Mathematical Recreations; June 1996; Scientific American Magazine; by Stewart; 2 Page(s)

Last month I described the mathematical sculptures of Alan St. George, who often makes use of the well-known "golden number." The catalogue of his Lisbon exhibition mentions a less glamorous relative, referring to a series of articles in which "the architect Richard Padovan revealed the glories of the ¿plastic number.¿ " The plastic number has little history, which is strange considering its great virtues as a design tool, but its provenance in mathematics is almost as respectable as that of its golden cousin. It doesn¿t seem to occur so much in nature, but, then, no one¿s been looking for it.

For purposes of comparison, let me start with the golden number: j=1+ 1/ j = 1.618034, approximately. The golden number has close connections with the celebrated Fibonacci numbers. This series can be illustrated by a spiraling system of squares [see upper illustration on this page]. The initial square (in gray) has side 1, as does its neighbor to the left. A square of side 2 is added above the first two, followed in turn by squares of side 3, 5, 8, 13, 21 and so on. These numbers, each of which is the sum of the previous two, form the Fibonacci series. The ratio of consecutive Fibonacci numbers tends to the golden number. For example, 21/13 = 1.615384.