List of Mathematical Games columns by Martin Gardner
This is a list of Martin Gardner's Mathematical Games columns . Over a period of 24 years (January 1957 - December 1980) wrote Martin Gardner 288 consecutive " Mathematical Games " -Kolumnen ( Mathematical Games ) for Scientific American magazines. He then alternated with other authors and produced 9 more under this title (February 1981 - June 1986), for a total of 297. These are listed below in chronological order.
The subjects of twelve of the columns made up the title article for the magazine in the month in which they were published. These columns are marked in the following table with the word "Cover" and a link to the corresponding title page.
Overview
| date | Title (translation) |
|---|---|
| 1957 Jan. | A new kind of magic square with remarkable properties (A new kind of magic square with remarkable properties) |
| 1957 Feb | An assortment of maddening puzzles (A selection of crazy puzzles) |
| 1957 March | Some old and new Versions of Tic-tac-toe (Some old and new versions of Tic-Tac-Toe) |
| 1957 Apr. |
Paradoxes dealing with birthdays, playing cards, coins, crows and red-haired typists (paradoxes with birthdays, playing cards, coins, crows and red-haired typists) |
| 1957 May | About the remarkable similarity between the Icosian Game and the Tower of Hanoi (About the remarkable similarity between the games A Journey Around the World and Towers of Hanoi) |
| 1957 June | Curious figures descended from the Möbius band , which has only one side and one edge (from the Möbius band with only one side and one edge) |
| 1957 July | Concerning the game of Hex , which Mai be played on the tiles of the bathroom floor (About the hex game that you can play on the tiles of the bathroom floor ) |
| 1957 Aug. | The life and work of Sam Loyd , a mighty inventor of puzzles (The life and work of Sam Loyd, a mighty inventor of puzzles) |
| 1957 Sep. | Concerning various card tricks with a mathematical message (via various card tricks with a mathematical message) |
| 1957 Oct. | How to remember numbers by mnemonic devices such as cuff links and red zebras (How to remember numbers with mnemonic devices such as cufflinks and red zebras) |
| 1957 Nov. | Nine titillating puzzles (nine ticklish puzzles) |
| 1957 Dec | More about complex dominoes (More about complex domino games) |
| 1958 Jan. | A collection of tantalizing fallacies of mathematics (a collection of tantalizing fallacies) |
| 1958 Feb | Concerning the game of Nim and its mathematical analysis (on the Nim game and its mathematical analysis) |
| 1958 March | About left- and right-handedness, mirror images and kindred matters (about left- and right-handedness, mirror images and related matters) |
| 1958 April | Concerning the celebrated puzzle of five sailors, a monkey and a pile of coconuts (About the famous puzzle of five sailors, a monkey and a pile of coconuts) |
| 1958 May | About tetraflexagons and tetraflexagation (About tetraflexagons and tetraflexagation) |
| 1958 June | About Henry Ernest Dudeney , a brilliant creator of puzzles (About Henry Ernest Dudeney, a brilliant puzzle creator ) |
| 1958 July | Some diverting tricks which involve the concept of numerical congruence (some amusing tricks that use the concept of numerical congruence ) |
| 1958 Aug. | A third collection of “ brain-teasers ” (a third collection of tough nuts) |
| 1958 Sept. | A game in which standard pieces composed of cubes are assembled into larger forms (a game in which standard soma cube build larger forms) |
| 1958 Oct. | Four mathematical diversions involving concepts of topology (four mathematical diversions involving concepts of topology ) |
| 1958 Nov. | How rectangles, including squares, can be divided into squares of unequal size - Cover |
| 1958 Dec | Diversions Which involve the five Platonic solids (distractions that use the five Platonic solids) |
| 1959 Jan. | About mazes and how they can be traversed (About mazes and how they can be traversed ) |
| 1959 Feb | "Brain-teasers" that involve formal logic ( Tough nuts that require formal logic) |
| 1959 March | Concerning the properties of various magic squares (The properties of various magic squares) |
| 1959 April | The mathematical diversions of a fictitious carnival man (The mathematical conversations of a fictional carnival man) |
| 1959 May | Another collection of "brain teasers" (More collection of hard nuts) |
| 1959 June | An inductive card game (An inductive card game) |
| 1959 July | About Origami , the Japanese art of folding objects out of paper (about origami, the Japanese art of paper folding) |
| 1959 Aug. | About phi , an irrational number that has some remarkable geometrical expressions (about the golden ratio, an irrational number that has some remarkable geometrical applications) |
| 1959 Sept. | Concerning mechanical puzzles , and how an enthusiast has collected 2,000 of them (About mechanical puzzles and how a fan collected 2000 from them) |
| 1959 Oct. | Involving problem questions of probability and ambiguity (problems to questions of probability theory and ambiguity) |
| 1959 Nov. | How three modern mathematicians disproved a celebrated conjecture of Leonhard Euler (How two modern mathematicians disproved a famous conjecture by Leonhard Euler) - Cover |
| 1959 Dec | Diversions that clarify group theory, particularly by the weaving of braids (digressions that explain group theory , especially braided patterns) |
| 1960 Jan. | A fanciful dialogue about the wonders of numerology (A fantastic dialogue about the wonders of numerology) |
| 1960 Feb | A fifth collection of “brain-teasers” (a fifth collection of puzzles) |
