Gardner was a journalist, a novelist, a magician, a philosopher and one of the earliest public debunkers of pseudoscience. In his monthly column Mathematical Games, which he wrote in Scientific American between the s and the s, he introduced many brainteasers as well as giving old classics new twists. His answer threw me. Yet when we continued the discussion I realised that my analogies were wrong. There is a difference between being good at puzzles and appreciating a good puzzle. Gardner wrote dozens of books on puzzles and recreational maths — here are eight puzzles taken from them.
Ten red socks and ten blue socks are all mixed up in a dresser drawer. The 20 socks are exactly alike except for their colour. The room is in pitch darkness and you want two matching socks. What is the smallest number of socks you must take out of the drawer in order to be certain that you have a pair that match? Two identical bolts are placed together so that their helical grooves intermesh as shown below.
If you move the bolts around each other as you would twiddle your thumbs, holding each bolt firmly by the head so that it does not rotate and twiddling them in the direction shown, will the heads. A logician vacationing in the South Seas finds himself on an island inhabited by two proverbial tribes of liars and truth-tellers. Members of one tribe always tell the truth, members of the other always lie. He comes to a fork in a road and has to ask a native bystander which branch he should take to reach a village. He has no way of telling whether the native is a truth-teller or a liar.
The logician thinks a moment, then asks one question only. From the reply he knows which road to take. What question does he ask? Using only elementary geometry not even trigonometry , prove that angle C equals the sum of angles A and B. With one straight cut you can slice a pie into two pieces. A second cut that crosses the first one will produce four pieces, and a third cut can produce as many as seven pieces. Field, Michael, and Martin Golubitsky.
McGuire, Michael. Reading, Mass. Peden, Douglas D. Bridges of mathematics, art, and physics. Science News Sept. Art of pursuit. Science News Online July Pursuing pursuit curves. Scrambled grids. Science News Online Aug.
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Art of the grid. Sliding pi. Science News Online June 3. Singapore: World Scientific. Mazes for the Mind: Computers and the Unexpected. Does God Play Dice? The Mathematics of Chaos.
Martin Gardner, puzzle master extraordinaire
Penrose tiling. Penrose tiling II. Tiling with convex polygons. Gailiunas, Paul. Spiral tilings. Penrose tiles. Tilings and Patterns. La Breque, Mort. Opening the door to forbidden symmetries. Mosaic 18 Winter : Penrose, Roger. On the cohomology of impossible figures. Clusters and decagons. Science News Oct. The fivefold way for crystals. Science News March 23 : Pentaplexity: A class of non-periodic tilings of the plane. Mathematical Intelligencer 2 No. Robbin, Tony. New Haven, Conn. Fourfield: Computers, Art, and the Fourth Dimension.
Boston: Little, Brown and Company. Painting and physics: Modeling artistic and scientific experience in four spatial dimensions. Leonardo 17 No. Coloring Penrose tiles. Schattschneider, Doris. In praise of amateurs. Klarner, ed. Mineloa, N. The fascination of tiling. Senechal, Marjorie. Quasicrystals and Geometry. Cambridge, England: Cambridge University Press. Steinhardt, Paul Joseph. Venters, Diana, and Elaine Krajenke Ellison. Mathematical Quilts: No Sewing Required! Bill, Max. The mathematical way of thinking in the visual art of our time. Brown, Ronald.
John Robinson's symbolic sculptures, knots and mathematics. Emmer, Michele. Mathematics and art: Bill and Escher. In Mathematical Magic Show. Isaksen, Daniel C. Perry, Charles O. Continuum, broken symmetry, and more. On the edge of science: The role of the artist's intuition in science. Science News Online June 9. Science News Online July 8. Recycling topology.
Extreme Physics (Scientific American Special Online Issue No. 12)
Rhapsody in White: A victory of mathematics. Mathematical Intelligencer 22 No. Dickson, Stewart.
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True 3D computer modeling: Sculpture of numerical abstraction. Gray, Alfred. Boca Raton, Fla.
A Kaleidoscope of Math and Art
Hildebrandt, Stefan, and Anthony Tromba. New York: Springer-Verlag. Hoffman, David, and William H. Meeks, III. Minimal surfaces based on the catenoid. American Mathematical Monthly 97 October : White narcissus. A minimal winter's tale.
Minimal snow. Science News Online March 6. Putting a handle on minimal helicoids. Adams, Colin C. Casselman, Bill. Pictures and proofs. Notices of the American Mathematical Society 47 November : Collins, Brent. Geometries of curvature and their aesthetics. Visualization: From biology to culture.
Merging paradigms. Finding an integral equation of design and mathematics. Evolving an aesthetic of surface economy in sculpture. Leonardo 30 No.
American Journal of Applied Mathematics :: Science Publishing Group
Topological sculptures. Interdisciplinary Science Reviews 18 No. Cox, Donna J. Caricature, readymades and metamorphosis: Visual mathematics in the context of art. Francis, George K. On knot-spanning surfaces: An illustrated essay on topological art. With an artist's statement by Brent Collins. Leonardo 25 No. Friedman, Nathaniel A.
Visual Mathematics 3 No. What do you see? Geometric sculpture for K Geos, hyperseeing, and hypersculpture. Form, space, and light. Hyperseeing, hypersculptures and space curves. The topology of knots. Worm paths. The five Platonic solids. Krawczyk, Robert J.
Curving spirolaterals. More curved spirolaterals. Krawczyk, Robert A. Spirolaterals, complexity from simplicity. Levine, Howard. See-duction: How scientists and artists are creating a third way of knowing. Humanistic Mathematics Network Journal No. Turtle tracks. Punctured polyhedra. Science News Online June Puzzling lines. Art of the tetrahedron.
Sculpture generator. Science News Online Oct. Analogies from 2D to 3D: Exercises in disciplined creativity. Computer-augmented inspiration. Art, math, and computers: New ways of creating pleasing shapes. Wenninger, Magnus J. Polyhedron Models. London, England: Cambridge University Press. Coxeter, H. Angels and devils. Emmer, R. Penrose, and M. Teuber, eds. Escher, Rome, Italy, March, Amsterdam: North-Holland.
Dunham, Douglas. Hyperbolic Celtic knot patterns. Artistic patterns in hyperbolic geometry. Transformation of hyperbolic Escher patterns.