The Geometer’s Sketchpad
®
for TI-89, TI-92 Plus, and
© 2000-2002 KCP Technologies, Inc.
80
Voyage™ 200 PLT User Guide and Reference Manual
Tips and Techniques
4
Once you understand how Sketchpad works and what you can do
with it, there are a variety of techniques you can use to work more
efficiently. This chapter describes many of those techniques.
A family of oscillating spirals. This sketch shows the family of
curves
θ
= 80r + 25 sin 400r + k, where
θ
is interpreted in
degrees. The graph of
θ
= 80r is a simple spiral, and adding
25 sin 400r to the right side causes the spiral to oscillate as it
moves away from the origin. Adding the varying parameter k
rotates the entire oscillating spiral about the origin. In this
sketch, k is the angle formed by a point on a circle, the circle’s
center, and a second point on the circle. Tracing the function
plot as one of the points on the circle animates around the circle
graphs a family of curves related by rotation.
Dilating a polar graph. This sketch is based
on the graph of r = sin 6
θ
+ 2, with
θ
interpreted in radians. Dilating a point on this
graph away from the origin, and then
connecting it to its dilated image with a
segment, creates one spoke of the inner
“flower.” Dilating this segment away from the
origin creates a second collinear spoke (on
the outer flower). The locus of the spokes
and their endpoints, as the original point
travels along the curve, completes the
figure. For complicated graphs like these,
Sketchpad requires a high number of plot
samples and ample time to calculate the
graph.