| 1960 March | The games and puzzles of Lewis Carroll (The games and puzzles by Lewis Carroll) |
| 1960 Apr. | About mathematical games did are Played On boards (About mathematical board games) |
| 1960 May | Reflections on the packing of spheres (reflections on the packing of spheres) |
| 1960 June | Recreations Involving folding and cutting sheets of paper (Entertainment by folding and cutting paper pages) |
| 1960 July | Incidental information about the extraordinary number pi (For extraordinary number pi) |
| 1960 Aug | An imaginary dialogue on "math magic" tricks based on mathematical principles (Imaginary dialogue on MatheMagics ; magic tricks are based on mathematical principles) |
| 1960 Sept. | The celebrated four-color map problem of topology (The famous four-color theorem of topology) |
| 1960 Oct. | A new collection of "brain teasers" (A new collection of riddles) |
| 1960 Nov. | More about the shapes that can be made with complex dominoes (More about the patterns that can be created with polyominoes) |
| 1960 Dec | Some recreations Involving the binary number system (Some games with the dual system) |
| 1961 Jan. | In which the author chats again with Dr. Matrix, numerologist extraordinary (Where the author chats again with the extraordinary numerologist Dr. Matrix) |
| 1961 Feb | Diversions that involve one of the classic conic sections: the ellipse (dispersions that involve one of the classic conic sections: the ellipse ) |
| 1961 March | How to play dominoes in two and three dimensions ( How to play dominoes in two and three dimensions ) |
| 1961 April | Concerning the diversions in a new book on geometry (On conversational mathematics in a new book on geometry) - Cover |
| 1961 May | In which the editor of this department meets the legendary Bertrand Apollinax (In which the author of this column meets the famous Bertrand Apollinax) |
| 1961 June | A new collection of “brain teasers” (a new collection of “tough nuts”) |
| 1961 July | Some diverting mathematical boardgames (Some entertaining math board games) |
| 1961 Aug. | Some entertainments did involve the calculus of finite differences (Some conversations that use the calculus of finite differences) |
| 1961 Sept. | Surfaces with edges linked in the same way as the three rings of a well-known design (surfaces with edges linked in the same way as the rings of a well-known design ) |
| 1961 Oct. | Diversions that involve the mathematical constant “e” (conversations with Euler's number) |
| 1961 Nov. | Wherein geometrical figures are dissected to make other figures (in which geometrical figures are divided up to create other figures) |
| 1961 Dec | On the theory of probability and the practice of gambling ( On the theory of probability and the practice of gambling ) |
| 1962 Jan. | An adventure in hyperspace at the Church of the Fourth Dimension (An adventure in the hyperspace of the Church of the Fourth Dimension) |
| 1962 Feb | A clutch of diverting problems (A collection of entertainment problems) |
| 1962 March | How to build a game-learning machine and teach it to play and win ( How to build a game-learning machine and teach it to play and win ) |
| 1962 Apr. | About three types of spirals and how to construct them (About three types of spirals and how to construct them ) |
| 1962 May |
Symmetry and asymmetry and the strange world of upside-down art (symmetry and asymmetry in the strange world of interchanged above and below) |
| 1962 June | The game of solitaire and some variations and transformations (The solitaire game and some variations and transformations) |
| 1962 July | Fiction about life in two dimensions (literature about life in two dimensions) |
| 1962 Aug. | A variety of diverting tricks collected at a fictitious convention of magicians ( A variety of diverting tricks collected at a fictional wizard conference) |
| 1962 Sept. | Tests that show whether a large number can be divided by a number from 2 to 12 ( Tests that show whether a large number can be divided by a number from 2 to 12 ) |
| 1962 Oct. | A collection of puzzles involving numbers, logic, and probability (a collection of puzzles with numbers, logic, and probability) |
| 1962 Nov. | Some puzzles based on checkerboards (some puzzles based on checkerboards ) |
| 1962 Dec | Some simple tricks and manipulations from the ancient lore of string play (Some simple tricks and manipulations of the ancient string play) |
| 1963 Jan. | The author pays his annual visit to Dr. Matrix, the numerologist |
| 1963 Feb. |
Curves of constant width , one of Which makes it possible to drill square holes (curves of constant width, one of which allows the drilling of square holes) |
| 1963 March | A new paradox, and variations on it, about a man condemned to be hanged (A new paradox and variations on it about a man condemned to be hanged ) |
| 1963 April | A bit of foolishness for April Fools' Day (A few follies for the first of April) |
| 1963 May | On rep-tiles, polygons that can make larger and smaller copies of themselves (via rep-tiles, polygons that produce enlarged and reduced copies of themselves) |
| 1963 June | A discussion of helical structures, from corkscrews to DNA molecules (A discussion of helical structures, from corkscrews to DNA molecules) |
| 1963 July | Topological diversions, including a bottle with no inside or outside ( topological diversions, including a bottle with no inside or outside ) |
| 1963 Aug. | Permutations and paradoxes in combinatorial mathematics (permutations and paradoxes in combinatorial mathematics) |
