DOCSLIB.ORG

History and Current State of Recreational Mathematics and Its Relation to Serious Mathematics

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
History and Current State of Recreational Mathematics and Its Relation to Serious Mathematics Charles University in Prague Faculty of Mathematics and Physics DOCTORAL THESIS Tereza B´artlov´a History and current state of recreational mathematics and its relation to serious mathematics Department of Mathematical Analysis Supervisor of the doctoral thesis: prof. RNDr. LuboˇsPick, CSc., DSc. Study programme: Mathematics Study branch: General Questions of Mathematics and Information Science Prague 2016 I declare that I carried out this doctoral thesis independently, and only with the cited sources, literature and other professional sources. I understand that my work relates to the rights and obligations under the Act No. 121/2000 Sb., the Copyright Act, as amended, in particular the fact that the Charles University in Prague has the right to conclude a license agreement on the use of this work as a school work pursuant to Section 60 subsection 1 of the Copyright Act. In Prague on June 28, 2016 Tereza B´artlov´a i Title: History and current state of recreational mathematics and its relation to serious mathematics Author: Tereza B´artlov´a Department: Department of Mathematical Analysis Supervisor: prof. RNDr. LuboˇsPick, CSc., DSc., Department of Mathematical Analysis Abstract: The present thesis is devoted to the study of recreational mathematics, with a particular emphasis on its history, its relation to serious mathematics and its educational benefits. The thesis consists of five papers. In the first one we investigate the history of recreational mathematics. We focus on the development of mathematical problems throughout history, and we try to point out the people who had an important influence on the progress of recreational mathematics. The second article is dedicated to Edwin Abbott Abbott and his book called Flatland. It is one of the first popularizing books on geometry. In the third article we review one of the prominent personalities of recreational mathematics, Martin Gardner. The fourth article is in some sense a sequel to the third one. It deals with treachery of mathematical intuition and mathematical April Fool's hoaxes. The last article is devoted to the implementation recreational mathematics to education of students. Keywords: recreational mathematics, mathematical puzzles, mathematical ga- mes, science center ii N´azevpr´ace:Historie a souˇcasnostrekreaˇcn´ımatematiky a jej´ıvztah k matema- tice odborn´e Autor: Tereza B´artlov´a Katedra: Katedra matematick´eanal´yzy Vedouc´ıdisertaˇcn´ıpr´ace:prof. RNDr. LuboˇsPick, CSc., DSc., Katedra mate- matick´eanal´yzy Abstrakt: Tato disertaˇcn´ıpr´aceje vˇenov´anastudiu rekreaˇcn´ımatematiky se zvl´aˇstn´ımzˇretelemna jej´ıhistorii, vztah k odborn´ematematice a didaktick´emu v´yznamu. Pr´acesest´av´az pˇetiˇcl´ank˚ua struˇcn´eho´uvodu. V prvn´ımˇcl´ankuzkou- m´amehistorii rekreaˇcn´ımatematiky. Zamˇeˇrujeme se na v´yvoj matematick´ych ´ulohv pr˚ubˇehu dˇejina snaˇz´ımese jmenovat v´yznamn´eosobnosti, kter´emˇelyvliv na v´yvoj rekreaˇcn´ı matematiky. Druh´yˇcl´anekje vˇenov´anEdwinu Abbottovi Abbottovi a jeho knize Flatland. Jedn´ase o jednu z prvn´ıch popularizaˇcn´ıch knih o geometrii. Ve tˇret´ımˇcl´ankuse vˇenujeme jedn´ez v´yznamn´ych osobnost´ı rekreaˇcn´ımatematiky, Martinu Gardnerovi. Na jeho pr´acivolnˇenavazuje ˇctvrt´y ˇcl´anek,kter´yse zab´yv´azr´adnost´ımatematick´ea fyzik´aln´ıintuice a ilustruje ji na matematick´ych apr´ılov´ych ˇzertech. Posledn´ıˇcl´anekje vˇenovan´yimplementaci rekreaˇcn´ımatematiky do vzdˇel´av´an´ıstudent˚u. Kl´ıˇcov´aslova: rekreaˇcn´ımatematika, matematick´eh´adanky, matematick´ehry, science centra iii I would like to express my deep gratitude to LuboˇsPick who was my PhD advisor. I am very grateful to him for introducing me into the field of recreational mathematics and his help during my study. I really enjoyed sharing the ideas with him. His endless optimism and great enthusiasm for everything he does helped to make my study at Charles University an unforgettable experience. I would like to thank Vejtek Musil for his help with the TEX system. Special thanks belong to my mother for her never-ceasing support of all kinds. iv Contents Which came first, the recreational mathematics or the serious mathematics? 