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Recreational mathematics is an umbrella term for mathematics carried out for recreation (including self-education and entertainment) rather than as a strictly research and application-based professional activity, although it is not necessarily limited to being an endeavor for amateurs. It often involves mathematical puzzles and games.
Many topics in this field require no knowledge of advanced mathematics, and recreational mathematics often appeals to children and untrained adults, inspiring their further study of the subject.
Some of the more well-known topics in recreational mathematics are magic squares, fractals, logic puzzles and mathematical chess problems, but this area of mathematics includes the aesthetics and culture of mathematics, peculiar or amusing stories and coincidences about mathematics, and the personal lives of mathematicians.
Mathematical games are multiplayer games whose rules, strategies, and outcomes can be studied and explained using mathematics. The players of the game may not need to use explicit mathematics in order to play mathematical games. For example, Mancala is a mathematical game, because mathematicians can study it using combinatorial game theory, but no mathematics is necessary in order to play it.
Mathematical puzzles require mathematics in order to solve them. They have specific rules, as do multiplayer games, but mathematical puzzles don't usually involve competition between two or more players. Instead, in order to solve such a puzzle, the solver must find a solution that satisfies the given conditions.
Logic puzzles are a common type of mathematical puzzle. Conway's Game of Life and fractals are also considered mathematical puzzles, even though the solver only interacts with them by providing a set of initial conditions.
As they often include or require game-like features or thinking, mathematical puzzles are sometimes also called mathematical games.
Other curiosities and pastimes of non-trivial mathematical interest include:
- patterns in juggling
- the sometimes profound algorithmic and geometrical characteristics of origami
- patterns and process in creating string figures such as Cat's cradles, etc.
- The journal Eureka published by the mathematical society of the University of Cambridge is one of the oldest publications in recreational mathematics. It has been published 60 times since 1939 and authors have included many famous mathematicians and scientists such as Martin Gardner, John Conway, Roger Penrose, Ian Stewart, Timothy Gowers, Stephen Hawking and Paul Dirac.
- 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 (1914-2010), in Scientific American. He inspired several generations of mathematicians and scientists, through his interest in mathematical recreations. "Mathematical Games" (1956-1981) was succeeded by "Metamagical Themas" (1981-1983), a similarly distinguished, but shorter-running, column by Douglas Hofstadter, then by "Mathematical Recreations" (19??-????), a column by Ian Stewart, and most recently "Puzzling Adventures" (????-present) by Dennis Shasha.
- The Recreational Mathematics Magazine, published by the Ludus Association, is electronic and semiannual, and focuses on results that provide amusing, witty but nonetheless original and scientifically profound mathematical nuggets. The issues are published in the exact moments of the equinox.
In popular culture
- In the episode titled "42" of the Doctor Who science fiction television series, the Doctor completes a sequence of happy primes. He then complains that schools no longer teach recreational mathematics.
- The Curious Incident of the Dog in the Night-Time, a book about a young boy with Asperger syndrome, discusses many mathematical games and puzzles.
Prominent practitioners and advocates of recreational mathematics have included:
|Full name||Last name||Born||Died||Nationality||Description|
|Lewis Carroll||Carroll||1832||1898||English||Mathematician, puzzlist, Anglican deacon and photographer best known as the author of Alice in Wonderland and Through the Looking-Glass|
|John Horton Conway||Conway||1937||—||English||Mathematician and inventor of Conway's Game of Life|
|Henry Dudeney||Dudeney||1857||1930||English||Civil servant regarded as England's "greatest puzzlist".|
|Martin Gardner||Gardner||1914||2010||American||Popular mathematics and science writer; author of Mathematical Games, a long-running Scientific American column|
|Solomon W. Golomb||Golomb||1932||—||American||Mathematician and engineer, best known as the inventor of polyominoes|
|Vi Hart||Hart||–||—||American||"Recreational mathemusician", creator of online recreational mathematics videos|
|D. R. Kaprekar||Kaprekar||1905||1986||Indian||Recreational mathematician and schoolteacher|
|Sam Loyd||Loyd||1841||1911||American||Chess player and composer and recreational mathematician, regarded as America's greatest puzzlist|
|Joseph Madachy||Madachy||1927||2014||American||Long-time editor of Journal of Recreational Mathematics, author of Mathematics on Vacation and Madachy's Mathematical Recreations, recreational mathematician and mathematician|
|Yakov Perelman||Perelman||1882||1942||Russian||Author of many popular science and mathematics books, including Mathematics Can Be Fun|
|Clifford A. Pickover||Pickover||1957||—||American||Author of numerous books on popular and recreational mathematics and science, editor of the IBM Journal of Research and Development for IBM Research|
- Kulkarni, D. Enjoying Math: Learning Problem Solving With KenKen Puzzles, a textbook for teaching with KenKen Puzzles.
- Newing, Angela (1994), "Henry Ernest Dudeney: Britain's Greatest Puzzlist", in Guy, Richard K.; Woodrow, Robert E., The Lighter Side of Mathematics: Proceedings of the Eugène Strens Memorial Conference on Recreational Mathematics and Its History, Cambridge University Press, pp. 294–301, ISBN 9780883855164.
- W. W. Rouse Ball and H.S.M. Coxeter (1987). Mathematical Recreations and Essays, Thirteenth Edition, Dover. ISBN 0-486-25357-0.
- Henry E. Dudeney (1967). 536 Puzzles and Curious Problems. Charles Scribner's sons. ISBN 0-684-71755-7.
- Sam Loyd (1959. 2 Vols.). in Martin Gardner: The Mathematical Puzzles of Sam Loyd. Dover. OCLC 5720955.
- Raymond M. Smullyan (1991). The Lady or the Tiger? And Other Logic Puzzles. Oxford University Press. ISBN 0-19-286136-0.
- Igor Kokcharov (2012). Math Puzzles for MBAs. eBook for iPad. ISBN 9781623141318.
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- Recreational Mathematics from MathWorld at Wolfram Research
- Mathematical treasure hunt on the Internet by CIJM (for highschool students and general public)
- QEDcat - fun mathematical resources by Burkard Polster and Marty Ross.
- 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
- Cotpi Weekly Puzzles
- Knot a Braid of Links
- Project Eureka - collection of mathematical problems and puzzles
- Vi Hart's YouTube channel
- A+Click: Math problems with difficulty level adapted to students' age
- Online Math Games in the form of flash games
- Maths based learning games