| 1963 Sept. | How to solve puzzles by graphing the rebounds of a bouncing ball ( How to solve puzzles by graphing the rebounds of bouncing balls) |
| 1963 Oct. | About two new and two old mathematical boardgames (About two new and two old math board games) |
| 1963 Nov. | A mixed bag of problems (A mixed bag of problems) |
| 1963 Dec | How to use the odd-even check for tricks and problem-solving ( How to use the even -odd parity for magic tricks and problems) |
| 1964 Jan. | Presenting the one and only Dr. Matrix, numerologist, in his annual performance (The unique Dr. Matrix, numerologist, in his annual performance) |
| 1964 Feb | The hypnotic fascination of sliding-block puzzles (The hypnotic fascination of puzzles with sliding blocks) |
| 1964 March | The remarkable lore of the prime numbers - cover |
| 1964 April | Various problems based on planar graphs , or sets of “vertices” connected by “edges” (Various problems about planar graphs or sets of corners connected by edges) |
| 1964 May | The tyranny of 10 overthrown with the ternary number system ( tyranny of 10 overthrown with the ternary number system ) |
| 1964 June | A collection of short problems and more talk of prime numbers (A collection of short problems and more about prime numbers) |
| 1964 July | Curious properties of a cycloid curve (curious properties of a cycloid ) |
| 1964 Aug. | Concerning several magic tricks based on mathematical principles (about some magic tricks based on mathematical principles) |
| 1964 Sept. | Puns, palindromes and other word games did partake of the mathematical spirit (tips, palindromes and other word games in the mathematical mind) |
| 1964 Oct. | Simple proofs of the Pythagorean theorem , and sundry other matters (simple proofs of the Pythagorean theorem and others) |
| 1964 Nov. | Some paradoxes and puzzles involving infinite series and the concept of limit (some paradoxes and puzzles with infinite series and the concept of limit) |
| 1964 Dec | On polyiamonds: shapes that are made out of equilateral triangles ( On polyiamonds: shapes that are made out of equilateral triangles ) |
| 1965 Jan. | Some comments by Dr. Matrix on symmetries and reversals (Some comments from Dr. Matrix on symmetries and reversals) |
| 1965 Feb. |
Tetrahedrons in nature and architecture, and puzzles Involving this simplest polyhedron (tetrahedra simplest in nature and architecture, and puzzles over this polyhedron) |
| 1965 March | A new group of short problems (A new group of short problems) |
| 1965 Apr. | The infinite regress in philosophy, literature and mathematical proof (The infinite regress in philosophy, literature and mathematical proof) |
| 1965 May | The lattice of integers considered as an orchard or a billiard table (the grid of integers as a garden or pool table) |
| 1965 June | Some diversions and problems from Mr. O'Gara, the postman (some conversations and problems from Mr. O'Gara, mail carrier) |
| 1965 July | On the relation between mathematics and the ordered patterns of Op art (Some connections between mathematics and the ordered patterns of Op art ) - Cover |
| 1965 Aug. | Thoughts on the task of communication with intelligent organisms on other worlds (thoughts on the task of communication with intelligent organisms in other worlds) |
| 1965 Sept. | The superellipse : a curve that lies between the ellipse and the rectangle ( The superellipse : a curve that lies between the ellipse and the rectangle ) |
| 1965 Oct. |
Pentominoes and polyominoes : five games and a sampling of problems (Pentominoes and Polyominoes: five games and a collection of problems) |
| 1965 Nov. | A selection of elementary word and number problems (A selection of elementary word and number problems) |
| 1965 Dec | Magic stars, graphs and polyhedrons (magic stars, graphs and polyhedra) |
| 1966 Jan. | Dr. Matrix returns, now in the guise of a neo- Freudian psychonumeralist (Dr. Matrix returns, now in the disguise of a neo- Freudian psychonumeralist) |
| 1966 Feb | Recreational numismatics, or a purse of coin puzzles (entertainment numismatics, or a purse of coin puzzles ) |
| 1966 March | The hierarchy of infinities and the problems it spawns ( The hierarchy of infinities and the problems it spawns ) |
| 1966 April | The eerie mathematical art of Maurits C. Escher (The uncanny mathematical art of MC Escher) |
| 1966 May | How to cook a puzzle, or mathematical one-uppery (how to create a puzzle, or mathematical superstructure) |
| 1966 June | The persistence (and futility) of efforts to trisect the angle (the persistence (and futility ) of efforts to trisect the angle ) |
| 1966 July | Freud's friend Wilhelm Fliess and his theory of male and female life cycles (Freud's friend Wilhelm Fliess and his theory of male and female life cycles) |
| 1966 Aug. | Puzzles that can be solved by reasoning based on elementary physical principles ( puzzles that can be solved by physical considerations) |
| 1966 Sept. | The problem of Mrs. Perkins 'quilt (The problem of Mrs. Perkins' quilt) |
| 1966 Oct. | Can the shuffling of cards (and other apparently random events) be reversed? (Can the shuffling of cards (and other apparently random events) be undone?) |
| 1966 Nov. | Is it possible to visualize a four-dimensional figure? (Is it possible to visualize a four-dimensional figure?) |
| 1966 Dec | The multiple charms of Pascal's triangle (The many attractions of Pascal's triangle) |
| 1967 Jan. | Dr. Matrix delivers a talk on acrostics (Dr. Matrix talks about acrostics) |
| 1967 Feb | Mathematical strategies for two-person contests (Mathematical strategies for two-person contests) |
