Microworld: Spherical
Logo : (All-in-One)
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the Hyperlink above to visit the Microworld.
Author:
James
White
Logo
has long been a favorite way of introducing students to computational Geometry
and Logic. The turtle lives in a Euclidean plane and knows three things: It
has a position, a direction, and a pen state. The pen may be up or down, and
it has a color. If it is down, then when the turtle moves, it leaves a path
drawn in the present color of the pen.
Logo
programs typically instruct the turtle to move in its current direction, or
to turn to a new direction. Like MathScript scripts, they are designed step-by-step,
and work collaboratively to bring about surprising effects.
Well,
the Turtle in this microworld discovered, like Einstein, that the world is
not necessarily flat. Her name is Terra, and she became interested in the
question: "If my world is round, then how will my Geometry be different?"
She has learned a great many things, and is eager to show them to you.
Terra
lives in a 2-dimensional world known (to mathematicians) as a "two sphere."
In her world, straight lines are "great circles" (like lines of
longitude, or the equator -- but not like other lines of latitude). These
are known to Terra and to the mathematicians, as "geodesics." But
she has learned that, surprisingly, there are no pairs of parallel lines in
her world. All pairs of lines meet in two points, or they coincide. And she
has discovered that the sum of angles in a triangle is not, as she imagined,
180 degrees, but is larger than that by an amount that depends somehow (She
hasn't figured it out yet.) on the area of the triangle!
Return to the listing of MathwrightWeb Microworlds
| - James E. White, Ph.D. , Library Director, | ||
| author of this website, Mathwright 2000, MindScapes, | ||
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