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The beautiful "Four Bugs Problem" [1]

['Mark Frauenfelder']

Date: 2024-09-19  

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.

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.

Previously:

• RIP Martin Gardner

• Martin Gardner puzzle: red, white, and blue weights

• Martin Gardner's 'Science Magic,' fun tricks you can try at home

• A surprising solution to the (in)famous 'Cross the Network' puzzle

• Free: scanned copy of Martin Gardner's Logic Machines and Diagrams (1958)

• The Missing Dollar puzzle from Martin Gardner's Aha! Gotcha book series

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