| 1967 March | An array of problems that can be solved with elementary mathematical techniques (about problems that can be solved with elementary mathematical techniques ) |
| 1967 Apr. | The amazing feats of professional mental calculators , and some tricks of the trade ( The amazing feats of mental calculators and some of their tricks) |
| 1967 May | Cube-root extraction and the calendar trick, or how to cheat in mathematics (drawing cube roots and the calendar trick, or: how to cheat in mathematics ) |
| 1967 June | The polyhex and the polyabolo, polygonal jigsaw puzzle pieces ( polyhex and the polyabolo, polygonal jigsaw puzzle pieces ) |
| 1967 July | Of sprouts and Brussels sprouts, games with a topological flavor (About Sprouts and Brussels-Sprouts, games of a topological nature) |
| 1967 Aug. | In which a computer prints out mammoth polygonal factorials ( in which a computer prints out huge polygonal factorials ) |
| 1967 Sept. | Double acrostics, stylized Victorian ancestors of today's crossword puzzle (double acrostichons, stylized Victorian ancestors of today's crossword puzzles) |
| 1967 Oct. | Problems that are built on the knight’s move in chess (problems with the knight in chess) |
| 1967 Nov. | A mixed bag of logical and illogical problems to solve (a mixture of logical and illogical problems) |
| 1967 Dec |
Game theory is applied (for a change) to games (game theory applied (for a change) to games) |
| 1968 Jan. | The beauties of the square, as expounded by Dr. Matrix to rehabilitate the hippie (The beauties of the square, explained by Dr. Matrix to rehabilitate the hippie) |
| 1968 Feb | Combinatorial problems Involving tree graphs and forests of trees (Combinatorial problems with tree graph and forests) |
| 1968 March | A short treatise on the useless elegance of perfect numbers and amicable pairs (A short treatise on the useless elegance of perfect and friendly numbers) |
| 1968 April | Puzzles and tricks with a dollar bill (puzzles and tricks with a dollar bill) |
| 1968 May | Circles and spheres, and how they kiss and pack (circles and spheres and how they kiss and pack) |
| 1968 June | Combinatorial possibilities in a pack of shuffled cards (Combinatorial possibilities of shuffling cards ) |
| 1968 July | On the meaning of randomness and some ways of achieving it (About the meaning of randomness and ways of generating it) |
| 1968 Aug. | An array of puzzles and tricks, with a few traps for the unwary (a collection of puzzles and tricks, with a few traps for the unsuspecting) |
| 1968 Sept. |
Counting systems and the relationship between numbers and the real world (number systems and the connection of numbers to the real world) |
| 1968 Oct. |
MacMahon 's color triangles and the joys of fitting them together (MacMahon's color triangles and the fun of fitting them together ) |
| 1968 Nov. | On the ancient lore of dice and the odds against making a point (about the old dice game and the odds against the player) |
| 1968 Dec | The world of the Möbius strip: endless, edgeless and one-sided ( The world of the Möbius strip: endless, edgeless and one-sided ) |
| 1969 Jan. | Dr. Matrix gives his explanation of why Mr. Nixon what elected president (Dr. matrix explains why Mr. Nixon was elected president) |
| 1969 Feb |
Boolean algebra , Venn diagrams and the propositional calculus (Boolean algebra, Venn diagrams and propositional logic) |
| 1969 March | The multiple fascinations of the Fibonacci sequence ( The multiple fascinations of the Fibonacci sequence ) |
| 1969 Apr. | An octet of problems that emphasize gamesmanship, logic and probability (eight problems about players, logic and probability) |
| 1969 May | The rambling random walk and its gambling equivalent (The Odyssey and its equivalent at gambling) |
| 1969 June |
Random walks , by semidrunk bugs and others, on the square and on the cube (wanderings of a half-drunk and others on the square and cube) |
| 1969 July | Tricks, games and puzzles that employ matches as counters and line segments (tricks, games and puzzles with matches for counting and as line segments) |
| 1969 Aug. |
Simplicity as a scientific concept : Does nature keep her accounts on a thumbnail? (Simplicity of a scientific concept: does nature do bookkeeping on a thumbnail?) |
| 1969 Sept. | Geometric constructions with a compass and a straightedge , and also with a compass alone (geometrical constructions with compass and a right angle) |
| 1969 Oct. | A numeranalysis by Dr. Matrix of the lunar flight of Apollo 11 (A numerical analysis by Dr. Matrix about the moon flight of Apollo 11) |
| 1969 Nov. | A new pencil-and-paper game based on inductive reasoning (A new pencil and paper game based on inductive reasoning ) - Cover |
| 1969 Dec | A handful of combinatorial problems based on dominoes |
| 1970 Jan. | The abacus : primitive but effective digital computer (The abacus, a primitive but effective digital computer) |
| 1970 Feb | Nine new puzzles to solve (Nine new puzzles) |
| 1970 March |
Cyclic numbers and Their properties (Cyclic numbers and their properties) |
| 1970 Apr. | Some mathematical curiosities embedded in the solar system (Some mathematical oddities in the solar system) |
| 1970 May | Of optical illusions , from figures that are undecidable to hot dogs that float (optical illusions, from undecidable figures to floating hot dogs) |
| 1970 June | Elegant triangle theorems not to be found in Euclid (elegant sentences about triangles that cannot be found in Euclid ) |
| 1970 July |
Diophantine analysis and the trouble of Fermat's theorem legendary load (Diophantine equations and the problem of Fermat's famous Last guess) |
