The greatest scientist of all time was quoted as saying that the reason that he saw further than others was that he stood on the shoulders of giants. As the title of this book suggests, there is another route, namely walking the same path as others. Given our individual differences and how we vary from day to day, even the most beaten of paths can present differing appearances. When walking through a forest, some days you may see the moss, other days the ground cover and then on others we pay particular attention to the leaves. In this collection of problems, Ross Honsberger proves once again that he is the best at picking the high quality, sturdy building material from the large, stable, yet uninspiring stack of wood. This is a collection of problems to build on. Many of the them were taken from those proposed and rejected from mathematics competitions, both national and international. Given the quality of these problems, those that were accepted in favor of them must have indeed been gems. It is fortunate that Crux Mathematicorum, a journal of the Canadian Mathematical Society, publishes problems of this type so that the rest of us may enjoy them. The range of topics is extensive, with very detailed proofs of all problems. The most striking aspect of many of them is that the approach used in the proof is "non-obvious." Which is the mathematical term for ,"now, how did they ever think of that?" Which is what makes them so charming and emphasizes how exciting mathematics is. There used to be a television game show where contestants competed by claiming that they could name a song in the fewest notes. If there was a similar contest concerning the elegance and directness of proofs, some of those in this book would provide stiff competition. Classic works of art or music always provide enjoyment, even after many repetitions. High quality, elegant proofs of mathematical problems do the same thing to those willing to experience them. This is one book that will allow you to do that.
Published in Smarandache Notions Journal, reprinted with permission
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Charles Ashbacher (CharlesAshbacher)
Charlie Ashbacher is a compulsive reader and writer about many subjects. His prime areas of expertise are in mathematics and computers where he has taught every course in the mathematics and computer … more
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Mathematics is often studied with an air of such seriousness that it doesn't always seem to be much fun. However, it is quite amazing how many surprising results and brilliant arguments one is in a position to enjoy with just a high school background. This is a book of miscellaneous delights, presented not in an attempt to instruct but as a harvest of rewards that are due to good high school students and, of course, those more advanced - their teachers and everyone in the university mathematics community. A half dozen essays are sprinkled among some hundred problems. Many subjects are represented - combinatorics, geometry, number theory, algebra, probability. The sections may be read in any order. The book concludes with twenty-five exercises and their detailed solutions. Something to delight will be found in every section - a surprising result, an intriguing approach, a stroke of ingenuity - and the leisurely pace and generous explanations make the book a pleasure to read.