Ten years ago the writer of a mathematicstextbook would have been consideredfrivolous by his colleagues if his book in-cluded puzzles and other entertainingtopics. This is no longer true. Exercises inthe first two volumes of Donald E. Knuth'smonumental work in progress,&nbsp; The Artof Computer Programming&nbsp; (Reading:Addison-Wesley, 1968, 1969), are filledwith recreational material. There are eventextbooks in which a recreational emphasisis primary.&nbsp; A&nbsp; delightful instance is HaroldR. Jacobs's&nbsp; Mathematics:&nbsp; A&nbsp; Human En-deavor,&nbsp; subtitled&nbsp; A&nbsp; Textbook for ThoseWho Think They Don't Like the Subject(San Francisco:&nbsp; W.&nbsp; H.&nbsp; Freeman and Co.,1970). Richard Bellman, Kenneth L. Cooke,and Jo Ann Lockett, authors of&nbsp; Algorithnzs,Graphs,&nbsp; and&nbsp; Computers&nbsp; (New York: Aca-demic Press, 1970), write in their preface,"The principal medium&nbsp; we&nbsp; have chosen toachieve our goals is the mathematicalpuzzle."The trend is not hard to understand. Itis part of the painfully slow recognition byeducators that students learn best who aremotivated best. Mathematics has neverbeen a dreary topic, although too often ithas been taught in the dreariest possibleway. There is no better way to relieve thetedium than by injecting recreational top-ics into a course, topics strongly tingedwith elements of play, humor, beauty, andsurprise. The greatest mathematicians al-ways looked upon their subject as a sourceof intense intellectual delight and seldomhesitated to pursue problems of a recre-ational nature. If you flip the leaves ofW. W.&nbsp; Rouse Ball's classic British work,Mathematical&nbsp; Recreations&nbsp; and Essays(first published by Macmillan in&nbsp; 1892&nbsp; andsoon to be issued in a twelfth revised edi-tion), you will find the names of celebratedmathematicians on almost every page.Euclid himself, among the earliest ofthe mathematical giants, wrote an entirebook (unfortunately it did not survive) ongeometrical fallacies. This is a topic cov-ered in standard works on recreationalmathematics but curiously avoided in most

Sixth Book of Mathematical Diversions PDF

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