| 1970 Aug | Backward run numbers, letters, words and sentences until boggles the mind (backwards for numbers, letters, words and sentences until the head spins) |
| 1970 Sept. | On the cyclical curves generated by wheels that roll along wheels (generated by rolling wheels via the cycloid) |
| 1970 Oct. | The fantastic combinations of John Conway ’s new solitaire game “life” (The fantastic combinations of John Conway’s new solitaire game Life ) |
| 1970 Nov. | A new collection of short problems and the answers to some of "life's" (A new collection of short problems and solutions to Life) |
| 1970 Dec | The paradox of the nontransitive dice and the elusive principle of indifference (The paradox of the intransitive dice and the elusive principle of indifference ) |
| 1971 Jan. | Lessons from Dr. Matrix in chess and numerology (lessons from Dr. Matrix in chess and numerology) |
| 1971 Feb | On cellular automata , self-reproduction, the Garden of Eden and the game “life” (About cellular automata , self-reproduction, the Garden of Eden and the game “Life”) - Cover |
| 1971 March | The orders of infinity, the topological nature of dimension and “supertasks” (the orders of infinity and the topological nature of dimension and supertasks ) |
| 1971 April | Geometric fallacies: hidden errors pave the road to absurd conclusions ( Geometric fallacies: hidden errors pave the way to absurd conclusions) |
| 1971 May | The combinatorial richness of folding a piece of paper ( The combinatorial richness of folding a piece of paper ) |
| 1971 June | The Turing game and the question it presents: Can a computer think? (The Turing Test and the Question It Raises: Can a Computer Think?) |
| 1971 July | Quickie problems: not hard, but look out for the curves (Quickie problems: not difficult, but note the curves) |
| 1971 Aug. |
Ticktacktoe and its complications (Tic-Tac-Toe and its complications) |
| 1971 Sept. | The plaiting of Plato's polyhedrons and the asymmetrical yin-yang-lee (The plaiting of Plato's polyhedra and the asymmetrical Yin-Yang-Lee) |
| 1971 Oct. | New puzzles from the game of Halma , the noble ancestor of Chinese checkers (New puzzles with the game Halma, the noble forerunner of the Chinese checkers game) |
| 1971 Nov. | Advertising premiums to beguile the mind: classics by Sam Loyd , master puzzle pose (advertising to seduce the mind: classics by Sam Loyd, the master puzzle inventor) |
| 1971 Dec | Further encounters with touching cubes, and the paradoxes of Zeno as “supertasks” (further encounters with cubes, and the paradox of Zeno as a super task ) |
| 1972 Jan. | How to triumph at nim by playing safe, and John Horton Conway's game “Hackenbush” (How to win with Nim through careful play, and John Horton Conway's game Hackenbush ) |
| 1972 Feb | Dr. Matrix poses some heteroliteral puzzles while peddling perpetual motion in Houston (Dr. Matrix poses some ambiguous word puzzles while peddling perpetual motion vehicles in Houston) |
| 1972 March | The graceful graphs of Solomon Golomb , or how to number a graph parsimoniously ( How to number a graph sparingly) |
| 1972 Apr. | A topological problem with a fresh twist, and eight other new recreational puzzles (A topological problem with a new twist and eight other new recreational mathematics puzzles) |
| 1972 May | Challenging chess tasks for puzzle buffs and answers to the recreational problems (Challenging chess puzzles for puzzle fans and answers to problems of recreational mathematics) |
| 1972 June | : A miscellany of transcendental problems simple to state but not at all easy to solve (: easy to make but not at all easy to solve various problems transcendent) |
| 1972 July | Amazing mathematical card tricks that do not require prestidigitation ( Amazing mathematical card tricks that do not require demonstration) |
| 1972 Aug. | The curious properties of the Gray code and how it can be used to solve puzzles (The strange properties of the Gray code and how it can be used to solve puzzles) |
| 1972 Sept. | Pleasurable problems with polycubes , and the winning strategy for Slither (Entertaining problems with Polywürfeln and a winning strategy for Slither ) |
| 1972 Oct. | Why the long arm of coincidence is usually not as long as it seems (Why the long arm of coincidence is usually not as long as it seems) |
| 1972 Nov. | On the practical uses and bizarre abuses of Sir Francis Bacon's biliteral cipher (On the practical and bizarre uses of Sir Francis Bacon's cipher ) |
| 1972 Dec | Knotty problem with a two-hole torus (Nodular problems with a torus with two holes) |
| 1973 Jan. |
Sim , Chomp and Race Track : new games for the intellect (and not for Lady Luck) (Sim, Chomp, Race Track: new games for the intellect (and not for Lady Luck)) |
| 1973 Feb | Up-and-down elevator games and Piet Hein ’s mechanical puzzles (games with elevators moving up and down and Piet Hein ’s mechanical puzzles ) |
| 1973 March | The calculating rods of John Napier , the eccentric father of the logarithm ( The calculating rods of John Napier , the eccentric father of the logarithm ) |
| 1973 Apr. | How to turn a chessboard into a computer and to calculate with negabinary numbers (How to turn a chessboard into a computer for calculating negabinary numbers) |
| 1973 May | A new miscellany of problems, and encores for Racetrack, Sim, Chomp and elevators (A new collection of various problems, and More about Racetrack, Sim, Chomp and lifts) |
| 1973 June | Plotting the crossing number of graphs (The recording of the crossing number of graphs) |
| 1973 July | Freewill revisited, with a mind-bending prediction paradox by William Newcomb (New reflections on free will and a spirit confusing paradox of Simon Newcomb) |
