Lissajous Curves

Parametric Cartesian equation:
x = a sin(nt + c), y = b sin(t)

Click below to see one of the Associated curves.

Definitions of the Associated curves Evolute
Involute 1 Involute 2
Inverse curve wrt origin Inverse wrt another circle
Pedal curve wrt origin Pedal wrt another point
Negative pedal curve wrt origin Negative pedal wrt another point
Caustic wrt horizontal rays Caustic curve wrt another point

Click THIS LINK to experiment interactively with this curve and its associated curves.

Lissajous curves or Lissajous figures are sometimes called Bowditch curves after Nathaniel Bowditch who considered them in 1815. They were studied in more detail (independently) by Jules-Antoine Lissajous in 1857.

Lissajous curves have applications in physics, astronomy and other sciences.

Nathaniel Bowditch (1773-1838) was an American. He learnt Latin to study Newton's Principia and later other languages to study mathematics in these languages. His New American Practical Navigator (1802) and his translation of Laplace's Mécanique céleste gave him an international reputation.

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JOC/EFR/BS January 1997

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