recreational mathematics
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Recreational mathematics is
mathematics Mathematics is an area of knowledge that includes the topics of numbers, formulas and related structures, shapes and the spaces in which they are contained, and quantities and their changes. These topics are represented in modern mathematics ...
carried out for
recreation Recreation is an activity of leisure, leisure being discretionary time. The "need to do something for recreation" is an essential element of human biology and psychology. Recreational activities are often done for happiness, enjoyment, amusement, ...
(entertainment) rather than as a strictly research and application-based professional activity or as a part of a student's formal education. Although it is not necessarily limited to being an endeavor for amateurs, many topics in this field require no knowledge of advanced mathematics. Recreational mathematics involves
mathematical puzzle Mathematical puzzles make up an integral part of recreational mathematics. They have specific rules, 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 sati ...
s and
games A game is a structured form of play, usually undertaken for entertainment Entertainment is a form of activity that holds the attention and interest of an audience or gives pleasure and delight. It can be an idea or a task, but ...
, often appealing to children and untrained adults, inspiring their further study of the subject. The
Mathematical Association of America The Mathematical Association of America (MAA) is a professional society that focuses on mathematics accessible at the undergraduate level. Members include university, college, and high school teachers; graduate and undergraduate students; pure a ...
(MAA) includes recreational mathematics as one of its seventeen Special Interest Groups, commenting: Mathematical competitions (such as those sponsored by
mathematical association The Mathematical Association is a professional society concerned with mathematics education in the UK. History It was founded in 1871 as the Association for the Improvement of Geometrical Teaching and renamed to the Mathematical Association in ...
s) are also categorized under recreational mathematics.


Topics

Some of the more well-known topics in recreational mathematics are
Rubik's Cube The Rubik's Cube is a Three-dimensional space, 3-D combination puzzle originally invented in 1974 by Hungarians, Hungarian sculptor and professor of architecture Ernő Rubik. Originally called the Magic Cube, the puzzle was licensed by Rubik t ...
s,
magic squares In recreational mathematics Recreational mathematics is mathematics carried out for recreation (entertainment) rather than as a strictly research and application-based professional activity or as a part of a student's formal education. Although ...
,
fractals In mathematics, a fractal is a geometric shape containing detailed structure at arbitrarily small scales, usually having a fractal dimension strictly exceeding the topological dimension. Many fractals appear similar at various scales, as illus ...
,
logic puzzle A logic puzzle is a puzzle deriving from the mathematics, mathematical field of deductive reasoning, deduction. History The logic puzzle was first produced by Charles Lutwidge Dodgson, who is better known under his pen name Lewis Carroll, the au ...
s and mathematical chess problems, but this area of mathematics includes the
aesthetics Aesthetics, or esthetics, is a branch of philosophy that deals with the nature of beauty and taste (sociology), taste, as well as the philosophy of art (its own area of philosophy that comes out of aesthetics). It examines aesthetic values, ...
and
culture Culture () is an umbrella term which encompasses the social behavior, institutions, and Social norm, norms found in human Society, societies, as well as the knowledge, beliefs, arts, laws, Social norm, customs, capabilities, and habits of the ...
of mathematics, peculiar or amusing stories and coincidences about mathematics, and the personal lives of
mathematician A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems. Mathematicians are concerned with numbers, data, quantity, mathematical structure, structure, space, Mathematica ...
s.


Mathematical games

Mathematical game A mathematical game is a game whose rules, strategies, and outcomes are defined by clear mathematics, mathematical parameters. Often, such games have simple rules and match procedures, such as Tic-tac-toe and Dots and Boxes. Generally, mathemati ...
s are
multiplayer game A game is a structured form of play (activity), play, usually undertaken for enjoyment, entertainment or fun, and sometimes used as an educational tool. Many games are also considered to be work (such as professional players of spectator s ...
s whose rules, strategies, and outcomes can be studied and explained using
mathematics Mathematics is an area of knowledge that includes the topics of numbers, formulas and related structures, shapes and the spaces in which they are contained, and quantities and their changes. These topics are represented in modern mathematics ...
. The players of the game may not need to use explicit mathematics in order to play mathematical games. For example,
Mancala The mancala games are a family of two-player Turns, rounds and time-keeping systems in games, turn-based Strategy game, strategy board games played with small stones, beans, or seeds and rows of holes or pits in the earth, a board or other pl ...
is studied in the mathematical field of
combinatorial game theory Combinatorial game theory is a branch of mathematics and theoretical computer science that typically studies sequential games with perfect information. Study has been largely confined to two-player games that have a ''position'' that the players ...
, but no mathematics is necessary in order to play it.