| 1973 Aug. | An astounding self-test of clairvoyance by Dr. Matrix (An Amazing Self-Test for Clairvoyance by Dr. Matrix) |
| 1973 Sept. | Problems on the surface of a sphere offer an entertaining introduction to point sets (problems on the surface of the sphere result in an entertaining introduction to point sets) |
| 1973 Oct. | "Look-see" diagrams did offer visual proof of complex algebraic formulas (charts provide a visual explanation of complex algebraic formulas) |
| 1973 Nov. | Fantastic patterns traced by programmed “worms” (Fantastic patterns generated by programmed worms ) |
| 1973 Dec | On expressing integers as the sum of cubes and other unsolved number-theory problems (About integers as sums of cubes and other unsolved math problems) |
| 1974 Jan. | The combinatorial basis of the " I Ching ," the Chinese book of divination and wisdom - Cover |
| 1974 Feb |
Cram , crosscram and quadraphage: new games having elusive winning strategies (Cram, Crosscram and Quadraphage: new games with elusive winning strategies) |
| 1974 March | Reflections on Newcomb's Problem : a prediction and free-will dilemma (reflections on Newcomb's problem: a prediction and the dilemma free will) |
| 1974 Apr. | Nine challenging problems, some rational and some not (Nine challenging problems, some rational and some not) |
| 1974 May | On the contradictions of time travel (On the contradictions of time travel) |
| 1974 June | Dr. Matrix brings his numerological Science to bear on the occult powers of the pyramid (Dr. Matrix applies numerological science to the occult properties of pyramids) |
| 1974 July | On the patterns and the unusual properties of figurate numbers (On the patterns and unusual properties of figurate numbers) |
| 1974 Aug. | On the fanciful history and the creative challenges of the puzzle game of tangrams (About the interesting history and creative challenges of the tangram game) |
| 1974 Sept. | More on tangrams : Combinatorial problems and the possibilities of game snug tangrams (More about Tangram: combinatorial problems and the possibilities of cozy Tangram as a game) |
| 1974 Oct. | On the paradoxical situations that arise from nontransitive relations (about the paradoxical situations that arise from non-transitive relations) |
| 1974 Nov. | Some new and dramatic demonstrations of number theorems with playing cards (some new and dramatic demonstrations of numerical problems in the card game) |
| 1974 Dec | The arts as combinatorial mathematics , or how to compose like Mozart with dice (The art of combinatorial mathematics , or how to compose like Mozart with dice ) |
| 1975 Jan. | The curious magic of anamorphic art - cover |
| 1975 Feb | How the absence of anything leads to thoughts of nothing (The absence of everything leads to reflections on nothing) |
| 1975 March | From rubber ropes to rolling cubes, a miscellany of refreshing problems (From rubber ropes to rolling cubes, a collection of refreshing problems) |
| 1975 Apr. | Six sensational discoveries did somehow or another have escaped public attention (six sensational discoveries that have escaped in one way or another public attention) |
| 1975 May | On the remarkable Császár polyhedron and its applications in problem solving (About the remarkable Csaszar polyhedron and its application to problem solving ) |
| 1975 June | Games of strategy for two players: star nim, meander, dodgem and rex (strategy games for two players: Star Nim, Meander, Dodgem and Rex) |
| 1975 July | On tessellating the plane with convex polygon tiles (On the tiling of the plane with convex polygons) |
| 1975 Aug. | More about tiling the plane : the possibilities of polyominoes, polyiamonds, and polyhexes ( More about tiling the plane : possibilities of polyominoes, polyiamonds and polyhexes) |
| 1975 Sept. | Dr. Matrix finds numerological wonders in the King James Bible (Dr. Matrix finds numerological wonders in the King James Bible) |
| 1975 Oct. | Concerning an effort to demonstrate extrasensory perception by machine (about the effort to demonstrate extrasensory perception with machines) |
| 1975 Nov. | On map projections (with special reference to some inspired ones) (About map projections (with special consideration of some particularly witty ones ) - Cover |
| 1975 Dec | A random assortment of puzzles, together with reader responses to earlier problems ( A random assortment of puzzles, with reader responses to previous problems) |
| 1976 Jan. | A breakthrough in magic squares, and the first perfect magic cube (A breakthrough in magic squares and the first perfect magic cube) |
| 1976 Feb | Some elegant brick-packing problems, and a new order-7 perfect magic cube (Some elegant brick packing problems, and a new order 7 perfect magic cube ) |
| 1976 March | On the fabric of inductive logic, and some probability paradoxes ( On the fabric of inductive logic and some probability paradoxes ) |
| 1976 Apr. | Snarks, Boojums and other conjectures related to the four-color-map theorem (Snarks, Boojums and other conjectures about the four-color problem) |
| 1976 May | A few words about everything there was, is and ever will be (a few words about everything there was, is and ever will be ) |
| 1976 June |
Catalan numbers : an integer sequence that materializes in unexpected places ( Catalan numbers : an integer sequence that appears in unexpected places ) |
| 1976 July | Fun and serious business with the small electronic calculator (fun and serious business with the small electronic calculator) |
| 1976 Aug. | The symmetrical arrangement of the stars on the American flag and related matters (The symmetrical arrangement of the stars on the American flag and related issues) |
