Domoryad / Sneddon / Stark Mathematical Games and Pastimes

Popular Lectures in Mathematics
1. Auflage 2014
ISBN: 978-1-4831-3782-7
Verlag: Elsevier Science & Techn.
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, 310 Seiten, Web PDF

Mathematical Games and Pastimes focuses on numerical solutions to mathematical games and pastimes. The book first discusses the binary system of notation and the system of notation with the base three. Congruences, Pythagorean and Heronic triples, and arithmetical pastimes are explained. The text takes a look at the nature of numerical tricks. Guessing the results of operations with unknown numbers; determination of numbers thought of using three tables; and extraction of roots of multidigit numbers are explained. The selection also touches on rapid calculations, games with piles of objects, Meleda, solitaire, and Lucas' game. Problems on determining ways to reach goals are also presented. Games that show the numerous ways to reach goals are discussed. The text also examines Euler squares, dominoes, and problems related to the chess board. Pastimes related to objects changing places are also highlighted. Topics include Lucas' problem, Ruma, and Monge's shuffle. The book is highly recommended for readers wanting to find solutions to mathematical games and pastimes.

Autoren/Hrsg.

Domoryad, A. P.

Sneddon, I. N.

Stark, M.

Inhaltsverzeichnis

1;Front Cover;1
2;Mathematical Games and Pastimes;6
3;Copyright Page;7
4;Table of Contents;8
5;Foreword;10
6;Chapter § 1. Various systems of notation;14
6.1;The Binary System of Notation;19
6.2;The System of Notation with the Base Three;20
7;Chapter § 2. Some Facts from the Theory of Numbers;23
7.1;Functions .(n) and S(n);24
7.2;Function x (the integral part of x);25
8;Chapter § 3. Congruences;28
8.1;Euler's Functions;30
9;Chapter § 4. Continued Fractions andIndeterminate Equations;33
10;Chapter § 5. Pythagorean and Heronic Triples;44
11;Chapter § 6. Arithmetical Pastimes;46
12;Chapter § 7. Numerical Tricks;50
12.1;Guessing a Number, Thought of by Someone;50
12.2;The Guessing of the Results oi Operations with an Unknown Number;51
12.3;The Determination of a Number Thought of, Using Three Tables;52
12.4;A Card Trick;53
12.5;Who Took What;53
12.6;The Extraction of Roots of Multidigit Numbers;54
13;Chapter § 8. Rapid Calculations;58
13.1;Abbreviated Multiplication;58
13.2;Abbreviated Division;59
13.3;The Abacus and Napier's Rods;60
13.4;The Extraction of the Square Root;62
13.5;Addition and Subtraction In Place of Multiplication;65
13.6;On Calculating Logarithms;67
14;Chapter § 9. Numerical Giants;70
15;Chapter § 10. Games with Piles of Objects;74
15.1;Sachet's Game;74
15.2;Tsyanshidzi (a game with two piles of objects);75
15.3;Nim (a game with three piles of objects);78
16;Chapter § 11. Meleda;84
17;Chapter § 12. Lucas' Game;88
18;Chapter §. 13. Solitaire;90
19;Chapter §. 14 The "Game of Fifteen"and Similar Games;92
20;Chapter 15. Problems on Determining the Number of Ways of Reaching a Goal;99
20.1;Problems about Jumpers;99
20.2;The problem about the Rook;102
20.3;A problem about a Spider;103
20.4;Polydimensional Problems;105
20.5;A chess Problem about a King;106
20.6;Miscellaneous Problems;107
21;Chapter § 16. Magic Squares;110
22;Chapter § 17. Euler Squares;118
23;Chapter § 18. Pastimes with Dominoes;120
24;Chapter § 19. Problems Connected with the Chess Board;122
24.1;A Problem about Rooks;122
24.2;A Problem about the Queens;123
24.3;A Problem about a Knight;127
24.4;Miscellaneous Problems;129
24.5;Questions for Consideration;131
25;Chapter § 20. Making up Timetables;133
26;Chapter § 21. The "Problem of Josephus Flavins"and Similar Ones;137
27;Chapter § 22. Pastimes Connected with Objects Changing Places;140
27.1;The transposition of objects in pairs;140
27.2;Lucas' Problem;141
27.3;The Gathering of Coins in Piles;142
27.4;Ruma;142
27.5;The Repeated Performance of the Same Operation;144
27.6;Monge's Shuffle;147
28;Chapter § 23. The Simplest Methods of Constructing Pleasing Patterns;149
28.1;Patterns on squared paper;149
28.2;Using Compasses and aRuler;151
28.3;Symmetrical Figures;152
29;Chapter § 24. Regular Polygons from Rhombi;155
30;Chapter § 25. The Construction of Figures from Given Parts;158
30.1;Mosaic;158
30.2;Figures out of Pieces of a Square;158
30.3;Rectangles Out of Squares;160
31;Chapter § 26. The Construction of Parquets;162
31.1;Two-colour Parquets;167
32;Chapter § 27. Re-cutting of Figures;171
33;Chapter §. 28. The Construction of Curves;179
33.1;Rosettes;179
33.2;Lissajous Curves;186
33.3;Cycloids, Epicycloids, Hypocycloids;190
33.4;Interesting Broken Lines;191
33.5;Ornate curves;195
34;Chapter § 29. Mathematical Borders;201
35;Chapter § 30. Models of Polyhedra;206
36;Chapter § 31. Pastimes with a Sheetand a Strip of Paper;215
36.1;Regular Polygons;216
36.2;Mobius' Strip;218
36.3;The Construction of a Regular Icosahedron;218
37;Chapter § 32. The Four-Colour Problem;220
38;Chapter § 33. Drawing Figures at one Stroke of the Pencil;224
39;Chapter § 34. Hamilton's Game;228
40;Chapter § 35. Arranging Points on a Planeand in Space;232
41;Chapter §. 36. Problems of a Logical Nature;235
41.1;Difficult Crossings;240
41.2;The Detection of a False Coin;241
41.3;Problems on Dividing Liquids;243
42;Chapter § 37. Rag-Bag;245
42.1;The Geometrical Demonstration of the Formula;245
42.2;Exercises for the Development of Geometrical Intuition;246
42.3;Interesting Identities;248
42.4;Optical Illusions;250
42.5;Miscellaneous Problems;252
42.6;Puzzles;256
43;Chapter § 38. Notes and Answers to Problems;259
44;Bibliography;310