2 0.1 The popular-scientific aspect . .3 0.1.1 Arithmetics . .4 0.1.2 Number theory . .5 0.1.3 Geometry . .5 0.1.4 Combinatorics . .5 0.1.5 Probability . .5 0.1.6 Graph theory . .6 0.2 The amusement aspect . .6 0.2.1 Mathematical games . .6 0.2.2 Mechanical puzzles . .7 0.2.3 Problems . .7 0.3 The pedagogical aspect . .8 0.4 The historical aspect of recreational mathematics . .8 Bibliography . .9 Paper I 11 Paper II 67 Paper III 84 Paper IV 108 Paper V 142 1 Which came first, the recreational mathematics or the serious mathematics? Before we fully delve into the study of recreational mathematics, we should con- sider what this label exactly means. Perhaps the most concise definition of recre- ational mathematics is the one that has been provided by the leading figure of recreational mathematics of all times, namely Martin Gardner, who claimed that recreational mathematics is that part of mathematics that \includes anything that has a spirit of play about it". However, of course, different people might have different opinions on which part of mathematics can be considered as fun. For some it may be a Sudoku in Sunday newspapers, for others it can be the Rubik's cube, and, not surpris- ingly, a completely different idea of what is \amusing mathematics" is shared by professional mathematicians. Not a single mathematician would say that he/she does not enjoy his/her job, even if he/she is studying functional analysis or other advanced mathematical topics. Many professional mathematicians regard their work as a form of play, in the same way professional golfers or basketball stars might. In general, math is considered recreational if it has a playful aspect that can be understood and appreciated by non-mathematicians. Consequently, such “definition” would be rather blurred as it would probably encompass almost all kinds mathematics and therefore it would be too general. So what is it that determines whether a problem or task is recreational or not? There are four, somewhat overlapping, aspects which altogether cover most of the topics that could be possibly labelled by recreational mathematics. 1. The popular-scientific aspect - recreational mathematics is that part of mathematics which is fun and which is popular. That is, the corresponding problems should be understandable to an interested layman, though the solutions may be harder. By recreational mathematics we can understand the approach using which we can make serious mathematics understandable or, at least, more palatable. 2. The amusement aspect - recreational mathematics is a mathematics that is used as a diversion from serious mathematics to one's amusement. For example, one of the prominent contemporary recreational mathematicians Ian Stewart perceives the role of recreational mathematics precisely in this sense. He is trying to view mathematics as a source of inspiration and joy. He often writes in his books that the amusement mathematics is that part of it which is not taught at school. The same point of view was held by Martin Gardner who moreover believed that even in the school the mathematics that is taught there should be fun to a certain degree. 3. The pedagogical aspect - recreational mathematics can be used for the teaching purposes. It seen as a great pedagogical utility. Its parts have 2 been present in the oldest known mathematics and this situation continues to the present day. 4. The historical aspect { recreational mathematics has always played a very important part in the history of mathematics and it was responsible for the origin of whole important mathematical theories and concepts that would not exist without it. All the four named aspects are interconnected and influence each other. They overlap considerably and there is no clear boundary between them and the \se- rious" mathematics. The recreational mathematics is somewhere on the border among all these four aspects and tries to find the balance between seriousness and frivolity. We shall now consider each of the above-mentioned aspects of recreational mathematics separately in detail. 0.1 The popular-scientific aspect Mathematical riddles have been boggling the willing minds of interested intelli- gent people from the dawn of mankind. Moreover, important connections exist between problems originally meant to amuse and mathematical concepts. As a motivation force, then, the inclination to seek diversion and entertainment has resulted in the unintended revelation of mathematical truths, while, at the same time, it provides a good training of mathematical logic. One of the areas in which recreational mathematics is interconnected with a serious one, include problems whose assignment is understandable to everyone, but not everyone knows how to solve them. These problems have usually caught the attention of both professional mathematicians and the public with its simple formulation and comprehensibility. In this way the recreational mathematics provides the utility