(Roughly) Daily

Mark Frauenfelder at Boing Boing with a glorious memory…

This cover from the July 1965 issue of Scientific American illustrates the “Four Bugs Problem” featured in Martin Gardner’s “Mathematical Games” column about op art [see here].

The setup: Four bugs are placed at the corners of a square. They start crawling clockwise (or counterclockwise) at a constant rate, with each bug moving directly toward its neighbor. As the bugs move, they always form the corners of a square that both diminishes in size and rotates. Each bug’s path forms a logarithmic spiral.

Gardner said this can be generalized to any number of bugs starting at the corners of a regular polygon with n sides. In these cases, the bugs will always form the corners of a similar polygon that shrinks and rotates as they move.

Here’s an animated version of the Four Bugs Problem you can try out. If you want to try it with a different number of bugs, go here.

Your correspondent still has his copy of that issue. “The beautiful ‘Four Bugs Problem’” from @Frauenfelder in @BoingBoing.

* Bertrand Russell, A History of Western Philosophy

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As we marvel, we might send carefully-calculated birthday greetings to Ian Stewart; he was born on this date in 1945. As a teenager, he was an avid reader of Gardner’s “Mathematical Games,” from which he developed a love of the subject that led him to become a mathematician who has gone on to make important contributions to the field, especially in catastrophe theory.

But Stewart is more widely known as a popularizer of math– who credits Gardner with modeling the skills needed to be an entertaining communicator. Indeed, from 1991 to 2001 Stewart took over the Scientific American column (which had been renamed “Mathematical Recreations”).

For a list of his (remarkable) books on math and science, see here.

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