Adventures in recreational mathematics / David Singmaster.

Format:

Book

Author/Creator:

Singmaster, David, author.

Contributor:

Edward Potts Cheyney Memorial Fund.

Series:

Problem solving in mathematics and beyond ; v. 21.

Problem solving in mathematics and beyond ; vol. 21

Language:

English

Subjects (All):

Mathematical recreations.

Mathematical recreations--History.

History.

Genre:

History.

Physical Description:

2 volumes : illustrations ; 23 cm.

Place of Publication:

Singapore ; Hackensack, NJ : World Scientific Publishing Co. Pte. Ltd., [2022]

Summary:

"The author believes in the presentation and teaching of mathematics as recreation. When the Rubik's Cube took off in 1978, based on thinly disguised mathematics, he became seriously interested in mathematical puzzles which would provide mental stimulation for students and professional mathematicians. In these 2-volume books, the readers shall have an adventure into previously unknown origins of ancient puzzles, which could be traced back to their Medieval, Chinese, Arabic and Indian sources. The puzzles are fully described, many with illustrations, adding interest to their history and relevance to contemporary mathematical concepts"-- Provided by publisher.

Contents:

Machine generated contents note: Preface

About the Author

1. What is Recreational Mathematics?

Bibliography

Part I. Ancient Puzzles

2. Puzzles from The Greek Anthology

2.1. The Problems

2.2. Solutions and Comments

3. Aryabhata and Other Early Indian Mathematicians

3.1. Pythagorean Recreations

3.2. Knowing What Each Pair Has

3.3. The Snail in the Well

4. Alcuin and his Propositiones

4.1. Alcuin

4.2. The Manuscripts

4.3. Managing the Text of Propositiones

4.4. An Annotated Translation of Propositiones

4.5. Summary and Discussions

5. The Problems of Abbot Albert

5.1. Summary

6. Pacioli: The First Book of Mathematical Puzzles

6.1. De Viribus Quantitatis

6.2. Recreational Material in De Viribus Quantitatis

7. Pacioli's Magic and Card Tricks

8. Some Early Topological Puzzles

8.1. The Chinese Wallet or Flick-Flack or Jacob's Ladder

8.2. The Alliance and Victoria Puzzle

8.3. Solomon's Seal or African Beads Puzzle

8.4. The Cherries Puzzle

8.5. Six-Piece Burrs

8.6. Borromean Rings

8.7. Chinese Rings

8.8. Puzzle Grills

8.9. Conclusions

Interlude: Finding a Sardinian Maze

Part II. New Ideas about Old Puzzles

9. A Legacy of Camels

9.1. Some History

9.2. Analysis of the 17 Camels Problem

9.3. Analysis of the 13 Camels Problem

10. Heronian Triangles

10.1. Determination of Pythagorean triples

10.2. Determination of Heronian triples

11. The Ass and Mule Problem

11.1. Analysis of the Original Problem

11.2. Doglies Variation

11.3. Another Simpler Variation

12. How to Count Your Chickens

12.1. Answers

13. The Monkey and the Coconuts

13.1. Determinate Versions

13.2. Indeterminate Versions

13.3. A General Solution

13.4. Other Variations

13.5. Solutions and Some Comments

14. Two River Crossing Problems

14.1. De Fontenay's Generalization

14.2. Dudeney's Solution

14.3. Improved Solutions

14.4. Proof of Optimality

14.5. Missionaries and Cannibals

14.6. Other Cultures

15. Sharing Barrels

15.1. The Barrels Problem

15.2. Integral Triangles

15.3. Triangular Coordinates

15.4. The Number of Integral Triangles

15.5. The Number of Incongruent Integral Triangles

15.6. Relation to Partitions

15.7. Other Versions

15.8. Fair Division of the First kn Integers into k Parts

16. Vanishing Area Paradoxes

16.1. Early Examples

Appendix A: Ancient and Important Sources

A.1. Bibliography of Early Work

A.2. Sources Project

A.3. Open Problems

Preface

1. Why Recreational Mathematics?

1.1. The Nature of Recreational Mathematics

1.2. The Utility of Recreational Mathematics

1.3. Some Examples of Useful Recreational Mathematics

1.4. Recreational Mathematics with Objects

1.5. Examples of Medieval Problems

1.6. Examples of Modern Recreational Problems

1.7. The Educational Value of Recreations

1.8. Why Is Recreational Mathematics So Useful?

2. On Round Pegs in Square Holes and Vice Versa

2.1. Extremal Spheres

2.2. Popular Conceptions

2.3. Educational Value

2.4. Appendix

3. Hunting for Bears

3.1. The Square Path Version

4. Sum = Product Sequences

5. A Cubical Path Puzzle

5.1. The Original Puzzle

5.2. Further Problems

6. Recurring Binomial Coefficients

6.1. Recurring Binomial Coefficients and Fibonacci Numbers

6.2. Computer Search

7. Sums of Squares and Pyramidal Numbers

8. The Bridges of Konigsberg

8.1. The Envelope Problem

8.2. The Pregel Bridges

8.3. Other Places

9. Triangles with Doubled Angles

9.1. Geometry

9.2. Diophantine Analysis

10. Quasicrystals and the University

11. The Wobbler

11.1. The Height of the Center of Gravity

11.2. The Distance Between Contacts

11.3. Some Problems

11.4. Paul Schatz's Oloid

11.5. Other Results

12. Calculating for Fun

12.1. The Chessboard Reward

12.2. The Landowner's Earth and Air

12.3. Buying Manhattan

12.4. "It's a Hard Rain a Gonna Fall!"

12.5. Permutations and the Number of Crosswords

12.6. Grains of Sand versus Stars in the Sky

12.7. "A Lottery is a Tax on the Innumerate."

12.8. Storing a Million Pounds

12.9. A4 Paper

12.10. Other Exercises

13. Three Rabbits or Twelve Horses

13.1. The Three Rabbits Puzzle

13.2. Four Horses, Twelve Horses and Other Puzzles.

Notes:

Includes bibliographical references.

Local Notes:

Acquired for the Penn Libraries with assistance from the Edward Potts Cheyney Memorial Fund.

Other Format:

Online version: Singmaster, David, Adventures in recreational mathematics

ISBN:

9789811225642

9811225648

9789811226304

981122630X

9789811226007

9811226008

9789811226502

9811226504

9789811226038

9811226032

9789811226519

9811226512

OCLC:

1259585033

Publisher Number:

99989027571