Mathematical Games
Mathematical games include many topics which are a part of recreational mathematics, but can also cover topics such as the mathematics of games, and playing games with mathematics. As far as two-player games are considered, what distinguishes a mathematical game from ordinary games is the emphasis on mathematical analysis of the game, rather than actually playing it.
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.
Mathematics of games
This can be a more serious subject than the name belies. It can include the statistical analysis of Card games to understand and improve play techniques.
- Game theory has wide social and military applications for tactical and strategic planning.
- Determinacy is the study of when one player or the other has a guaranteed winning strategy for an infinitely long game, and has important consequences in set theory and descriptive set theory.
- Conway's combinatorial game theory and surreal numbers
Playing games with mathematics
The foremost popularizers of recreational mathematics in recent years have been
John Horton Conway
Martin Gardner
Douglas Hofstadter
Ian Stewart
Other figures in recreational mathematics history have included:
Henry Dudeney
Piet Hein
Sam Loyd
Specific mathematical games and puzzles
Angels and Devils
Chomp
Domineering
Dots and boxes
Eight queens puzzle
Fifteen Puzzle
Four fours
Hackenbush
Hex
Hexaflexagons
Knight's Tour
L game
Life
Monty Hall problem
Nim
No-three-in-line problem
Penrose dominoes
Pentominoes
Philosopher's football
Prisoner's dilemma
Rhythmomachy
Rubik's Cube
Sim
Soma cube
Sprouts
Squaring the square
Sudoku
Tangram
Think-a-Dot
Three cottage problem
Tower of Hanoi
Verbal arithmetic
Wire-and-string puzzles (knot theory, topology)
Some sort of mathematics can be found in nearly all types of games.
Other games and pastimes of non-trivial mathematical interest:
- Juggling (juggling patterns)
- Origami (many mathematical results, some deep)
See also:
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