|Photo: Manil Suri|
In 1975, a San Diego woman named Ms Marjorie Rice read in her son's Scientific American magazine that there were only eight known pentagonal shapes that could entirely tile, or tessellate, a plane. Despite having had no mathematics lessons beyond high school, she resolved to find another. By 1977, she had discovered not just one, but four new tessellations - a result noteworthy enough to be published the following year in a maths journal.
|Photo: The Straits Times|
The article that turned Ms Rice into an amateur researcher was by the legendary polymath Martin Gardner. His "Mathematical Games" series, which ran in Scientific American for more than 25 years, introduced millions worldwide to the joys of recreational maths. I read him in Mumbai as an undergraduate, and even dug up his original 1956 column on "hexaflexagons" (folded paper hexagons that can be flexed to reveal different flower-like faces) to construct some myself.
|Photo courtesy of Jim Gardner |
Source: Mathematical Association of America
"Recreational maths" might sound like an oxymoron to some, but the term can broadly include immensely popular puzzles such as Sudoku and KenKen, in addition to various games and brain teasers. The qualifying characteristics are that no advanced mathematical knowledge such as calculus be required, and that the activity engages enough of the same logical and deductive skills used in maths.
Unlike Sudoku, which always has the same format and gets easier with practice, the disparate puzzles that Gardner favoured required different, inventive techniques to crack. The solution in such a puzzle usually pops up in its entirety, through a flash of insight, rather than emerging steadily via step-by-step deduction as in Sudoku. An example: How can you identify a single counterfeit penny, slightly lighter than the rest, from a group of nine, in only two weighings?
Gardner's great genius lay in using such basic puzzles to lure readers into extensions requiring pattern recognition and generalisation, where they were doing real maths. For instance, once you solve the nine-coin puzzle above, you should be able to figure it out for 27 coins, or 81, or any power of three, in fact. This is how maths works, how recreational questions can quickly lead to research problems and striking, unexpected discoveries...
Yet, Gardner's work lives on through websites that render it in the visual and animated forms favoured by today's audiences, through a constellation of his books that continue to sell, and through the biannual "Gathering 4 Gardner" recreational maths conferences.
In his final article for Scientific American, in 1998, Gardner lamented the "glacial" progress resulting from his efforts to have recreational maths introduced into school curriculums "as a way to interest young students in the wonders of mathematics". Indeed, a paper this year in the Journal Of Humanistic Mathematics pointed out that recreational maths can be used to awaken maths-related "joy," "satisfaction," "excitement" and "curiosity" in students, which the educational policies of several countries (including China, India, Finland, Sweden, England, Singapore and Japan) call for in writing. In contrast, the Common Core in the United States does not explicitly mention this emotional side of the subject, regarding maths as only a tool.
Martin Gardner (Wikipedia, the free encyclopedia)
The Top 10 Martin Gardner Scientific American Articles
Read an interview with Martin Gardner from the November 2004 issue of MAA FOCUS here (PDF)
Source: The Straits Times