MAA Focus October/November 2014 : Page 12

12 Honoring a Century of Martin Gardner By Ivars Peterson T tional types and more than 60 distinct tessellations by he foyer of the historic building that houses MAA headquarters in Washington, D.C., features a unique pentagons. Rice sent her discoveries to Gardner, and Gardner’s floor tiling made up of identical pentagons. Discovered mathematical grapevine—an extensive network of in 1995 by Marjorie Rice and adapted for use in the experts and amateurs with whom Gardner regularly lobby by Doris Schattschneider (Moravian College), exchanged information and checked out ideas—helped this distinctive tiling pattern also serves as a tribute to spread the word. Schattschneider was one of those who renowned mathematics writer Martin Gardner. This year marks the centennial of Gardner’s birth. He received news of Rice’s findings and, as time went on, began to correspond died in 2010 after a long directly with Rice to career, penning more follow her progress than 100 books, which and provide advice and ranged from annotated pertinent references. editions of Alice’s Adven-Schattschneider tures in Wonderland to herself had also become strong attacks on pseu-interested in the prob-doscience. His popular lem and, after present-and influential “Mathe-ing a talk on tiling with matical Games” column, convex pentagons at which ran from 1956 to a recreational math 1981 in Scientific Ameri-conference, was invited can, introduced a wide to write an article on audience to flexagons, the topic for Mathemat-polyominoes, John H. ics Magazine. The final Conway’s Game of Life, version of her article, Penrose tilings, public-A close-up of the tiling in the foyer of MAA headquarters inspired published in the Janu-key cryptography, the by a Martin Gardner column about convex polygon tiles. ary 1978 issue, included art of M. C. Escher, frac-up-to-the-minute news of Rice’s discoveries and other tals, and much more of mathematical interest. advances. The article itself, “Tiling the Plane with Con-The story of MAA’s floor tiling begins with Gardner’s gruent Pentagons,” went on to win the Carl B. Allendo-July 1975 column, “On Tessellating the Plane with erfer Award for expository writing. Convex Polygon Tiles.” Tiles in the shape of regular Rice continued exploring pentagonal tessellations and pentagons, for example, fail to cover a flat surface with-subsequently came up with the variant that became out leaving gaps. However, by easing angle and length the basis of the floor pattern displayed in the lobby of constraints, certain types of convex pentagons (such as MAA headquarters. Schattschneider was instrumental pentagons having a pair of parallel sides) do fit together in arranging for the fabrication and installation of the to cover the plane. In his article, Gardner described the custom tiles. eight known classes of convex, plane-tiling pentagons Appreciation of just such highly productive, column-and noted that this list was thought to be complete. inspired interactions led the MAA in 1976 to award Marjorie Rice, a homemaker in San Diego and avid Gardner an honorary life membership in the associa-Gardner fan, regularly read her son’s copies of Scientific American and took particular note of Gardner’s original tion. In its resolution, the MAA Board of Governors lauded Gardner for “the substantial contributions he article and its December follow-up, which announced has made to the public appreciation of mathematics by the surprise discovery of a ninth class of plane-tiling his superb exposition.” The citation continued, “The pentagons. enjoyment and humor which he conveys have been an Inspired by the articles, Rice began her own search for inspiration to many and are a model for all.” additional pentagonal tilings. She developed a unique Gardner was not present to receive his plaque, but he notation and procedure for systematically investigating provided a written response. “It is true that I never took the possibilities and eventually discovered four addi-0$$)2&86v2FWREHU1RYHPEHU
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Honoring a Century of Martin Gardner

