The following is the README file from a set of Sketchpad files now available on the Forum ftp/gopher site (soon to be a Mosaic site, as well!).
The sketches are currently in Mac form only, as a self-extracting, binhexed archive, and can be found as
I hope to have a zipped PC version of the file available early next week.
If you have any problems with these files, or have any questions about how to retrieve things via ftp or gopher, please let me know.
What follows are descriptions of sketches made by Bill Finzer, Rob Berkelman, and Dan Bennett while employed at Key Curriculum Press in Berkeley. If you would like more information about the sketches, feel free to contact me (Rob) at email@example.com or by calling Key Curriculum Press at 1-510-548-2304. We hope you enjoy the sketches as much as we enjoyed creating them. We would love to see any work that you have done with these or other ideas using Sketchpad.
Four ants located in the plane--each crawls continuously toward the next ant. What paths do the ants describe? The sketches and scripts in this folder show how to investigate this with Sketchpad. Try generalizing to more ants, or (?) fewer ants.
Chase Four This is a completed sketch. Move the starting places of the ants to see the paths change.
Chase Four Starter Use this sketch as a starting place from which to run the script. This enables you to set your own number of steps that the ants take.
Chase Four.Script Use this script in conjuntion with ``Chase Four Starter'' to move your own ants.
These two sketches demonstrate useful Sketchpad animation techniques. ``Clock'' shows how to the hour and minute hands at different rates. ``Clock Switch'' shows how to turn analog motion into digital switches.
Derivative and Integral:
Sketchpad can nicely demonstrate elementary calculus concepts as these two sketches show. In each sketch two graphs of curves appear, approximated by a few data points. The bottom graph shows the derivative of the top graph; i.e. the y-coordinate of each point on the bottom represents the slope of the segment joining the two points above it in the top graph.
You can move the points in the derivative graph and see the effect on the graph at the top.
You can move the points in the top graph and see the effect on the derivative.
Jean Marie Laborde (the creator of Cabri Geometri) has shown how to model force fields. These two sketches demonstrate the techniques.
Here a capacitor is modeled with five positive charges on one side and five negative ones on the other. You can ``see'' the nearly uniform field between the two rows of charges.
Plus and Minus Charges
A test charge is moved around in the presence of fixed positive and negative charges.
This is a dynamic model of the exponential function where the base of the exponential function is equal to the ratio of length of two line segments. The equation is also dynamically updated.
Don't try these sketches on a slow machine. Too frustrating!
Compleat Sine Wave
You can use this sketch in demos in trig class to illustrate the roles of amplitude, phase, and frequency in a sine curve.
This geometric model of a Fourier series allows you go specify the amplitude of components and shows you a neat way to visualize how the wave is generated.
Here we have a sketches showing the platonic solids in true perspective. You have control over the placement of the picture plane, the station point, and the horizon. An animation button rotates the figure for you. Some of the sketches show in 3D if you have a pair of 3D glasses. (The colors may be a bit off on your monitor.)
Here is a draggable line on an xy-coordinate system that dynamically updates the equation of the line.
The midpoint quadrilateral, constructed by connecting the midpoints of any quadrilateral, is always a parallelogram. Under what conditions is it a rhombus? Use this sketch to investigate.
This is a sketch of a tessalation made in the pattern of a Navajo rug.
This sketch was created recursively, replicating a segment and an angle thus creating various polygons when the angle is changed.
Parallelogram Area vs.Per
This is a figure which is minimally constrained to be a parallelogram with constant area and perimeter.
Here is an animation of a pendulum. You can vary its length and amplitude. Take some data. What is the dependence of the period on these two parameters. Does it behave like a physical pendulum?
This is a dynamic perspective drawing of a road and a railroad track receding into the distance.
This is a dynamic polygon generator created using the same techniques as in N-gon but using two different angles and two different lengths of segments, all of which are changing at different rates.
Here we have five scripts that demonstrate ways to use Sketchpad to investigate random phenomena.
2D Fractal Mountain Script
Generate a random, fractal skyline.
3D Landscape Script
Generate a 3-D landscape using random fractals.
Select a starting point and a segment that specifies how large the steps are. The depth of recursion indicates how many steps will be taken. Each step is in a random direction.
Select any two segments and run the script. You will get a collection of random length toothpicks within the parallelogram defined by the segments.
With a simple script, you can model the motion of a ball in a uniform gravitational field. With a bit more work, you can find the focus and directrix of the resulting parabola. Finally, you can animate a ball along the path. This sketch could present some very good challenges for advanced students!
These two sketches illustrate a problem posed by Wittgenstein.
A stick passes through a sleeve (in which it can smoothly slide). The sleeve is nailed to the wall. As one endpoint of the stick describes a circle, what does the other endpoint describe?
Be sure and look at Witt Engine before Witt Path.
Here is a straightforward demonstration of the problem.
In this sketch the path is shown dynamically as you vary the parameters.