contain extensions to the original problems…The problems are suitable for college-level and might be within reach of superior high school students….a nice addition to the library of any problem solver since it contains a collection of thought-provoking , demanding problems that are unlikely to be duplicated in any other single book. The Mathematics Teacher — The Mathematics TeacherThis stimulating little book is a collection of the 191 of the best “Problem of the Week” mathematical problems and puzzles that appeared over the last 25 y ears at Macalester College. This tradition was started by Joe Konhauser, a “great believer in the value of problem solving activity,” and later continued by Stan Wagon., The problems appear to follow Joe’s dictum that “they had to involve almost no prerequisites and be succinctly stated and inherently attractive.”…there is sufficient variety included to appeal to most mathematically oriented people. — AAAS Science Books and FilmsThis work…is exceptionally well written and well prepared technically…The carefully stated problems are grouped into categories…Following the problem statements are well-written solutions to each problem. Besides being appropriate for teachers, the book might also interest advanced high school and college mathematics students who would independently engage in the challenge of mathematical puzzles and be entertained by the surprising twists required to solve them. — Choice Book Description The best problems selected from over 25 years of the Problem of the Week at Macalester College. Book Description This book contains the best problems selected from over 25 years of the Problem of the Week at Macalester College. The collection contains a variety of other unusual and interesting problems in geometry, algebra, combinatorics, and number theory. Complete solutions to the 191 problems are included along with problem variations and topics for investigation. About the Author Joseph D. E. Konhauser was an avid problemist throughout his years at Macalester College (1968-1991). He studied at Penn State University, and obtained his doctorate there in 1963. He held teaching positions at Penn State and the University of Montana before coming to Macalester. He was a very active problemist and served on many contest committees such as those governing the USA Mathematical Olympiad and the William Lowell Putnam Mathematics Competitions. He served as editor of the “Pi Mu Epsilon Journal,” and as book review editor for the “American Mathematical Monthly.” Dan Velleman received his PhD from the University of Wisconsin. He has taught at the University of Texas and the University of Toronto, and since 1983 he has taught at Amherst College. Currently, he is Chair of the Editorial Board for the Dolciani Mathematical Expositions Series (for the Mathematical Association of America). He is the author of “How to Prove it” (Cambridge University Press.) Stan Wagon received his PhD from Dartmouth College. He taught at Smith College until coming to Macalester in 1990. Throughout his career has enjoyed the special beauty of succinctly stated and surprising mathematical facts. this led to his book on the Banach-Tarski paradox (Cambridge University Press), and with Victor Klee a book on unsolved problems in mathematics (MAA). Recently he has been intrigued with how “Mathematica” can help us see mathematical constructions in new ways, and he has written several books illustrating the power of this software: “Mathematica in Action” (Freeman), “The Power of Visualization” (Front Range Press), “Animating Calculus” (Springer) to name a few. Read more

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐The best mathematics problem book I’ve ever seen. Love it.

⭐A lovely collection of neat problems.

⭐The book has many intriguing problems that are sure to capture the minds of any mathematician. It also contains a very nice answer section. The only throwback is that most of the problems take significant thought and require some time to solve completely. However, the nice answer section takes care of the problem should you become obsessed with a problem you can’t quickly solve, and the overall quality of the problems warrant a 5-star rating.

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