introduces many tools for integrating dynamic geometry with dynamic
algebra. The sketches in this gallery illustrate some possibilities, from the
equation for a line, to integration of a cubic. They all make use of dynamic
plotting of points from measured or calculated quanitities, and the ones that
plot curves make use of constructed loci.
To get started constructing your own, try a Primer
The sketches on this page are available individually (below) or can be downloaded
as a package.
Slope and Intercept
Use this sketch as an electronic blackboard or exploratory environment for
looking at the relationship between the equation for a line, the angle the line
makes with the x-axis, and the tangent of that angle.
A cubic equation of the form y = a (x - p) (x - q) (x - r) is plotted. The
curve responds dynamically to changes in the coefficients a, p, q, and r. Two
limits of integration, x1 and x2, are given, and between these limits, eight
rectangles are constructed to approximate the area under the curve. The total
integral is computed both by adding the areas of the rectangles and by an exact
computation. It is interesting to compare the results of the two computations.
This sketch provides an interactive demonstration of the effect of varying
the amplitude, period, and phase of a sinusoidal curve. Dragging points within
the sketch changes the coefficients.
Two complex numbers and their product are shown in the complex plane. As the
given numbers are changed by dragging, their product changes accordingly.
Some questions to investigate include: What number when squared equals -1? Is
this the only number? What is the geometric result of multiplying a number by i?
By -i? Can you find a number which, when squared, equals i?
Return to the Foyer.
Sketches, scripts, and web pages by Bill Finzer
and Nick Jackiw.