of a way to communicate a mathematical ideal to the public at large. Sometimes we can even wait centuries before mathematicians find a solution to a particular problem because the solution requires a nontrivial and advanced mathematical knowledge. These problems include for example Three classical geometrical problems which have eventually been proved to be impossible to solve but these proofs took incredible twenty-four centuries. Similar fate we have seen in connection with further problems such as the Archimedes's cattle problem, the Four-color theorem or the Fermat's last theorem. All these problems and others are mentioned in more detail below in the article about the history of recreational mathematics [2]. Another area in which the recreational mathematics is intertwined with the serious one, includes problems that are both understandable and at the same time have quite an easy solution. On the one hand, for a mathematician, it is not difficult to solve such a task, on the other hand the problem might become more mathematically interesting when one tries to generalize it.
Load more

Recommended publications
  • 1970-2012 TOPIC INDEX for the College Mathematics Journal (Including the Two Year College Mathematics Journal)
    1970-2012 TOPIC INDEX for The College Mathematics Journal (including the Two Year College Mathematics Journal) prepared by Donald E. Hooley Mathematics Department Bluffton University, Bluffton, Ohio Each item in this index is listed under the topics for which it might be used in the classroom or for enrichment after the topic has been presented. Within each topic entries are listed in chronological order of publication. Each entry is given in the form: Title, author, volume:issue, year, page range, [C or F], [other topic cross-listings] where C indicates a classroom capsule or short note and F indicates a Fallacies, Flaws and Flimflam note. If there is nothing in this position the entry refers to an article unless it is a book review. The topic headings in this index are numbered and grouped as follows: 0 Precalculus Mathematics (also see 9) 0.1 Arithmetic (also see 9.3) 0.2 Algebra 0.3 Synthetic geometry 0.4 Analytic geometry 0.5 Conic sections 0.6 Trigonometry (also see 5.3) 0.7 Elementary theory of equations 0.8 Business mathematics 0.9 Techniques of proof (including mathematical induction 0.10 Software for precalculus mathematics 1 Mathematics Education 1.1 Teaching techniques and research reports 1.2 Courses and programs 2 History of Mathematics 2.1 History of mathematics before 1400 2.2 History of mathematics after 1400 2.3 Interviews 3 Discrete Mathematics 3.1 Graph theory 3.2 Combinatorics 3.3 Other topics in discrete mathematics (also see 6.3) 3.4 Software for discrete mathematics 4 Linear Algebra 4.1 Matrices, systems of linear
    [Show full text]
  • C-Space Tunnel Discovery for Puzzle Path Planning
    C-Space Tunnel Discovery for Puzzle Path Planning XINYA ZHANG, The University of Texas at Austin ROBERT BELFER, McGill University PAUL G. KRY, McGill University ETIENNE VOUGA, The University of Texas at Austin Fig. 1. Puzzles we solve using our approach, roughly ordered by difficulty from left to right. Top row: alpha, alpha-z, alpha-j, alpha-g, double-alpha, claw, and enigma. Bottom row: duet (with 4 different grid sizes), Mobius, ABC, and Key. All but the alpha variants are Hanayama puzzles. Rigid body disentanglement puzzles are challenging for both humans and 1 INTRODUCTION motion planning algorithms because their solutions involve tricky twisting The Piano Mover’s Problem asks whether one can move a piano and sliding moves that correspond to navigating through narrow tunnels in between rooms through a sequence of rigid-body motions. This the puzzle’s configuration space (C-space). We propose a tunnel-discovery problem has inspired a great deal of work in computational geometry and planning strategy for solving these puzzles. First, we locate important features on the pieces using geometric heuristics and machine learning, and and robotics because it has a vast number of practical applications, then match pairs of these features to discover collision free states in the from collision-free navigation in automated warehouses, to path puzzle’s C-space that lie within the narrow tunnels. Second, we propose planning in pharmaceutical drug design. Rigid disentanglement a Rapidly-exploring Dense Tree (RDT) motion planner variant that builds puzzles are an interesting variant of the problem because they are tunnel escape roadmaps and then connects these roadmaps into a solution specifically designed to be difficult to take apart: they are notoriously path connecting start and goal states.