| 1976 Sept. |
John Horton Conway ’s book covers an infinity of games (John Horton Conway’s book covers an infinite number of games) |
| 1976 Oct. | Combinatorial problems, some old, some new and all newly attacked by computer ( computer attacked some old, some new, and all new) |
| 1976 Nov. | In which DM (Dr. Matrix) is revealed as the guru of PM (Pentagonal Meditation) (In which Dr. Matrix emerges as the guru of PM (Pentagonal Meditation)) |
| 1976 Dec | In which “monster” curves force redefinition of the word “curve” (In the monster curves force a redefinition of the word curve) |
| 1977 Jan. |
Extraordinary nonperiodic tiling that enriches the theory of tiles (An extraordinary nonperiodic tiling enriches the theory of tiling ) - Cover |
| 1977 Feb | The flip-strip sonnet, the lipogram and other mad modes of wordplay (The flip-strip sonnet, the lipogram and other crazy types of wordplay) |
| 1977 March | Cornering a queen leads unexpectedly into corners of the theory of numbers (About a queen who unexpectedly leads into the fringes of number theory) |
| 1977 Apr. | The pool-table triangle, a limerick paradox and divers other challenges (The pool table triangle, a Limerick paradox and various other challenges) |
| 1977 May | The “jump proof” and its similarity to the toppling of a row of dominoes (The jump proof and its similarity to knocking over a row of dominoes) |
| 1977 June | The concept of negative numbers and the difficulty of grasping it (the concept of negative numbers and the difficulty of grasping it ) |
| 1977 July | Cutting things into equal parts leads into significant areas of mathematics (breaking things down into equal parts leads to significant areas of mathematics) |
| 1977 Aug. | A new kind of cipher that would take millions of years to break (a new type of secret code that would take millions of years to resolve) |
| 1977 Sept. | On conic sections , ruled surfaces and other manifestations of the hyperbola (about conics , ruled surfaces and other manifestations of the hyperbola ) |
| 1977 Oct. | On playing New Eleusis, the game that simulates the search for truth (About the game of New Eleusis , a game that simulates the search for truth ) |
| 1977 Nov. | In which joining sets of points by lines leads into diverse (and diverting) paths (in which the connection of points to lines leads to different (and deviating) paths) |
| 1977 Dec | Dr. Matrix goes to California to apply punk to rock study (Dr. Matrix goes to California to apply point to the study of rock) |
| 1978 Jan. | The sculpture of Miguel Berrocal can be taken apart like an interlocking mechanical puzzle (The sculpture of Miguel Berrocal can be dismantled like an interlocking mechanical puzzle) |
| 1978 Feb | On checker jumping, the Amazon game, weird dice, card tricks and other playful pastimes (about checkers jumping, the amazon game, strange dice, card tricks and other playful pastimes) |
| 1978 March | Count Dracula, Alice, Portia and many others consider various twists of logic ( Count Dracula, Alice, Portia and many others consider various twists of logic ) |
| 1978 Apr. | White and brown music, fractal curves and one-over-f fluctuations (white and brown music, fractal curves and 1 / f fluctuations) - Cover |
| 1978 May |
The Bells : versatile numbers that can count partitions of a set, primes and even rhymes (Die Bellschen : versatile numbers that can count decompositions of a set, prime numbers and even rhymes) |
| 1978 June | A mathematical zoo of astounding critters, imaginary and otherwise (A mathematical zoo of amazing creatures, imaginary and otherwise) |
| 1978 July | On Charles Sanders Peirce : philosopher and gamesman (About Charles Sanders Peirce: philosopher and gambler) |
| 1978 Aug. | A Möbius band has a finite thickness, and so it is actually a twisted prism (A Möbius band has a finite thickness and is therefore actually a twisted prism) |
| 1978 Sept. | Puzzling over a problem-solving matrix, cubes of many colors and three-dimensional dominoes (puzzling over a problem-solving matrix, cubes with many colors and three-dimensional dominoes) |
| 1978 Oct. | Puzzles and number-theory problems arising from the curious fractions of ancient Egypt ( puzzles and number-theory problems arising from the fractures of the ancient Egyptians) |
| 1978 Nov. | In which a mathematical aesthetic is applied to modern minimal art ( In which a mathematical aesthetic is applied to modern minimal art ) |
| 1978 Dec | Is it a superintelligent robot or does Dr. Matrix ride again? (Is it a super intelligent robot or is it Dr. Matrix again?) |
| 1979 Jan. | The diverse pleasures of circles did are tangent to one another (the different pleasures of circles that touch each other) |
| 1979 Feb | About rectangling rectangles, parodying Poe and many another pleasing problem (parodying Poe, and other entertainment problems) |
| 1979 March | On altering the past, delaying the future and other ways of tampering with time (about changing the past, delaying the future and other ways of manipulating time) |
| 1979 April | In which players of Tic-tac-toe are taught to hunt bigger game (In which players of Tic-Tac-Toe learn to chase a bigger game) |
| 1979 May | How to be a psychic, even if you are a horse or some other animal (How to be gifted with psychic perception, even if you are a horse or another animal) |
| 1979 June |
Chess problems on a higher plane, including mirror images, rotations and the superqueen (chess problems on a higher plane, including mirror images and the super queen) |
