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Institute of Mathematics and Computer
Wroclaw University of Technology
The Cycloid Family of Curves
continued . . .
Create Your Own
graphics in this deposit were created
Deposit # 132
Sampler for the Student . . . .
Study this work sheet.
Then click on the work
sheet or the link to see the animation. These are
large JAVA files downloading GeoGebra. Be
may have to download a
newer version of Java. With Java present, your
computer should download the Java
driven animation files. There is also the option of
downloading GeoGebra. Both are free.
Now you may enjoy seeing other
animations of the cycloid.
Go to . . . .
Arguably, the Cycloid Family of
curves features the most distinguished group of investigators in
Galileo and Father Mersenne are credited with being the first to name
and discuss its special properties (1599). They were
by Torricelli, Fermat, Descartes, Roberval, Wren, Huygens, Desargues,
Johann Bernoulli, Leibniz, Newton, Jakob Bernoulli, L'Hôpital and
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.
birth of the calculus, especially the calculus of variations,
among these remarkable men who were determined to understand its many
Because of the frequency of
disputes among mathematicians in the 17th century, the cycloid became
of Geometers." The name is appropriately based on
Helen was the most beautiful woman in the world. The Trojan war
that followed her capture was one of the fiercest conflicts in ancient
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
Encyclopedia of MATHEMATICS, Chapman & Hall/ CRC, 2nd ed., 2003.
|For MATHEMATICA ® code that
will also create many
Gray, A., MODERN
DIFFERENTIAL GEOMETRY of Curves and Surfaces with
Mathematica®, 2nd. ed., CRC Press, 1998.
For Maplesoft code
to create several members of the cycloid family see < http://curvebank.calstatela.edu/cycloidmaple/cycloid.htm >
For an interesting "Proof Without Words" see John Martin, Area of
a Cycloidal Arch, The College
Mathematics Journal, vol. 41 (1) January, 2010, p. 28.