    [Show full text]
  • History of Mazes a Mind Boggling Collection Of
    A mind boggling collection of mazes, 3-D puzzles & full-body brain games. Engage in critical & creative thinking, individual & group challenges, and see what makes your own brain better at problem solving. Music Maze Maze of Illusions Say Colors Bird In The Which Lines Bush Bumpy Longer? Giant Tower of Shapes Flag Not There Hanoi How Many See Through Colors Colors Shadow Floating Circle Squares Red Parallel Circles Squares Purple Lines Columns Vases Seeing First Time Bird In Cage Creature Bigger Mirror With Peek Holes Portrait Mirrored Area Columns Impossible Tube See Color? Spots Mirror What’s Fun Shapes An Illusion Welcome Cube House Illusions Mirrors Wheel Prism Play Colored Shadow David Anson Russo Wall Labyrinthian Gallery Light Color Library Spiral Area Web-Maze Brain Teaser Puzzles History of Mazes Headlong Maze Arrow Maze Mathematica Maze Make-A-Maze Senior Puzzle Maze Finger Mazes Marble Mazes “…one of the best “Mazes inspires teamwork and problem exhibits we’ve solving in visitors, accomplishing just what ever had!” “The frst exhibition I have our missions aims for! We saw our member - Senior Floor Faculty families come back for multiple visits and COSI Columbus seen where ALL ages are engaged equally.” the multi-generational experience that the - Jeannie Colton exhibit provided appealed to all visitors.” Visitor Services Manager - Chevy Humphrey Arizona Science Center President and CEO Arizona Science Center "TAG teachers loved this exhibition.” - Senior Floor Faculty COSI Columbus Word on the street “Mazes was a hit that our family audience The exhibit has been LOVED! They wanted it to stay much “We saw complete strangers wonderful.
    [Show full text]
  • Area Maze Madness : Stretch Your Brain with Fun Math and Challenging Logic Puzzles Pdf, Epub, Ebook
    AREA MAZE MADNESS : STRETCH YOUR BRAIN WITH FUN MATH AND CHALLENGING LOGIC PUZZLES PDF, EPUB, EBOOK Graham Jones | 128 pages | 19 Nov 2019 | Ulysses Press | 9781612439426 | English | none Area Maze Madness : Stretch Your Brain with Fun Math and Challenging Logic Puzzles PDF Book Following written and even oral directions can be a difficult task for many students. But this is a word search with a twist. Controls are easy and the puzzles are fun. By Jon Flippin. Nov 6, One complaint, though. Already have an account? Crosswords Links to daily crossword puzzles and resources. By Jason Hamilton. So I have to just guess? Hundred is a square grid, whose cells are to be filled by some digits. I think it would be cool if some of the answers had another layer of hand holding to help guide me through solutions a little more, and how I can think differently through areas where I probably got stuck. By Colleen McCallum. Puzzles are known to boost brain power—they improve memory, spatial awareness, logic, and problem-solving. The Monty Hall Problem: Beyond…. Lawyers defend man who stole lectern during capital riots TZ. Suguru Sometimes called Tectonics or Number Blocks , these puzzles have very simple rules but can be extremely challenging. I would have liked some harder levels the further you went along. Just using the grid doesn't help as much with the relationships that the clues give. The collection has grid-based logic puzzles for you to try your hand at, ranging from easy to exceptionally challenging. One solution can be found here.