Mathematical puzzles

Mathematical puzzle Mathematical puzzles make up an integral part of recreational mathematics. They have specific rules, 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 sati ...
s require mathematics in order to solve them. They have specific rules, as do
multiplayer game A game is a structured form of play (activity), play, usually undertaken for enjoyment, entertainment or fun, and sometimes used as an educational tool. Many games are also considered to be work (such as professional players of spectator s ...
s, but mathematical puzzles do not usually involve competition between two or more players. Instead, in order to solve such a
puzzle A puzzle is a game, Problem solving, problem, or toy that tests a person's ingenuity or knowledge. In a puzzle, the solver is expected to put pieces together (Disentanglement puzzle, or take them apart) in a logical way, in order to arrive at th ...
, the solver must find a solution that satisfies the given conditions.
Logic puzzle A logic puzzle is a puzzle deriving from the mathematics, mathematical field of deductive reasoning, deduction. History The logic puzzle was first produced by Charles Lutwidge Dodgson, who is better known under his pen name Lewis Carroll, the au ...
s and
classical cipher In cryptography, a classical cipher is a type of cipher that was used historically but for the most part, has fallen into disuse. In contrast to modern cryptographic algorithms, most classical ciphers can be practically computed and solved by hand. ...
s are common examples of mathematical puzzles.
Cellular automata A cellular automaton (pl. cellular automata, abbrev. CA) is a discrete model of computation studied in automata theory. Cellular automata are also called cellular spaces, tessellation automata, homogeneous structures, cellular structures, tessel ...
and
fractals In mathematics, a fractal is a geometric shape containing detailed structure at arbitrarily small scales, usually having a fractal dimension strictly exceeding the topological dimension. Many fractals appear similar at various scales, as illus ...
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.


Mathemagics

Magic tricks Magic, which encompasses the subgenres of illusion, stage magic, and close up magic, among others, is a performing art in which audiences are entertainment, entertained by tricks, effects, or illusions of seemingly impossible feats, using natu ...
based on mathematical principles can produce self-working but surprising effects. For instance, a
mathemagician A mathemagician is a mathematician who is also a Magician (illusion), magician. The term "mathemagic" is believed to have been introduced by Royal Vale Heath with his 1933 book "Mathemagic"."Mathemagic" by Royal Vale Heath and Jerome Sydney Meyer, ...
might use the
combinatorial Combinatorics is an area of mathematics primarily concerned with counting, both as a means and an end in obtaining results, and certain properties of finite set, finite Mathematical structure, structures. It is closely related to many other ar ...
properties of a deck of
playing cards A playing card is a piece of specially prepared card stock, heavy paper, thin cardboard, plastic-coated paper, cotton-paper blend, or thin plastic that is marked with distinguishing motifs. Often the front (face) and back of each card has a Pap ...
to guess a volunteer's selected card, or
Hamming codes In computer science and telecommunication, Hamming codes are a family of linear code, linear error-correcting codes. Hamming codes can detect one-bit and two-bit errors, or correct one-bit errors without detection of uncorrected errors. By contr ...
to identify whether a volunteer is lying.


Other activities

Other curiosities and pastimes of non-trivial mathematical interest include: * patterns in
juggling Juggling is a physical skill, performed by a juggler, involving the object manipulation, manipulation of objects for recreation, entertainment, art or sport. The most recognizable form of juggling is toss juggling. Juggling can be the manipula ...
* the sometimes profound algorithmic and geometrical characteristics of
origami ) is the Japanese paper art, art of paper folding. In modern usage, the word "origami" is often used as an inclusive term for all folding practices, regardless of their culture of origin. The goal is to transform a flat square sheet of pape ...
* patterns and process in creating
string figure A string figure is a design formed by manipulating twine, 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 o ...
s such as
Cat's cradle Cat's cradle is a game involving the creation of various string figures between the fingers, either individually or by passing a loop of string back and forth between two or more players. The true origin of the name is debated, though the fi ...
s, etc. * fractal-generating software


Online blogs, podcasts, and YouTube channels

There are many blogs and audio or video series devoted to recreational mathematics. Among the notable are the following: *
Cut-the-knot Alexander Bogomolny (January 4, 1948 July 7, 2018) was a Soviet The Soviet Union,. officially the Union of Soviet Socialist Republics. (USSR),. was a List of former transcontinental countries#Since 1700, transcontinental country that sp ...
by Alexander Bogomolny * Futility Closet by Greg Ross *
Numberphile ''Numberphile'' is an Educational entertainment, educational YouTube channel featuring videos that explore topics from a variety of fields of mathematics. In the early days of the channel, each video focused on a specific number, but the channe ...
by
Brady Haran Brady John Haran (born 18 June 1976) is an Australian-British independent film An independent film, independent movie, indie film, or indie movie is a feature film or short film that is film production, produced outside the major film studi ...
* Mathologer by Burkard Polster * 3Blue1Brown by Grant Sanderson * The videos of
Vi Hart Victoria Hart (born 1988), commonly known as Vi Hart (), is an American mathematician and YouTuber. They describe themselves as a "recreational mathemusician" and are well-known for creating mathematical videos on YouTube. Hart founded the virt ...

Stand-Up Maths
by
Matt Parker Matthew Thomas Parker (born 22 December 1980) is an Australian recreational mathematics, recreational mathematician, author, comedian, YouTube personality and science communicator based in the United Kingdom. His book ''Humble Pi'' was the firs ...