Ivars Peterson

<br /> The foyer of the historic building that houses MAA headquarters in Washington, D.C., features a unique floor tiling made up of identical pentagons. Discovered in 1995 by Marjorie Rice and adapted for use in the lobby by Doris Schattschneider (Moravian College), this distinctive tiling pattern also serves as a tribute to renowned mathematics writer Martin Gardner.<br /> <br /> This year marks the centennial of Gardner’s birth. He died in 2010 after a long career, penning more than 100 books, which ranged from annotated editions of Alice’s Adventures in Wonderland to strong attacks on pseudoscience. His popular and influential “Mathematical Games” column, which ran from 1956 to 1981 in Scientific American, introduced a wide audience to flexagons, polyominoes, John H. Conway’s Game of Life, Penrose tilings, publickey cryptography, the art of M. C. Escher, fractals, and much more of mathematical interest.<br /> <br /> The story of MAA’s floor tiling begins with Gardner’s July 1975 column, “On Tessellating the Plane with Convex Polygon Tiles.” Tiles in the shape of regular pentagons, for example, fail to cover a flat surface without leaving gaps. However, by easing angle and length constraints, certain types of convex pentagons (such as pentagons having a pair of parallel sides) do fit together to cover the plane. In his article, Gardner described the eight known classes of convex, plane-tiling pentagons and noted that this list was thought to be complete.<br /> <br /> Marjorie Rice, a homemaker in San Diego and avid Gardner fan, regularly read her son’s copies of Scientific American and took particular note of Gardner’s original article and its December follow-up, which announced the surprise discovery of a ninth class of plane-tiling pentagons.<br /> <br /> Inspired by the articles, Rice began her own search for additional pentagonal tilings. She developed a unique notation and procedure for systematically investigating the possibilities and eventually discovered four additional types and more than 60 distinct tessellations by pentagons.<br /> <br /> Rice sent her discoveries to Gardner, and Gardner’s mathematical grapevine—an extensive network of experts and amateurs with whom Gardner regularly exchanged information and checked out ideas—helped spread the word. Schattschneider was one of those who received news of Rice’s findings and, as time went on, began to correspond directly with Rice to follow her progress and provide advice and pertinent references.<br /> <br /> Schattschneider herself had also become interested in the problem and, after presenting a talk on tiling with convex pentagons at a recreational math conference, was invited to write an article on the topic for Mathematics Magazine. The final version of her article, published in the January 1978 issue, included up-to-the-minute news of Rice’s discoveries and other advances. The article itself, “Tiling the Plane with Congruent Pentagons,” went on to win the Carl B. Allendoerfer Award for expository writing.<br /> <br /> Rice continued exploring pentagonal tessellations and subsequently came up with the variant that became the basis of the floor pattern displayed in the lobby of MAA headquarters. Schattschneider was instrumental in arranging for the fabrication and installation of the custom tiles.<br /> <br /> Appreciation of just such highly productive, column inspired interactions led the MAA in 1976 to award Gardner an honorary life membership in the association. In its resolution, the MAA Board of Governors lauded Gardner for “the substantial contributions he has made to the public appreciation of mathematics by his superb exposition.” The citation continued, “The enjoyment and humor which he conveys have been an inspiration to many and are a model for all.”<br /> <br /> Gardner was not present to receive his plaque, but he provided a written response. “It is true that I never took a college course in math—my major was philosophy— but math was my favorite subject in high school, and I never lost that enthusiasm and love for math that is characteristic of the amateur,” he wrote. “If the Association feels that my scribblings have contributed to a better public understanding of the beauty and usefulness of math, then I am pleased beyond measure.”<br /> <br /> Nearly two decades later, Gardner was again honored, this time receiving the Joint Policy Board for Mathematics Communications Award. He couldn’t attend the award ceremony, so JPBM sent a delegation to Gardner’s home in Hendersonville, North Carolina, to present the award and to interview him on camera.<br /> <br /> Recently unearthed video footage of that visit reveals a relaxed, playful, characteristically modest Gardner. He couldn’t resist showing off a few of his favorite magic tricks and talked at length about his work.<br /> <br /> Asked about the value of recreational math in teaching and learning, Gardner noted, “I’ve always thought that the best way to get students interested in mathematics is to give them something that has a recreational flavor—a puzzle or a magic trick or a paradox, or something like that. I think that hooks their interest faster than anything else.”<br /> <br /> On the subject of writing about mathematics for the public, Gardner said, “It’s good not to know much about mathematics. . . . I have to work hard to understand anything that I am writing about, so that makes it easier for me to explain it, perhaps, in a way that the general public can understand.”<br /> <br /> In passing, Gardner also made particular mention of the American Mathematical Monthly and Mathematics Magazine as important sources of new material for his writing.<br /> <br /> The year 1994 saw not only the JPBM award but also Gardner’s first article for Math Horizons (“Delicious Dissections”). His 1997 article “The Square Root of Two = 1.41421 35621 73095…” received the Trevor Evans award for expository writing. Along with Fan K. Chung and Ronald L. Graham, his name was on another awardwinning article, “Steiner Tiles on a Checkerboard,” published in Mathematics Magazine.<br /> <br /> Over the years, the MAA republished a number of Gardner’s books, including a special CD-ROM edition of the books containing all of his Scientific American columns.<br /> <br /> In his autobiography, Undiluted Hocus-Pocus (Princeton University Press, 2013), Gardner commented on the years during which he wrote his column. “One of the pleasures in writing the column was that it introduced me to so many top mathematicians, which of course I was not,” he wrote.<br /> <br /> Gardner’s correspondents included Solomon Golomb, Piet Hein, John Horton Conway, Raymond Smullyan, Donald Knuth, Benoit Mandelbrot, Ronald L. Graham, and Roger Penrose, among many others. Again and again, he had the pleasure of introducing one mathematician and his or her ideas to another—to the benefit of all. Indeed, Gardner was at the center of a wonderfully productive beehive of mathematical activity and research.<br /> <br /> Gardner also influenced careers. Many of an entire generation of mathematicians attribute their current positions (and passions) to a Gardner spark.<br /> <br /> In a special public address at MAA MathFest in Portland in celebration of the Gardner centennial, Persi Diaconis (Stanford University) spoke about the role that Gardner played in his life and career. As a 13-year-old, Diaconis first met Gardner in New York City at a cafeteria where magicians liked to hang out. From then on, the two talked and corresponded regularly, and Diaconis often turned to Gardner for advice, especially as he made the transition from a life as a magician on the road to statistics professor.<br /> <br /> Some years ago, Diaconis wrote the following blurb for one of Gardner’s books: “Warning: Martin Gardner has turned dozens of innocent youngsters into math professors and thousands of math professors into innocent youngsters.”<br /> <br /> That legacy continues.<br /> <br /> Ivars Peterson is director of publications at MAA.

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