    [Show full text]
  • A Systems Approach to Visualization of the Problem Solved Algorithms and the Programming Language LOGO
    Advances in Sensors, Signals, Visualization, Imaging and Simulation A systems approach to visualization of the problem solved algorithms and the programming language LOGO MICHAL MUSILEK, STEPAN HUBALOVSKY Department of Informatics University of Hradec Kralove Rokitanskeho 62, Hradec Kralove CZECH REPUBLIC [email protected], [email protected], http://www.musilek.eu/michal Abstract: - One of the most important tasks in teaching of algorithm development and programming is to use a suitable method of developing theoretical knowledge of this area. Drawing on their experience, the authors have found that the best method to be used is the system approach. This method, described in the paper, is presented through the simulation and visualization of two real processes – Tower of Hanoi brain teaser and decrypting of the Daisy cipher. The solution is demonstrated step by step – it starts with the problems definition, then the strategy solution analyses are shown and finally visualization of the processes is presented in illustrative form in LOGO programming language. Key-Words: Algorithmic thinking, LOGO programming language, system approach, multidisciplinary learning, problem solving, education, computer simulation and modeling, visualization, turtle geometry. 1 Introduction The process can be understood as series of The term algorithm can be also connected with transformations that changes the input values to the terms system, model, simulation, output values. From the system point of view the multidisciplinary approach, which are important in process is dynamic system in which the values of current approach to scientific, technological and the characteristic of the system elements are professional practice. Many universities are changed under the influence of the external realizing that modeling and simulation is becoming elements.
    [Show full text]
  • The Tower of Hanoi and the Experience of Lived Number
    The Tower of Hanoi and the Experience of Lived Number With Krista Francis-Poscente As the study of experience, phenomenology lays claim to subject mat- ter that is of great interest in both e-learning and technical design: this is the experience of users or of students in their various engagements with technology. The term “experience” has recently played a promi- nent role in discussions of computer technologies and other topics, with release in recent years of books on “user experience design” (e.g., Press & Cooper, 2003) and “experiential marketing” (e.g., Len- derman, 2005). In their book Technology as Experience, McCarthy and Wright (2004) explain the prominence of this term in the context of the recent “explosion” of new popular technologies and innovations: Interaction with technology is now as much about what people feel as it is about what people do. It is as much about children playing with GameBoys, teenagers gender swapping, and elderly people socializing on the Internet as it is about middle-aged executives managing knowledge assets, office work- ers making photocopies, or ambulance controllers dispatching ambulances. The emergence of the computer as a consumer product has been accompa- nied by very explicit attention to user experience. (p. 9) Technologies and their design require new ways of understanding and studying experiential vicissitudes bound up with their uses. McCarthy and Wright and before them, authors like Paul Dourish, Terry Winograd, and Fernando Flores, make significant use of her- meneutic phenomenology and related “experiential” approaches to provide these kinds of studies of technologies. In the case of e-learning research, attention to experience has taken a rather different character, but one that is no less forceful and explicit.
