A harmonograph uses two pendulums swinging in perpendicular planes to create a graphic representation of harmonies. This device uses the same relationships found in musical harmonies, but at the much lower frequencies of pendulums. The design for this harmonograph came from "100 Amazing Award Winning Science Fair Projects" by Glen Vecchione, with minor alterations during the build and test phases. Another interesting book on this topic is Anthony Ashton's "Harmonograph: A Visual Guide to the Mathematics of Music".

The curve traced out by a point on the rim of a circle rolling along a straight line is called a cycloid. Let the radius of the circle be . Allowing the tracing point to be either within or without the circle at a distance from the center generates "curtate" or "prolate" cycloids, respectively.

Here is the story of the Archimedes Palimpsest, a lost text of his found underneath a recycled prayerbook. Some of what he wrote about involves centers of mass computed with infinitesimals. I.e., Calc II!

Please read and act accordingly.

Slides from my Calc I Lecture

My lecture on substitution from Calc I

Integration using U-Substitution of Indefinite Integrals.

Ilustrations of several u-substitution problems

This applet is designed for the exploration of Riemann sums. The user can overlay the graph of the function with the area represented by the chosen method of sums, the piecewise linear approximation to the antiderivative, and the graph of a guess at the antiderivative.