Experiment in Hyperbolic Geometry
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You may either download NonEuclid.zip or run the appet "NonEuclid". Do the following.
In the Poincaré model, follow Euclid's proof of proposition 1 to construct an equilateral triangle ABC.
Draw line segment AB
Draw circle with center A and radius AB
Draw circle with center B and radius BA
Construct the points of intersection C, D
Draw line segments, AC, BC
Measure triangle ABC
Move points A and B around the space and answer the following questions:
Are the sides of your triangle always equal?
Are the angles of your triangle always equal?
What is the largest angle sum possible? What does the triangle look like when you get close to this sum?
What is the smallest angle sum possible? What does the triangle look like when you get close to this sum?
Change to the half plane model of hyperbolic geometry and repeat steps 1, 2, 3.
Last Update: October 4, 2006
Ronald K. Smith
Lamoni, IA 50140