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Download 1.HO.Happy Birthday Martin Gardner.PS Happy Birthday Martin Gardner (October 21) CMC-S Palm Springs October 24, 2014 with Michael Serra © 2014 Michael Serra 1 www.michaelserra.net Martin Gardner Born October 21, 1914 Childhood in Tulsa Oklahoma Bachelor's degree in 1936 from University of Chicago Served in the U.S. Navy during WWII Writer at Humpty Dumpty magazine in the late 40’s For 25 years, wrote a monthly column Mathematical Games for Scientific American (1956–1981) Gardner and family lived in Hastings-on-Huston, NY In 1979, semi-retired and moved to Hendersonville, NC In 1993 Atlanta puzzle collector Tom Rodgers persuaded Gardner to attend an evening devoted to Gardner’s puzzle-solving efforts, called “Gathering for Gardner.” Gardner's wife Charlotte died in 2000 and two years later he returned to Norman, OK Martin Gardner died there on May 22, 2010 “Gathering for Gardner” continues every even year and now this past year was the 11th gathering (G4G11). The gatherings are written G4Gn, where n stands for the number of the event. I was invited and attended this past March. Pulitzer Prize–winning cognitive scientist Douglas Hofstadter described Martin Gardner as “one of the greatest intellects produced in this country in this century.” Paleontologist Stephen Jay Gould remarked that Gardner was “the single brightest beacon defending rationality and good science against the mysticism and anti-intellectualism that surrounds us.” Linguist Noam Chomsky described his contribution to contemporary intellectual culture as “unique—in its range, its insight, and its understanding of hard questions that matter.” In his obituary in The Economist they said of him, “No wonder it is sometimes said that Mr. Gardner made mathematicians out of children and children out of mathematicians.” A good math puzzle, paradox, or magic trick can stimulate a child’s imagination much faster than a practical application … and if the game is chosen carefully, it can lead almost effortlessly into significant mathematical ideas. – Martin Gardner What is the relationship between fun math and serious math? When you play a game, if you learn to be good at it, you find what it is you should be thinking about… That is what we do in mathematics. – John Horton Conway The PBS TV series "The Nature of Things” with David Suzuki showcases Martin Gardner in an episode titled "Mystery and Magic of Mathematics: Martin Gardner and Friends." © 2014 Michael Serra 2 www.michaelserra.net Topics from Martin Gardner’s Mathematical Games Polyominoes Fibonacci Numbers Game of Racetrack Tangrams Game of Hex Penrose Tilings Tower of Hanoi Fractals Game of Life Magic Squares Escher Art Cryptanalysis Anamorphic Art Graeco-Latin Squares Rep-tiles Math Magic Tricks Soma Cube Dissections Knight’s Tour Origami The Mathematical Practices CCSS MP1: Make sense of problems and persevere in solving them. CCSS MP2: Reason abstractly and quantitatively. CCSS MP3: Construct viable arguments and critique the reasoning of others. CCSS MP4: Model with mathematics. CCSS MP5: Use appropriate tools strategically. CCSS MP6: Attend to precision. CCSS MP7: Look for and make use of structure. CCSS MP8: Look for and express regularity in repeated reasoning. Gardner Classics © 2014 Michael Serra 3 www.michaelserra.net If tic-tac-toe players are allowed to play either X or O on each move, prove that the first player can always win. If tic-tac-toe players play on the grid to the right, prove that the first player can always win. © 2014 Michael Serra 4 www.michaelserra.net Polyominoes In 1953 Mathematician Solomon Golumb introduced polyominoes to the world of recreational mathematics at the Harvard Mathematics Club. Soon after his original presentation was published in the American Mathematical Monthly. A few years later polyominoes appeared in Martin Gardner’s Mathematical Games column in the May 1957 issue of Scientific American. Polyomino play is now a classic in recreational mathematics. The list of contributors to the study (or play) of polyominoes reads like a “Who’s Who of contemporary mathematics.”1 What are Polyominoes? Polyominoes are shapes made by connecting congruent squares complete side to complete side. The name came from the domino. Dominoes are examples of two squares connected side to side. Tetromino Pentomino Octomino Not polyominoes Two polyominoes are considered different (distinct) if and only if they cannot be obtained from each other by rotating or flipping. These are the same These are different The twelve pentominoes are named for the 12 letters of the alphabet that they "closely" resemble. T U V W X Y Z F L I P N Polyominoes are the shapes that you will be searching for in the pirate treasure games and puzzles in this session. 1 Ball, W. W. R. and Coxeter, H. S. M. Mathematical Recreations and Essays; Berlekamp, E. R.; Conway, J. H; and Guy, R. K. Winning Ways for Your Mathematical Plays; Gardner, M. Mathematical Games; Madachy, J. S. Pentominoes: Some Solved and Unsolved Problems, to name just a few. © 2014 Michael Serra 5 www.michaelserra.net © 2014 Michael Serra 6 www.michaelserra.net © 2014 Michael Serra 7 www.michaelserra.net Racetrack Racetrack is a pencil on graph paper race between two players. At each racecar driver’s turn the driver relocates the car to a new grid point according to three rules. The first to cross the finish line wins. Rule 1. A car can maintain its speed in either direction or it can change speed by only one unit per move either horizontally, vertically, or both. Since you are not moving at the start, your pre- game speed is (0,0). Rule 2. The new grid point and the segment connecting it to the preceding grid point must lie entirely within the track. Rule 3. No two cars may occupy the same grid point at the same time (no crashes). © 2014 Michael Serra 8 www.michaelserra.net Hex The Game of Hex is a 2-person game where players take turns placing X’s and O’s on unoccupied hexagon spaces. The game is won when one player creates an unbroken chain of their X’s connecting the two X sides or an unbroken chain of their O’s connecting the two O sides. x o o x © 2014 Michael Serra 9 www.michaelserra.net Tour Puzzles Rook’s Tour Puzzle King’s Tour Puzzle Knight’s Tour Puzzle 47 46 43 42 33 32 31 24 23 7 7 48 22 4 10 14 49 21 52 20 3 13 11 53 19 19 12 62 18 3 5 20 17 63 17 68 16 69 70 71 72 73 74 3 2 1 Escher Tessellations Piet Hein’s Puzzle and the Soma Cube Puzzle What are all the possible non-convex solids created by four or fewer cubes joined face to face? Resources Pirate Math at www.michaelserra.net Smart Moves at www.michaelserra.net Discovering Geometry An Investigative Approach published by Kendall Hunt Email: [email protected] © 2014 Michael Serra 10 www.michaelserra.net .
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