Mathematical Games And Pastimes (Popular Lectures In Mathematics Vol 10)- Domoryad

In this post, we will see the book Mathematical Games And Pastimes (Popular Lectures In Mathematics Vol 10) by A. P. Domoryad.

About the book

The greater part of this book is devoted to classical games. The first few chapters deal with various systems of notation and with certain topics in the theory of numbers, the knowledge of which is necessary for the understanding of the theory of various mathematical games. But for some readers these chapters might be interesting in themselves. The theory of some isolated games is presented fairly fully here; in other cases only results are given; and reference is made to sources, where proof of these results can be found. Side by side with classical pastimes, the book devotes much space also to “contemporary” pastimes quick reckoning, re-cutting of figures, construction of curves, and models of polyhedra. Deserving particular attention are the problems which admit a practically inexhaustible or even infinite number of solutions (“Construction of parquets”, “Construction of pleasing patterns”, etc.).
Here, everybody, by applying persistence and inventiveness, can attempt to obtain interesting results.
Whereas such classical pastimes as, for example, constructing “magic squares” may be enjoyed by a comparatively narrow section of people, the cutting out of, say, symmetrical figures in paper, the construction of pleasing patterns, searching for numerical curiosities, by not requiring any mathematical preparation, might give pleasure to both amateur and professional mathematicians. The same can be said about pastimes requiring knowledge confined to that obtained in the 8th to 10th classes of the secondary school (construction of parquets, of interesting curves and borders, etc.).
In group activities it is possible to arrange competitions in making up original parquets, in the construction of curves and borders, in obtaining attractive symmetrical figures cut out of paper, and so on. Each participant in such competitions can dazzle with his inventiveness, accuracy of execution, or artistry of colouring the figures obtained. Such collective activity can be rounded off by compiling an album or by organizing an exhibition of the best items. Many pastimes and even single problems may suggest to the amateur mathematician themes for independent investigations (the use of knight’s moves instead of the “short” moves of the fook in the “game of 15”, the search for interesting identities — see § 37 —, the generalization of the problem about tourists — problem No. 13 in §37 —and so on). On the whole, this book caters for readers with mathematical knowledge within the limits of the 9th and 10th classes of the secondary school, even though the greatest part of the material is accessible to pupils of the 8th class, and some topics — even to school- children of the 5th and 6th classes. Many chapters can be used by teachers of mathematics for extracurricular activities.
Various categories of readers can use the book in various ways: persons not particularly fond of mathematics can become acquainted with curious properties of numbers or figures, without going into the fundamentals of the games and pastimes, and taking for granted single propositions; amateur mathematicians are advised to study certain parts of the book with pencil and paper, solving the problems given and answering the questions posed. § 38 gives answers to the problems to be found in the text, questions and hints towards their solution and also proofs of certain of the theorems mentioned in the text. References to the appropriate section of § 38 are given in small figures between ordinary brackets.
References to books in which the reader may find a more detailed discussion of the topics touched upon are given by a number enclosed in square brackets. This number refers to the corresponding entry in the bibliography at the end of the book.

The book was translated from Russian by Halina Moss and was published in 1963.

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  1. Various systems of Notations 1
  2. Some facts from the Theory of Numbers 10
  3. Congruences 15
  4. Continued Fractions and Indeterminate Equations 20
  5. Pythagorean and Heronic Triples 31
  6. Arithmetical Pastimes 33
  7. Numerical Tricks 37
  8. Rapid Calculations 45
  9. Numerical Giants 57
  10. Games with Piles of Objects 61
  11. Meleda 71
  12. Lucas’ Game 75
  13. Solitaire 77
  14. The “Game of Fifteen” and Similar Games 79
  15. Problems on determining the Number of ways of reaching a goal 86
  16. Magic Squares 97
  17. Euler Squares 105
  18. Pastimes with Dominoes 107
  19. Problems Connected with Chessboard 109
  20. Making up Timetables 120
  21. The “Problem of Josephus Flavius” and similar ones 124
  22. Pastimes connected with Objects Changing Places 127
  23. Simplest methods of Constructing Pleasing Patterns 136
  24. Regular Polygons from Rhombi 142
  25. The Construction of Figures from Given Parts 145
  26. The Construction of Parquets 149
  27. Re-cutting of Figures 158
  28. The Construction of Curves 166
  29. Mathematical Borders 188
  30. Models of Polyhedra 193
  31. Pastimes with a sheet and strips of paper 202
  32. The Four Colour Problem 207
  33. Drawing Figures at one stroke of the pencil 211
  34. Hamilton’s Game 215
  35. Arranging Points on a Plane and in Space 219
  36. Problems on a Logical Nature 222
  37. Rag-Bag 232
  38. Notes and Answers to Problems 246

Bibliography 297

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