Jules Antoine Lissajous1822–1880
Harmonic figures, 1857
French physicist who reflected light between two vibrating tuning forks to draw the closed harmonic figures now named after him.
Lissajous Grid
A plate of figures, one for every pair of whole-number frequencies. The ratio is legible from the shape alone.
About this pattern
Jules Antoine Lissajous, 1857 · specimen plate
Lissajous set a mirror on each of two tuning forks at right angles and bounced a beam between them. The figure closes only when the two frequencies are in whole-number ratio, and the number of times it touches each side of its box gives that ratio directly, which made it the way to measure an unknown frequency against a known one for most of a century. Laid out as a plate, each cell is a different pair.
Behind the mathematics
Nathaniel Bowditch1773–1838
The same curves by pendulum, 1815
American mathematician and navigator who studied the same harmonic curves with a compound pendulum decades before Lissajous.