Lissajous or Bowditch Curves

Nathaniel Bowditch (1773 - 1838) was the first American to receive international recognition as a mathematician.  Moreover, he was the first to investigate a family of curves now usually named for the French physicist, Jules-Antoine Lissajous.  Lissajous independently published his work much later in 1857.

Bowditch, working in the isolation of New England's Salem and Boston areas, held a life-long fascination with doing tedious calculations.  He learned Latin and several other languages in order to read the mathematical publications being imported from Europe.  In particular, he is known to have studied Newton's Principia and Laplace's Mécanique celeste, an important guidebook for astronomers. 

Be reminded that a copy of Euclid's Elements was not printed in the newly independent country until 1803 in Philadephia.  During Bowditch’s lifetime in Boston, one printed mathematics book would commonly be imported by a professor.  Students were then expected to learn from notes and notebooks hand copied in the classroom.   This atmosphere may have contributed to Bowditch's refusal of chairs of mathematics at several universities.  He preferred being president of the Essex Fire and Marine Insurance Company (1804 - 1823).

Also be reminded that the principal means of international communication as well as commerce was the open sea.  Mathematics was a navigational necessity.  In 1802 Bowditch published the New American Practical Navigator.  This book became known as "the seaman's Bible" and is still published.

Lissajous (1822 - 1880) is thought to have encountered these curves when he collected data for his optical method of studying vibrations.