sketch of one curve . . . .
Notice the animated tangent to the parabola in the upper right hand
corner. The parabola is undoubtedly the most studied curve in the
history of mathematics. A treatise, Conic Sections,
written by Euclid (ca. 300 B.C.), has been
lost but is thought to have provided a foundation for Apollonius' first
books of the same name. Both the scholar and
can trace this work through the Alexandrian school. Hypatia (d.
A.D.), the first woman in the history of mathematics known by name, is
to have made the translation.
These manuscripts can then be traced to Western
Europe via Arab conquest, first through North Africa, and then into
Spain. Toledo, Cordova and Seville were outstanding centers of
learning from the 9th to the llth centuries.
Later, Galileo (1564 - 1642) discovered that a
cannonball follows a parabolic path. Scientists, monarchs and
military leaders immediately took great interest! The aiming of a
cannon became a function of measuring the precise angle of a
trajectory, the "throw weight" and its momentum. With these
experiments and especially the famous dropping of objects from the top
of the Leaning Tower of Pisa, Galileo revolutionized science. He
introduced the "scientific method" as a permanent contribution to
civilization. Later his heliocentric theory of the universe
almost cost him his life.
Descartes, in writing La
chose the parabola to illustrate his innovative analytic
this time in publishing history, all math figures were difficult to
create and to print.
In 1992, R. A. Marcus of the California Institute
of Technology won the Nobel Prize in Chemistry for his work showing
that parabolic reaction surfaces can be used to calculate how fast
electrons travel in molecules.
His most famous theoretical result, an inverted rate-energy parabola,
predicts electron transfer will slow down at very high reaction free
Millions of students in recent centuries will
remember the parabola as the introductory curve leading into study of