    [Show full text]
  • Algebra Brain Teasers Worksheets
    Algebra Brain Teasers Worksheets Gliomatous and aeronautical Bartholemy never inactivated his yapoks! Unreluctant Padraig take-off, his superscriptions jibes cross-examined passably. Muffin transmogrifying his pallet shredded covertly, but supposable Jefry never silverises so inodorously. Enter all letters from your game. Free printable Brain Teasers For Kids with answers featuring a mix of logical puzzles. National Institute of Environmental Health Sciences Skip Navigation The student had almost completed a difficult problem. There is keep a back to download a Free Printable PDF Math Riddles. Logic Puzzles & Riddles Worksheets & Free Printables. We devote great fun with our Halloween Logic Puzzles, Hangman, try excel draw a map of image area; repeat this. The water and games for more good job somewhere between these. Brain Teaser Worksheets FREE Printable Worksheets. Algebra Picture Puzzle Difficulty Popularity You can find an odd multiplication in the figure. Most puzzles and here we have numerous opportunities for these four levels with numbers with lid game: strategy was once in a more than square addition and! How many can you solve? And algebra riddles and critical thinking cap dusted off your child has hands with algebra worksheets brain teasers gifs with answer! Our printable christmas tree, algebra crossword math behind sarah sharing ebook then you have convenient answers: algebra brain teasers worksheets. Printable Brain 30 Math Brain Teasers And Answers To Solve 2021. Comprise puzzles for your brain: above anything else, how to help your middle of your mind games rebus belongs to algebra brain teasers worksheets are added. Brain teasers with answers. What concept of wonder has the shell.
    [Show full text]
  • Philip K's Puzzle List
    (from http://hjem.get2net.dk/philip-k/puzzles/puzzlist.htm, December 2006) Philip K's Puzzle List Early Rubik Puzzles (late 70's): Büvös Kocka, Hungarian Cube in blue cardboard box, Politoys Zauberwürfel, German Cube in blue cardboard box, Spielewaren Magic Domino Rubik's Cheese (from about 1982) Rubik Puzzles released by Ideal 1980 - 1983: Rubik's Cube Rubik's Pocket Cube Rubik's Revenge Rubik's Master Cube (Arxon 1982) Rubik's Perpetual Calendar Rubik's World Rubik's Game (2 - 6 players) Rubik's ZigZaw Puzzle Rubik's Brain Game (2-player game) Rubik’s Race (2-player board game) Other Puzzles released by Ideal: Alexander's Star Color Match (2 - 6 players) Missing Link Trillion Rubik Puzzles released by Matchbox 1986 - 1990: Rubik's Magic (link the rings) Rubik's Master Magic (unlink the rings) Rubik's Magic (create the cube) Rubik's Magic Picture Game (monster sports) Rubik's Magic, Malev Airlines Mini Version (4 tiles) Rubik's Magic, Merit Cigarettes adv. (4 tiles) Rubiks' Magic Strategy Game (2-player board game) Rubik's Clock Rubik's Dice Rubik's Fifteen Rubik's Illusion (2-player board game) Rubik's Tangle Rubik's Triamid Rubik Puzzles released by Hasbro/Parker 1993: Rubik's Maze Rubik's Mini Cube, w/Power Rangers Rubik’s Rabbits Rubik Puzzles released by Oddzon/Hasbro 1995 - 2000: Rubik's Bart Simpson Cube Rubik's Darth Maul Cube Rubik's Bricks Rubik's Double Tangram Rubik's Eclipse (2-player board game) Rubik's Games (cd-rom) Rubik's Harry Potter Cube Rubik's Harry Potter Magic Rubik's Harry Potter Cube Rubik's Hello Kitty Cube
    [Show full text]
  • Games to Post 6-29-08
    Introduction to Using Games in Education: A Guide for Teachers and Parents Introduction to Using Games in Education: A Guide for Teachers and Parents First edition 8/15/06. Second edition 6/29/08. Dave Moursund Teacher Education, College of Education University of Oregon 97403 Email: [email protected] Web: http://uoregon.edu/~moursund/dave/index.htm Web: http://IAE-Pedia.org Web: http://I-A-E.org/ Edited by Dick Ricketts The second edition reflects careful editing of the first edition, with hundreds of small changes. A little material has been added, and a little material has been deleted. All of the references have been brought up to date. Page 1 Introduction to Using Games in Education: A Guide for