Recreational mathematics
Encyclopedia
Recreational mathematics is an umbrella term
, referring to mathematical puzzle
s and mathematical games.
Not all problems in this field require a knowledge of advanced mathematics, and thus, recreational mathematics often attracts the curiosity of non-mathematicians, and inspires their further study of mathematics.
s and other puzzles that require deductive reasoning, the aesthetics
of mathematics, and peculiar or amusing stories and coincidences about mathematics and mathematicians. Some of the more well-known topics in recreational mathematics are magic squares and fractals.
s whose rules, strategies, and outcomes can be studied and explained by mathematics
. The players of the game may not need to use mathematics in order to play mathematical games. For example, Mancala
is a mathematical game, because mathematicians can study it using combinatorial game theory
, even though no mathematics is necessary in order to play it.
, the solver must find a solution that satisfies the given conditions.
Logic puzzle
s 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.
Sometimes, mathematical puzzles are referred to as mathematical games as well.
In popular culture
Umbrella term
An umbrella term is a word that provides a superset or grouping of concepts that all fall under a single common category. Umbrella term is also called a hypernym. For example, cryptology is an umbrella term that encompasses cryptography and cryptanalysis, among other fields...
, referring to mathematical puzzle
Mathematical puzzle
Mathematical puzzles make up an integral part of recreational mathematics. They have specific rules as do multiplayer games, but they do not usually involve competition between two or more players. Instead, to solve such a puzzle, the solver must find a solution that satisfies the given conditions....
s and mathematical games.
Not all problems in this field require a knowledge of advanced mathematics, and thus, recreational mathematics often attracts the curiosity of non-mathematicians, and inspires their further study of mathematics.
Topics
This genre of mathematics includes logic puzzleLogic puzzle
A logic puzzle is a puzzle deriving from the mathematics field of deduction.-History:The logic puzzle was first produced by Charles Lutwidge Dodgson, who is better known under his pen name Lewis Carroll, the author of Alice's Adventures in Wonderland...
s and other puzzles that require deductive reasoning, the aesthetics
Aesthetics
Aesthetics is a branch of philosophy dealing with the nature of beauty, art, and taste, and with the creation and appreciation of beauty. It is more scientifically defined as the study of sensory or sensori-emotional values, sometimes called judgments of sentiment and taste...
of mathematics, and peculiar or amusing stories and coincidences about mathematics and mathematicians. Some of the more well-known topics in recreational mathematics are magic squares and fractals.
Mathematical games
Mathematical games are multiplayer gameMultiplayer game
A multiplayer video game is one which more than one person can play in the same game environment at the same time. Unlike most other games, computer and video games are often single-player activities that put the player against preprogrammed challenges and/or AI-controlled opponents, which often...
s whose rules, strategies, and outcomes can be studied and explained by mathematics
Mathematics
Mathematics is the study of quantity, space, structure, and change. Mathematicians seek out patterns and formulate new conjectures. Mathematicians resolve the truth or falsity of conjectures by mathematical proofs, which are arguments sufficient to convince other mathematicians of their validity...
. The players of the game may not need to use mathematics in order to play mathematical games. For example, Mancala
Mancala
Mancala is a family of board games played around the world, sometimes called "sowing" games, or "count-and-capture" games, which describes the game-play. Mancala games play a role in many African and some Asian societies comparable to that of chess in the West, or the game of Go in Eastern Asia...
is a mathematical game, because mathematicians can study it using combinatorial game theory
Combinatorial game theory
Combinatorial game theory is a branch of applied mathematics and theoretical computer science that studies sequential games with perfect information, that is, two-player games which have a position in which the players take turns changing in defined ways or moves to achieve a defined winning...
, even though no mathematics is necessary in order to play it.
Mathematical puzzles
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 puzzlePuzzle
A puzzle is a problem or enigma that tests the ingenuity of the solver. In a basic puzzle, one is intended to put together pieces in a logical way in order to come up with the desired solution...
, the solver must find a solution that satisfies the given conditions.
Logic puzzle
Logic puzzle
A logic puzzle is a puzzle deriving from the mathematics field of deduction.-History:The logic puzzle was first produced by Charles Lutwidge Dodgson, who is better known under his pen name Lewis Carroll, the author of Alice's Adventures in Wonderland...
s are a common type of mathematical puzzle. Conway's Game of Life
Conway's Game of Life
The Game of Life, also known simply as Life, is a cellular automaton devised by the British mathematician John Horton Conway in 1970....
and fractals are also considered mathematical puzzles, even though the solver only interacts with them by providing a set of initial conditions.
Sometimes, mathematical puzzles are referred to as mathematical games as well.
Others
Other curiosities and pastimes of non-trivial mathematical interest:- JugglingJugglingJuggling is a skill involving moving objects for entertainment or sport. The most recognizable form of juggling is toss juggling, in which the juggler throws objects up to catch and toss up again. This may be one object or many objects, at the same time with one or many hands. Jugglers often refer...
(juggling patterns) - OrigamiOrigamiis the traditional Japanese art of paper folding, which started in the 17th century AD at the latest and was popularized outside Japan in the mid-1900s. It has since then evolved into a modern art form...
