Back to . . . .
Curve Bank Home
Dr. Paul Chabot
Department of Mathematics
California State Univ.,
Los Angeles

The Cycloid Family of
Curves
Cycloid, Trochoid,
Epicycloid, Hypocycloid, Epitrochoid and Hypotrochoid
Create Your Own
Animations Using Maple!

The graphics in this deposit were
created using Maple software.

NCB Deposit # 30

A
Sampler for the Student . . . .
Each animation in the left
column will repeat twice.


These are very large files.
Be patient! 
Dr. Chabot's Maple Work Sheets
can be altered to graph any curve in the cycloid family on any
domain. However, you must own a copy of the Maple software.

Arguably, the Cycloid Family of
curves features the most distinguished group of investigators in
mathematics.
Galileo and Father Mersenne are credited with being the first to name
and discuss its special properties (1599). They were
followed
by Torricelli, Fermat, Descartes, Roberval, Wren, Huygens, Desargues,
Johann Bernoulli, Leibniz, Newton, Jakob Bernoulli, L'Hôpital and
others.
This is probably too brief a list.
One might assert that a
fascination with the motion of the cycloidal curves led a century of
civilization's greatest mathematicians into modern mathematics.
Certainly, the
birth of the calculus, especially the calculus of variations,
flourished
among these remarkable men who were determined to understand its many
special
qualities.
Because of the frequency of
disputes among mathematicians in the 17th century, the cycloid became
known as
the "Helen of Geometers."
The name is appropriately based on Greek
mythology.
Helen was the most beautiful woman in the world. The Trojan war
that followed her capture was one of the fiercest conflicts in ancient
times.

Shikin, Eugene V., Handbook
and Atlas of Curves, CRC Press, 1995.
Yates, R. C., Curves
and their Properties, NCTM, 1952. Also in A Handbook on
Curves and their Properties, various publishers including the NCTM.
Weisstein, Eric. W., CRC
Concise Encyclopedia of MATHEMATICS, Chapman & Hall/ CRC, 2nd
ed., 2003.

For Mathematica® code that
will create many of these graphs:
Gray,
A., MODERN DIFFERENTIAL GEOMETRY of Curves and Surfaces with
Mathematica®, 2nd. ed., CRC Press, 1998.
< http://mathworld.wolfram.com/Cycloid.html >