Teachers and Parents Contents ...........................................................................................2 About Dave Moursund, the Author .................................................6 Preface..............................................................................................7 Learning Through Game Playing .............................................8 Computational Thinking...........................................................8 Puzzles ......................................................................................9 Brief Overview of Contents......................................................9 Chapter 1: Thinking Outside the Box ............................................11 Puzzle Problems......................................................................12 Problems and Problem Solving
    [Show full text]
  • Algebra Brain Teasers Worksheets
    Algebra Brain Teasers Worksheets Anchoretic and Oscan Caspar always jam libellously and varnish his vicomte. Is Alf wasp-waisted when Amos disrobed drudgingly? Uniaxial and isopodous Lloyd braids almost blamably, though Inglebert shut-offs his jubilances whinny. The tacks are parallel to the floor. These puzzles are designed to test with Numerical ability, Logical thinking, Maths problem solving with sp Find the answer to these questions and many more in our Bible quizzes. The man poured enough water onto the plate to cover it. Outwit your enemies, navigate strange labyrinths and think outside the box to survive and succeed. What is going on? If eleven plus two equals one, what does nine plus five equal? Protection of human dignity essay. This is a prominent choice since it is easy to print, it is simple to distribute as well as it is extremely helpful. Math Puzzles SMBC is a daily comic strip about life, philosophy, science, mathematics, and dirty jokes. Brain teasers are made with the aim of having fun while spending time. At home, they split the sacks equally. University cancer and blood center athens ga. Brain Teasers Fun Sheets Common Core Sheets Answers. Can you solve the magic triangle? How old is Jennie? Download Brain Teaser Riddles, Questions, and Answers, Games, etc. Must be zero find the value of the race remains these mathematics riddles with answers to! To print or download to Twitter Share to Twitter Share to Facebook Share to Share. What is light as a feather, but even the strongest man cannot hold it more than a few minutes? The key to this math riddle is realizing that the one place must be zero.
    [Show full text]
  • FAMOUS PUZZLES of Great Mathematicians
    FAMOUS PUZZLES of Great Mathematicians Miodrag S. Petkovic ®AMS AMB .IU Cd.N M~TI:I£.MA1'J C AL SOCI£T1' Providence, Rhode Island 2000 MC1 tlr.ema:ti"" Subject Cla:11rifimtion, Primary OOA08, 97 A20, 01A05 , 01A70, 05A05, 05045, 05C90, ll004, 11009, 51E:l0, 51Ml6, 52015, 52C22, 97040. Por additiona l infon1ut.tion and upd ates o n t his book: visit www.ams.o rg/ b ookpages/mbk-63 Libra ry of Congress C ataloging-in-Publication Data Petlowit, Miodrag. Famous puzzles of great mathematicians / M iodrag S. PetkoviC. p . em. [ucJudes bibliographical references and index. ISBN 978-0-8218-4814-2 (alk. paper) 1. Mathemat ic:al rec reations. 2. Ma.thEJmatics- Populnr works. I. T itle. QA95.P4358 2009 5 l0-dc22 20090l'l018 Copy ing and re print ing. (udh,;dua.l readers of this pubHcatiou, and nonp1·ofit libra ries acting for t hem, are 1>ermiUed to make fair use of the material, such as to copy a chapter for use in teaching or research. Permission is granted to quote brief passages from this publication in reviews, provided the <; \Ust..ornary tl<:knowl(;ldgment of tbe $tll..m;e }$given. Republi<:a.t.ion, l5'y.sterntttic copying, or muJt.iple reprodutt.ioo of any rrmterittl in ~hi1; publit<-ttiou is permitted only under license from the American Mathematical Society. R<E-quests for such permission should be addressed to the Acquisitions Depa.rtment, American !\{atbematical Society, 201 Charles Street, Providence, Rhode Island 02004-2294 USA. Requests can also be made by e-mail 'o r eprint - per!QieeionCama.
    [Show full text]