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DOCUMEWT RESUME ED 121 522 SE 020 770 AUTHOR Schaaf, Willie' L. TITLE A Bibliography of Recreational Mathematics, Volume 1. Fourth, Edition. INSTITUTION National Council of Teachers of Mathematics, Inc., Reston, Va. PUB DATE 70 NOTE 160p.; For related documents see Ed 040 874 and ED 087 631 AVAILABLE FROMNational Council of Teachers of Mathematics, Inc., 1906 Association Drive, Reston, Virginia 22091 EDRS PRICE MP-$0.83 Plus Postage. HC Not Available from EDRS. DESCRIPTORS *Annotated Bibliographies; *Games; Geometric Concepts; History; *Literature Guides; *Mathematical Enrichment; Mathematics; *Mathematics Education; Number Concepts; Reference Books ABSTRACT This book is a partially annotated bibliography of books, articles, and periodicals concerned with mathematical games, puzzles, and amusements. It is a reprinting of Volume 1 of a three-volume series. This volume, originally published in 1955, treats problems and recreations which have been important in the history of mathematics as well as some of more modern invention. The book is intended for use by both professional and amateur mathematicians. Works on recreational mathematics are listed in eight broad categories: general works, arithmetic and algebraic recreations, geometric recreations, assorted recreations, magic squares, the Pythagorean relationship, famous problems of antiquity, and aathematical 'miscellanies. (SD) *********************************************************************** Documents acquired by ERIC include many informal unpublished * materials not available from other sources. ERIC sakes every effort * * to obtain the best copy available. Nevertheless, items of marginal * * reproducibility are often encountered and this affects the quality* * of the microfiche and hardcopy reproductions ERIC aakes available * * via the ERIC Document Reproduction Service (EDRS). EDRS is not * responsible for the quality of the original document. Reproductions * * supplied by EDPS are the best that can be made from the original. * *********************************************************************** U S DEPARTMENT OF HEALTH EDUCATION &WELFARE NATIONAL INSTITUTE of EDUCATION TTi DOCUMENT HAS SEEN REPRO- DUCED EXACTLY AS RECEIVED FROM THE PERSON OR 000,001A/10N OR*CoN AT.NO I T POINTS OF VIEW OR OPINIONS %TATE° DO NOT NECESSARILY REPaE- setooceciaL NATIONAL INSTITUTE OF EDUCATION POSITION OR POLICY A IOLIOGRAPHY Of recreational mathematics VOLUME I RESE4Dm "97q SCHOOLS . i7J0 PHILJNIT hilliAlIVANIA 19103 3 as. Front J. Ozanant:Dietionaire Mathiweatique. Ant,terdain. 1691 4 I1 BIBLIOGRAPHY OF recreational mathematics VOLUME 1 William L. Schaaf Professor Emeritus Brooklyn College The City University of New York aer+A,.004 10 REPRODUCE ImS t.O *RP;HTED MATERIAL $Y MICRO FICHE ONLY HAS BEEN .PANTED By ,r, ERIC----01 ONO OROcTil NIZAT.OHS OPERAT .Lic,u14DER A0REEMENt$ 'PITH THE HA TONAL .14StIturE OF EOUCAT,04 vOilit-tf R REPRODUCT ION OUtS'OE THE ERIC SYSTEM REQUIRES PERM'S *p0H C: THE COP',R.004t OWNER NATIONAL COUNCIL OF TEACHERS OF MATHEMATICS 1201 Sixteenth Street, N.W.p Washington, D.C. 20036 5 Copyright 0 1955, 1958, 1963, 1970, by V THE NATIONAL COUNCIL OF TEACHERS OF MATHEMATICS, INC. All rights reserved FOURTH EDITION (1970) PRINTED IN THE UNITED STATES OF AMERICA 6 PREFACE Since itsfirst appearance fifteen years ago, this monograph has been twice revised and updated. Meanwhile, the literature of recreational mathe matics has proliferated to such an extent that instead of merely updating the original bibliography once more it seemed desirable to issue a second volume which would not only be more timely but also enlarged in scope and improved in format. The two volumes thus complement one another and provide a comprehensive coverage of the field. When used together, they should hopefully serve the reader well, whether an amateur or a professional. W. L. S. Boca Raton. Florida September. 1969 PREFACE TO THE FIRST EDITION The late G. H. Hardy once observed that there are few more "popular" subjects than mathematics. His contention is amply borne out by the uni- versal interest manifested in mathematical recreations for over 2000 years, ranging from the loculus of Archimedes and the talismen magic squares of the early Chinese to the cryptanalysis and topological recreations of modern times. One need only recall how testament problems, ferrying problems, coin problems, problems of pursuit and problems of arrangements have come down through the ages, ever dressed anew, yet always the same old friends.Labyrinths, dissections, acrostics, tangrams, palindromes, and so on, are likewise virtually ageless. Hence it should occasion little surprise that an enormous body of literature has arisen in the last 300 years. It has been my purpose to gather a considerable part of this material between the covers of one book for the convenience of students and teach ers, as well as laymen and specialists. The more than 2000 entries by no means represent a complete or exhaustive compilation. But enough has been given, I hope, to be of real help. I have tried to meet