| 1979 July | Douglas R. Hofstadter's " Gödel, Escher, Bach " (Douglas R. Hofstadter's "Gödel, Escher, Bach") |
| 1979 Aug | The imaginableness of the imaginary numbers (The imaginability of the imaginary numbers) |
| 1979 Sept. | In some patterns of numbers or words there may be less than meets the eye (in some number patterns there may be less than you see) |
| 1979 Oct. | Some packing problems that cannot be solved by sitting on the suitcase (some packing problems that cannot be solved when sitting on the suitcase ) |
| 1979 Nov. | The random number omega bids fair to hold the mysteries of the universe (The random number Omega could contain the secrets of the universe) |
| 1979 Dec | A pride of problems, including one that is virtually impossible (a showcase list of problems, including one that is literally unsolvable) |
| 1980 Jan. |
Checkers , a game that can be more interesting than one might think (Das Damespiel, a game that can be more interesting than you think) |
| 1980 Feb | The coloring of unusual maps leads into uncharted territory (The coloring of unusual maps leads to unknown territory) |
| 1980 March | Graphs that can help cannibals, missionaries, wolves, goats and cabbages get there from here (graphs that can help get cannibals, missionaries, wolves, goats and cabbages from here to there) |
| 1980 Apr. | Fun with eggs: uncooked, cooked and mathematic (fun with eggs: uncooked, cooked and mathematic) |
| 1980 May | What unifies dinner guests, strolling schoolgirls and handcuffed prisoners? (What do evening guests, walking schoolgirls and prisoners in handcuffs have in common?) |
| 1980 June | The capture of the monster : a mathematical group with a ridiculous number of elements (Capturing the monster: a mathematical group with an incredible number of elements) |
| 1980 July | The pleasures of doing Science and technology in the planiverse (The joys of science and technology in the plains ) |
| 1980 Aug | On the fine art of putting players, pills and points into Their proper pigeonholes (classify the art player, pills and points in their respective drawers) |
| 1980 Sept. | Dr. Matrix, like Mr. Holmes, comes to an untimely and mysterious end (Dr. Matrix, like Mr. Holmes, finds an untimely and mysterious end) |
| 1980 Oct. | From counting votes to making votes count: the mathematics of elections (From counting votes to methods of giving weight to votes: The mathematics of elections) |
| 1980 Nov. |
Taxicab geometry offers a free ride to a non-Euclidean locale ( Taxicab geometry offers a free ride to a non-Euclidean locale ) |
| 1980 Dec | Patterns in primes are a clue to the strong law of small numbers (prime number patterns indicate the strong law of small numbers) |
| 1981 Feb. | Gauss's congruence theory what mod as early as 1801 (The Kongruenztheorie Gauss was mod already as early as 1801) |
| 1981 Apr. | How Lavinia finds a room on University Avenue, and other geometric problems ( How Lavinia finds a room on University Avenue and other geometric problems) |
| 1981 June | The inspired geometrical symmetries of Scott Kim (The inspiring geometrical symmetries of Scott Kim) |
| 1981 Aug. | The abstract parabola fits the concrete world (The abstract parabola describes the real world) |
| 1981 Oct. | Euclid's parallel postulate and its modern offspring ( Euclid's parallel postulate and its modern descendants) |
| 1981 Dec | The Laffer curve and other laughs in current economics (The Laffer curve and other jokes of the current economic science) |
| 1983 Aug. | Tasks you cannot help finishing no matter how hard you try to block finishing them (tasks whose solution cannot be promoted, no matter how hard you try to block their solution) |
| 1983 Sept. | The topology of knots, plus the results of Douglas Hofstadter 's Luring Lottery (The topology of knots, plus the results of Douglas Hofstadter's lottery) |
| 1986 June | Casting a net on a checkerboard and other puzzles of the forest (throwing a net on a chessboard and other puzzles of the forest) |
Other articles by Gardner in Scientific American
Gardner wrote five other articles for Scientific American . His December 1956 Flexagon article was, so to speak, the first in the Mathematical Games column series, leading directly to the series that began the following month. These five articles are listed below.
| date | Title |
|---|---|
| 1952 March | Logic Machines (logical machines) |
| 1956 Dec |
Flexagons (Flexagons) |
| 1967 Jan. | Can time go backward? (Can time go backwards?) |
| 1998 Aug | A Quarter-Century of Recreational Mathematics (A quarter of a century recreational mathematics) |
| 2007 March | Is Beauty Truth and Truth Beauty? [book review] (Is beauty truth and truth beauty?) |
Individual evidence
- ^ A b Scientific American January 1957 Issue: Mathematical Games
- ^ A Gardner's Dozen — Martin's Scientific American Cover Stories
- ^ Scientific American February 1957 Issue: Mathematical Games
- ↑ [cover]
- ↑ [cover]
- ↑ [cover]
- ↑ [cover]
- ↑ [cover]
- ↑ [cover]
- ↑ [cover]
- ↑ [cover]
- ↑ [cover]
- ↑ [cover]
- ↑ [cover]
- ↑ [cover]
- ↑ Book review of Martin Gardner's Undiluted Hocus-Pocus by Teller, The New York Times, January 3, 2014
- ^ Scientific American March 1952 Issue: Logic Machines
- ^ Scientific American December 1956 Issue: Flexagons
- ^ Scientific American January 1967 Issue: Can Time go Backward?
- ^ Scientific American August 1998 Issue: A Quarter-Century of Recreational Mathematics
- ↑ Scientific American March 2007 Issue: Is Beauty Truth and Truth Beauty? How Keats's famous line applies to math and science Review of Why Beauty is Truth: A History of Symmetry , by Ian Stewart