Microworld
Title Page:
Surfaces of Revolution
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Microworld:
Surfaces
of Revolution: (All in One)
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to visit the Microworld.
Author:
James
White
This
Microworld, inspired by a suggestion of Mathwright author Kwok-Wai Mok, is
designed to illustrate how our new OpenGL based 3D Graphics Objects may be
used to support visualization. For Mathwright authors, it provides a few examples
that may guide them in the construction of their own dynamic 3D Microworlds.
And for students, there are some utilities that they can use to visualize
a few interesting constructions in geometry. The four page Microworld contains
the following 2 explorations:
In
Revolution of Graphs, you may define and graph a function, f(x) of
a single variable. You define the function, choose the domain and draw the
space graph using the Control Panel:
Next,
you may select a start angle (degrees) and an end angle through which to rotate
the graph. The surface that is "swept out" is drawn in yellow, and
the beginning graph is drawn in green, and the end graph is drawn in red.
Use the Control panel below for that.
You
will see a color-coded "volume of revolution" swept out that you
can rotate or fly through using the Navigation Instructions below the Portal.
See the picture at the top of this page.
Next,
in Revolution of Curves, you may define and graph a curve in the XY
plane, c(t) with variable t. You define the curve, choose its domain and draw
the space curve using the Control Panel:
Next,
you may select a start angle (degrees) and an end angle through which to rotate
the curve. The surface that is "swept out" is drawn in yellow, and
the beginning curve is drawn in green, and the end curve is drawn in red.
Use the Control panel below for that.
Author: James E. White (based on a suggestion of Kwok-Wai Mok)
Author Email:mathwrig@gte.net
Topics: space graphs and curves, sweeping out surfaces of revolution, simulations with 3D models
Suggested Use: Visualization of surfaces of revolution
Number of Pages: 4
Animation:Yes
Grade Level:13-16
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| - James E. White, Ph.D. , Library Director, | ||
| author of this website, Mathwright 2000, MindScapes, | ||
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