(many mathematical results, some deep) - Cat's cradleCat's cradleCat's cradle is a well known series of string figures created between two people as a game. The name of the entire game, the specific figures, their order, and the names of the figures vary. Versions of this game have been found in indigenous cultures all over the world—from the Arctic to the...
and other string figureString figureA string figure is a design formed by manipulating string on, around, and using one's fingers or sometimes between the fingers of multiple people. String figures may also involve the use of the mouth, wrist, and feet. They may consist of singular images or be created and altered as a game, known as...
s
Publications
- The journal "Eureka" published by the mathematical society of the University of CambridgeUniversity of CambridgeThe University of Cambridge is a public research university located in Cambridge, United Kingdom. It is the second-oldest university in both the United Kingdom and the English-speaking world , and the seventh-oldest globally...
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 GardnerMartin GardnerMartin Gardner was an American mathematics and science writer specializing in recreational mathematics, but with interests encompassing micromagic, stage magic, literature , philosophy, scientific skepticism, and religion...
, John ConwayJohn Horton ConwayJohn Horton Conway is a prolific mathematician active in the theory of finite groups, knot theory, number theory, combinatorial game theory and coding theory...
, Roger PenroseRoger PenroseSir Roger Penrose OM FRS is an English mathematical physicist and Emeritus Rouse Ball Professor of Mathematics at the Mathematical Institute, University of Oxford and Emeritus Fellow of Wadham College...
, Ian StewartIan Stewart (mathematician)Ian Nicholas Stewart FRS is a professor of mathematics at the University of Warwick, England, and a widely known popular-science and science-fiction writer. He is the first recipient of the , awarded jointly by the LMS and the IMA for his work on promoting mathematics.-Biography:Stewart was born...
, Timothy Gowers, Stephen HawkingStephen HawkingStephen William Hawking, CH, CBE, FRS, FRSA is an English theoretical physicist and cosmologist, whose scientific books and public appearances have made him an academic celebrity...
and Paul DiracPaul DiracPaul Adrien Maurice Dirac, OM, FRS was an English theoretical physicist who made fundamental contributions to the early development of both quantum mechanics and quantum electrodynamics...
. - The Journal of Recreational MathematicsJournal of Recreational MathematicsThe Journal of Recreational Mathematics is an American journal dedicated to recreational mathematics, started in 1968. It is published quarterly by the Baywood Publishing Company....
is the largest publication on this topic. - Mathematical Games was the title of a long-running column on the subject by Martin GardnerMartin GardnerMartin Gardner was an American mathematics and science writer specializing in recreational mathematics, but with interests encompassing micromagic, stage magic, literature , philosophy, scientific skepticism, and religion...
, in Scientific AmericanScientific AmericanScientific American is a popular science magazine. It is notable for its long history of presenting science monthly to an educated but not necessarily scientific public, through its careful attention to the clarity of its text as well as the quality of its specially commissioned color graphics...
. He inspired several new generations of mathematicians and scientists, through his interest in mathematical recreations. Mathematical Games was succeeded by Metamagical ThemasMetamagical ThemasMetamagical Themas is a collection of eclectic articles written for Scientific American during the early 1980s by Douglas Hofstadter, and published together as a book in 1985 by Basic Books ....
, a similarly distinguished, but shorter-running, column by Douglas HofstadterDouglas HofstadterDouglas Richard Hofstadter is an American academic whose research focuses on consciousness, analogy-making, artistic creation, literary translation, and discovery in mathematics and physics...
, then by Mathematical Recreations, a column by Ian StewartIan Stewart (mathematician)Ian Nicholas Stewart FRS is a professor of mathematics at the University of Warwick, England, and a widely known popular-science and science-fiction writer. He is the first recipient of the , awarded jointly by the LMS and the IMA for his work on promoting mathematics.-Biography:Stewart was born...
, and most recently Puzzling Adventures by Dennis Shasha.
In popular culture
- In the Doctor WhoDoctor WhoDoctor Who is a British science fiction television programme produced by the BBC. The programme depicts the adventures of a time-travelling humanoid alien known as the Doctor who explores the universe in a sentient time machine called the TARDIS that flies through time and space, whose exterior...
episode "4242 (Doctor Who)"42" is an episode of the British science fiction television series Doctor Who. It was first broadcast on BBC One on 19 May 2007, and is the seventh episode of Series 3 of the revived Doctor Who series....
", the DoctorDoctor (Doctor Who)The Doctor is the central character in the long-running BBC television science-fiction series Doctor Who, and has also featured in two cinema feature films, a vast range of spin-off novels, audio dramas and comic strips connected to the series....
completes a sequence of happy primesHappy numberA happy number is defined by the following process. Starting with any positive integer, replace the number by the sum of the squares of its digits, and repeat the process until the number equals 1 , or it loops endlessly in a cycle which does not include 1...
, 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 Asperger syndromeAsperger syndromeAsperger's syndrome that is characterized by significant difficulties in social interaction, alongside restricted and repetitive patterns of behavior and interests. It differs from other autism spectrum disorders by its relative preservation of linguistic and cognitive development...
