Recreational mathematics includes many mathematical games, and can be extended to cover such areas as logic and other puzzles of deductive reasoning. Even some of the most interesting problems in this field do not require a knowledge of advanced mathematics. The subject can include other topics such as the aesthetics of mathematics, and peculiar or amusing stories and coincidences about mathematics and mathematicians. Its greatest contribution is its ability to pique curiosity and inspire the further study of mathematics. Some of the more well known topics in recreational mathematics are magic squares and fractals. Recreational mathematics can be divided into two main topics: games and puzzles. In short, puzzles have zero or one "players" and games have two or more players.
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Mathematical games
These curiosities involve two or more players which try to win, or at least not lose. Games of chance and probability are covered in the field of game theory, while games of no chance are analyzed using combinatorial game theory (a relatively new topic invented by John Horton Conway). Sometimes mathematical puzzles (below) are referred to as games as well.
Mathematical puzzles
In most puzzles, there is no interaction between two sides who are trying to achieve a goal before the other, but rather one (or no) person trying to find a solution that satisfies conditions in a problem. There is also the smaller group of so called "puzzles" that are just an interesting thing or pattern such as Conway's Game of Life or fractals. Do not confuse with mathematical games, as puzzles are often referred to.
Other
Other curiosities and pastimes of non-trivial mathematical interest:
- Juggling (juggling patterns)
- Origami (many mathematical results, some deep)
- Cat's cradle and other string figures
Publications
The Journal of Recreational Mathematics is the largest publication on this topic. Mathematical Games was the title of a long-running column on the subject by Martin Gardner in Scientific American. He inspired several new generations of mathematicians and scientists through his interest in mathematical recreations. Mathematical Games was succeeded by Metamagical Themas, a similarly distinguished but shorter-running column by Douglas Hofstadter, and afterwards by Mathematical Recreations, a column by Ian Stewart.
In popular culture
In the Doctor Who episode "42", the Doctor completes a sequence of happy primes, then complains that schools no longer teach recreational mathematics. The Curious Incident of the Dog in the Nighttime, a book about a young boy with Aspergers Syndrome, discusses many mathematical games and puzzles.
People
The foremost advocates of recreational mathematics have included:
- Lucy Baker
- John Horton Conway
- H. S. M. Coxeter
- Henry Dudeney
- Martin Gardner, author of Mathematical Games, a long running column in Scientific American
- Bobby Govier
- Piet Hein
- Douglas Hofstadter
- Maurice Kraitchik - possibly one of the earliest
- Sam Loyd
- Clifford A. Pickover, author of numerous books on recreational mathematics
- Ed Pegg, Jr.
- Walter William Rouse Ball
- David Singmaster
- Raymond Smullyan
- Ian Stewart
- Yakov Perelman
- Hugo Steinhaus
- Marilyn vos Savant, author of "Ask Marilyn", a long running column in Parade Magazine
- Aidz
- Miodrag Petković
References
- mathpuzzle.com by Ed Pegg, Jr.
- Puzzles of the Month by Gianni A. Sarcone
- The Unreasonable Utility of Recreational Mathematics by David Singmaster
- Nick's Mathematical Puzzles
- Knot a Braid of Links
See also
Bibliography
- Ball, W.W. Rouse; H.S.M. Coxeter (1987). Mathematical Recreations and Essays, Thirteenth Edition, Dover. ISBN 0-486-25357-0.
- Dudeney, Henry E. (1967). 536 Puzzles and Curious Problems. Charles Scribner's sons. ISBN 0-684-71755-7.
- Loyd, Sam (1959. 2 Vols.). in Martin Gardner: The Mathematical Puzzles of Sam Loyd. Dover. OCLC 5720955.
- Smullyan, Raymond M. (1991). The Lady or the Tiger? And Other Logic Puzzles. Oxford University Press. ISBN 0-19-286136-0.
