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 or fun, and sometimes used as an educational tool. Many games are also considered to be work (such as professional players of spectator sports or games) or art (su ...

, 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 associations) 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 3-D combination puzzle originally invented in 1974 by Hungarian sculptor and professor of architecture Ernő Rubik. Originally called the Magic Cube, the puzzle was licensed by Rubik to be sold by Pentangle Puzzles i ...

magic squares In recreational mathematics, a square array of numbers, usually positive integers, is called a magic square if the sums of the numbers in each row, each column, and both main diagonals are the same. The 'order' of the magic square is the number o ...

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 mathematical 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 ...

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, as well as the philosophy of art (its own area of philosophy that comes out of aesthetics). It examines aesthetic values, often expressed th ...

and

culture Culture () is an umbrella term which encompasses the social behavior, institutions, and norms found in human societies, as well as the knowledge, beliefs, arts, laws, customs, capabilities, and habits of the individuals in these group ...

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, structure, space, models, and change. History ...

Mathematical games

Mathematical games are multiplayer games whose rules, strategies, and outcomes can be studied and explained using

. 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 turn-based strategy board games played with small stones, beans, or seeds and rows of holes or pits in the earth, a board or other playing surface. The objective is usually to capture all or some ...

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 player ...

, 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 games, 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, or toy that tests a person's ingenuity or knowledge. In a puzzle, the solver is expected to put pieces together ( or take them apart) in a logical way, in order to arrive at the correct or fun solution of the puzzle ...

, the solver must find a solution that satisfies the given conditions.

Logic puzzle A logic puzzle is a puzzle deriving from the mathematical 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 ...

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 and

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 based on mathematical principles can produce self-working but surprising effects. For instance, a mathemagician 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 structures. It is closely related to many other areas of mathematics and has many ap ...

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 fi ...

to guess a volunteer's selected card, or Hamming codes 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 manipulation of objects for recreation, entertainment, art or sport. The most recognizable form of juggling is toss juggling. Juggling can be the manipulation of one object ...

* the sometimes profound algorithmic and geometrical characteristics of

origami ) is the Japanese 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 paper into a fi ...

* patterns and process in creating string figures such as Cat's cradles, 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-born Israeli-American mathematician. He was Professor Emeritus of Mathematics at the University of Iowa, and formerly research fellow at the Moscow Institute of Electronics and M ...

by Alexander Bogomolny * Futility Closet by Greg Ross * Numberphile by Brady Haran * Mathologer by Burkard Polster * 3Blue1Brown by Grant Sanderson * The videos of Vi Hart
Stand-Up Maths
by Matt Parker

Publications

* The journal ''

Eureka Eureka (often abbreviated as E!, or Σ!) is an intergovernmental organisation for research and development funding and coordination. Eureka is an open platform for international cooperation in innovation. Organisations and companies applying t ...

'' 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, micromagic, philosophy, religion, and literatureespecially the writings of Lew ...

, John Conway,

Roger Penrose Sir Roger Penrose (born 8 August 1931) is an English mathematician, mathematical physicist, philosopher of science and Nobel Laureate in Physics. He is Emeritus Rouse Ball Professor of Mathematics in the University of Oxford, an emeritus fel ...

, Ian Stewart, Timothy Gowers, 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'' 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 whose rules, strategies, and outcomes are defined by clear mathematical parameters. Often, such games have simple rules and match procedures, such as Tic-tac-toe and Dots and Boxes. Generally, mathematical games n ...

'' (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

. He inspired several generations of mathematicians and scientists through his interest in mathematical recreations. "Mathematical Games" was succeeded by 25 " Metamagical Themas" 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, an ...

, 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:

References

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 ...

Wolfram Research Wolfram Research, Inc. ( ) is an American multinational company that creates computational technology. Wolfram's flagship product is the technical computing program Wolfram Mathematica, first released on June 23, 1988. Other products include ...

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 metagrobologist, he has a huge personal collection of mechanical puzzles and books of brain teasers. He is mo ...

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