, discusses many mathematical games and puzzles.
People
The foremost advocates of recreational mathematics have included:- Lewis CarrollLewis CarrollCharles Lutwidge Dodgson , better known by the pseudonym Lewis Carroll , was an English author, mathematician, logician, Anglican deacon and photographer. His most famous writings are Alice's Adventures in Wonderland and its sequel Through the Looking-Glass, as well as the poems "The Hunting of the...
, author, mathematician and puzzlist - John Horton ConwayJohn Horton ConwayJohn Horton Conway is a prolific mathematician active in the theory of finite groups, knot theory, number theory, combinatorial game theory and coding theory...
, mathematician and inventor of Conway's Game of lifeConway's Game of LifeThe Game of Life, also known simply as Life, is a cellular automaton devised by the British mathematician John Horton Conway in 1970.... - Henry DudeneyHenry DudeneyHenry Ernest Dudeney was an English author and mathematician who specialised in logic puzzles and mathematical games. He is known as one of the country's foremost creators of puzzles...
, regarded as England's greatest puzzlist - Martin GardnerMartin GardnerMartin Gardner was an American mathematics and science writer specializing in recreational mathematics, but with interests encompassing micromagic, stage magic, literature , philosophy, scientific skepticism, and religion...
, author of Mathematical Games, a long running column in Scientific AmericanScientific AmericanScientific American is a popular science magazine. It is notable for its long history of presenting science monthly to an educated but not necessarily scientific public, through its careful attention to the clarity of its text as well as the quality of its specially commissioned color graphics... - Sam LoydSam LoydSamuel Loyd , born in Philadelphia and raised in New York, was an American chess player, chess composer, puzzle author, and recreational mathematician....
, regarded as America's greatest puzzlist - Clifford A. PickoverClifford A. PickoverClifford A. Pickover is an American author, editor, and columnist in the fields of science, mathematics, and science fiction, and is employed at the IBM Thomas J. Watson Research Center in Yorktown, New York.- Biography :He received his Ph.D...
, author of numerous books on recreational mathematics - Marilyn vos SavantMarilyn vos SavantMarilyn vos Savant is an American magazine columnist, author, lecturer, and playwright who rose to fame through her listing in the Guinness Book of World Records under "Highest IQ"...
, author of "Ask Marilyn", a long running column in PARADEParade (magazine)Parade is an American nationwide Sunday newspaper magazine, distributed in more than 500 newspapers in the United States. It was founded in 1941 and is owned by Advance Publications. The most widely read magazine in the U.S., Parade has a circulation of 32.2 million and a readership of nearly 70... - Malba TahanMalba TahanMalba Tahan, full name Ali Yezzid Izz-Edin ibn-Salim Hanak Malba Tahan, was a fictitious Persian scholar. He was the creation and frequent pen name of Brazilian author Júlio César de Mello e Souza.-Biography:...
, pseudonym of Júlio César de Mello e SouzaJúlio César de Mello e SouzaJúlio César de Mello e Souza , was a Brazilian writer and mathematics professor. He is well known in Brazil and abroad by his books on recreational mathematics, most of them published under the pen names of Malba Tahan and Breno de Alencar Bianco.He has been called by one biographer "the only...
, author of several books figuring recreational mathematics, including The Man Who CountedThe Man Who CountedThe Man Who Counted is a book on recreational mathematics and curious word problems by Brazilian writer Júlio César de Mello e Souza, published under the pen name Malba Tahan... - Yakov Perelman, Russian author of many popular science books, including Mathematics Can Be Fun
Further reading
- W. W. Rouse BallW. W. Rouse Ball-External links:*...
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 LoydSam LoydSamuel Loyd , born in Philadelphia and raised in New York, was an American chess player, chess composer, puzzle author, and recreational mathematician....
(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.
External links
- Recreational Mathematics from MathWorldMathWorldMathWorld is an online mathematics reference work, created and largely written by Eric W. Weisstein. It is sponsored by and licensed to Wolfram Research, Inc. and was partially funded by the National Science Foundation's National Science Digital Library grant to the University of Illinois at...
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.Ed Pegg, Jr.Ed Pegg, Jr. is an expert on mathematical puzzles and is a self-described recreational mathematician. He creates puzzles for the Mathematical Association of America online at Ed Pegg, Jr.'s Math Games. His puzzles have also been used by Will Shortz on the puzzle segment of NPR's Weekend Edition...
- Puzzles of the Month by Gianni A. SarconeGianni A. SarconeGianni A. Sarcone and Marie-Jo Waeber are writers and authors of columns and articles for newspapers and magazines featuring visual puzzles and math brain teasers. They are contributing editors to 'Focus Giochi' and 'Rivista Magia'...
- The Unreasonable Utility of Recreational Mathematics by David Singmaster
- Nick's Mathematical Puzzles
- Knot a Braid of Links
- Project Eureka - collection of mathematical problems and puzzles
- A+Click: Math problems with difficulty level adapted to students' age