# Curves

### Lissajous Curves

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

### Description

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.

### Associated Curves

Definitions of the Associated curves