the needs of almost any readerthe beginner, the dilettante, the professional scholar. Hence I have deliberately included some "popular- articles along with erudite and 7 technical discussions; many contemporary and recent publications. as well as some of an earlier period; sonic that are readily accessible, and others that are to be found only in important libraries; most of them in English, some in French. German, and Italian; most of them significant, a few, some- what superficial. In this way, it is hoped, both the neophyte and the sophis- ticated authority will find what they need. The task of organizing this material yielded a more or less arbitrary classification of mathematical recreations. Occasionally, where helpful, en- u'es have been annotated; to have commented upon each item seemed quite unnecessary, and would in any event have been prohibitive. It would scarcely seem necessary to suggest how this guide may be used. To be sure, a number of entries listed under each of the more than 50 head. ings will not be available to the reader unless the facilities of a large library are at hand; yet there will almost surely be some that are accessible. In most instances the reader will have little difficulty in selecting items per- taining to a given topic: he should be guided by the title of the book or article; by the annotation. if any; by the sort of periodical. whether scholarly. popular. professional. newsy, and so on; and, to some extent, by the length of an article. Naturally, the reader's purpose, as well as his familiarity with the subject. will loom large as factors in helping him select items to be consulted. Nor should he be deterred by references in a foreign language; after all. the mathematical symbols and geometric figures are essentially the same. so that even a moderate facility in French or German often suffices. This guide will serve as a place to begin to look for source materials.It will help the student pursuing his mathematical studies in high school or college; the mathematics club looking for program and project material; the teacher gathering human interest or motivation material; the more ad- vanced student engaged in research; the amateur mathematician or the proverbial layman happily engaged in that most delectable of all activities a hobby or a recreation. May following these trails afford the reader as much pleasure as it has been for me to map them out for him. 1 W. L. S. I July 1954 8 Contents Chapter 1.General Works 1 1.1Early Twentieth Century Books-1900.1924 2 1.2Contemporary Books-From 1925 On 4 1.3Periodical Literature 12 1.4Mathematics Club Programs; Plays 16 1.5Mathematics and Philately 18 1.6Mathematical Contests 19 1.7Mathematical Models 20 1.8Mathematical Instruments 23 1.9The Abacus 24 Chapter 2.Arithmetical and Algebraic Recreations 26 2.1General Arithmetical Recreations 26 2.2Specific Problems and Puzzles 29 2.3Number Pleasantries 34 2.4Calculating Prodigies 39 2.5Theory of Numbers-Factorizations-Primes 42 2.6Perfect Numbers-Mersenne's Numbers 45 2.7Fermat's Last Theorem 47 2.8Fibonacci Numbers and Series 49 Chapter 3.Geometric Recreations 51 3.1General Geometric Problems and Puzzles 51 3.2Geometric Fallacies-Optical Illusions 54 3.3Geometric Dissections-Tangrams 55 3.4Regular Polygons and Polyhedrons 57 3.5Geometric Constructions 60 3.6 ' Mascheroni Constructions 63 3.7Linkages-The Pantograph 64 3.8Mechanical Construction of Curves 66 Chapter 4.Assorted Recreations 68 4.1Ross Puzzle 68 4.2Card Tricks - Manipulative Puzzles 69 4.3Chessboard Problems 71 9 4.4Topological Questions 71 4.5String Figures-Theory of Knots 73 4.6 The Mobius Strip 74 4.7MapColoring Problems 74 4.8Paper Folding 76 4.9Unicursal Problems-Labyrinths 78 Chapter 5.Magic Squares 79 5.1Books--1900-1924 79 5.2Contemporary Books--From 1925 On 81 5.3Periodical Literature 83 Chapter 6.The Pythagorean Relationship 89 6.1The Theorem of Pythagoras 89 6.2Pythagorean Numbers-Rational Right Triangles 93 6.3Special Triangles-Heronian Triangles 96 6.4Miscellaneous Pythagorean Recreations 98 Chapter 7.Famous Problems of Antiquity 100 7.1Classical Constructions 100 7.2Trisecting an Angle 102 7.3Duplicating a Cube 105 7.4Squaring a Circle 106 7.5History and Value of Pi in) 109 7.6Zeno's Paradoxes 112 Chapter 8.Mathematical Miscellanies 114 8.1Mathematics in Nature 114 8.2Machines That Think 116 8.3Cryptography and Cryptanalysis 120 8.4Probability, Gambling, and Game Strategy 124 8.5The Fourth Dimension 131 8.6Repeating Ornament 134 8.7Dynamic Symmetry 136 8.8The Golden Section 139 8,9Mathematics and Music 142 Chapter 9.SupplementBooks and Pamphlets 144 10 "But leaving those of the Body, I shall proceed to such Recreations as adorn the Mind; of which those of the Mathematicks are inferior to none." WILLIAM LEYBOURN: Pleasure with Profit 41694). 11 Principal Abbreviations Used Am.M.Mo. = American Mathematical Monthly M. Gaz. = Mathematical Gaaette M. Mag. = Mathematics Magazine M. T. = Mathematics Teacher N. M. M. = National Mathematics Magazine N. C. T. M. = Nacional Council of Teachers of Mathematics lt.
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