Publications

* The journal '' Eureka'' published by the mathematical society of the
University of Cambridge The University of Cambridge is a Public university, public collegiate university, collegiate research university in Cambridge, England. Founded in 1209 and granted a royal charter by Henry III of England, Henry III in 1231, Cambridge is the world' ...
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 Martin Gardner (October 21, 1914May 22, 2010) was an American popular mathematics and popular science writer with interests also encompassing scientific skepticism, Close-up magic, micromagic, philosophy, religion, and literatureespecially the w ...
, John Conway,
Roger Penrose Sir Roger Penrose (born 8 August 1931) is an English mathematician, mathematical physicist, Philosophy of science, philosopher of science and Nobel Prize in Physics, Nobel Laureate in Physics. He is Emeritus Rouse Ball Professor of Mathematics ...
, Ian Stewart,
Timothy Gowers Sir William Timothy Gowers, (; born 20 November 1963) is a British mathematician. He is Professeur titulaire of the Combinatorics chair at the Collège de France, and director of research at the University of Cambridge and Fellow of Trinity Col ...
, Stephen Hawking and
Paul Dirac Paul Adrien Maurice Dirac (; 8 August 1902 – 20 October 1984) was an English theoretical physicist who is regarded as one of the most significant physicists of the 20th century. He was the Lucasian Professor of Mathematics at the Univer ...
. * The ''
Journal of Recreational Mathematics The ''Journal of Recreational Mathematics'' was an American journal dedicated to recreational mathematics, started in 1968. It had generally been published quarterly by the Baywood Publishing Company, until it ceased publication with the last issue ...
'' was the largest publication on this topic from its founding in 1968 until 2014 when it ceased publication. * ''
Mathematical Games A mathematical game is a game A game is a structured form of play (activity), play, usually undertaken for enjoyment, entertainment or fun, and sometimes used as an educational tool. Many games are also considered to be work (such as p ...
'' (1956 to 1981) was the title of a long-running ''
Scientific American ''Scientific American'', informally abbreviated ''SciAm'' or sometimes ''SA'', is an American popular science magazine. Many famous scientists, including Albert Einstein and Nikola Tesla, have contributed articles to it. In print since 1845, it i ...
'' column on recreational mathematics by
Martin Gardner Martin Gardner (October 21, 1914May 22, 2010) was an American popular mathematics and popular science writer with interests also encompassing scientific skepticism, Close-up magic, micromagic, philosophy, religion, and literatureespecially the w ...
. He inspired several generations of mathematicians and scientists through his interest in mathematical recreations. "Mathematical Games" was succeeded by 25 "
Metamagical Themas ''Metamagical Themas'' is an eclectic collection of articles that Douglas Hofstadter Douglas Richard Hofstadter (born February 15, 1945) is an American scholar of cognitive science, physics, and comparative literature whose research incl ...
" columns (1981-1983), a similarly distinguished, but shorter-running, column by
Douglas Hofstadter Douglas Richard Hofstadter (born February 15, 1945) is an American scholar of cognitive science, physics, and comparative literature whose research includes concepts such as the sense of self in relation to the external world, consciousness, ...
, then by 78 "Mathematical Recreations" and "Computer Recreations" columns (1984 to 1991) by A. K. Dewdney, then by 96 "Mathematical Recreations" columns (1991 to 2001) by Ian Stewart, and most recently "Puzzling Adventures" by Dennis Shasha. * Th
Recreational Mathematics Magazine
published by th
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.


People

Prominent practitioners and advocates of recreational mathematics have included professional and amateur mathematicians:


See also

* List of recreational number theory topics


References


Further reading

* W. W. Rouse Ball and H.S.M. Coxeter (1987). ''Mathematical Recreations and Essays'', Thirteenth Edition, Dover. . * Henry E. Dudeney (1967). ''536 Puzzles and Curious Problems. Charles Scribner's sons''. . *
Sam Loyd Samuel Loyd (January 30, 1841 – April 10, 1911), was an American chess player, chess composer, puzzle author, and recreational mathematics, recreational mathematician. Loyd was born in Philadelphia but raised in New York City. As a chess com ...
(1959. 2 Vols.). in Martin Gardner: The Mathematical Puzzles of Sam Loyd. Dover. . * Raymond M. Smullyan (1991). ''The Lady or the Tiger? And Other Logic Puzzles''. Oxford University Press. .


External links


Recreational Mathematics
from
MathWorld ''MathWorld'' 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 Dig ...
at
Wolfram Research Wolfram Research, Inc. ( ) is an American Multinational corporation, multinational company that creates computational technology. Wolfram's flagship product is the technical computing program Wolfram Mathematica, first released on June 23, 1988 ...

The Unreasonable Utility of Recreational Mathematics
by
David Singmaster David Breyer Singmaster (born 1938) is an emeritus professor of mathematics at London South Bank University, England. A self-described Metagrobology, metagrobologist, he has a huge personal collection of mechanical puzzles and books of brain teas ...
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