|Analysis index||History Topics Index| The terminology for
elliptic integrals and functions has changed during their
investigation. What were originally called elliptic functions
are now called elliptic integrals and the term elliptic
functions reserved for a different idea. We will therefore use
modern terminology throughout this article to avoid confusion.
It is important to understand how mathematicians thought
differently at different periods. Early algebraists had to prove
their formulas by geometry. Similarly early workers with
integration considered their problems solved if they could
relate an integral to a geometric object. Many integrals arose
from attempts to solve mechanical problems. For example the
period of a simple pendulum was found to be related to an
integral which expressed arc length but no form could be found
in terms of 'simple' functions. The same was true for the
deflection of a thin elastic bar. The study of elliptical
integrals can be said to start in 1655 when Wallis began to
study