8C20.35 - Non-Euclidean Geometry

Code Number:
Demo Title:
Non-Euclidean Geometry
Geometry of Curved Surfaces
Area of Study:
Astronomy and Mathematics
One Large Grapefruit, Glass Tray, Knife, Scissors, Inner Tube, Small Black Chalk Globe, Three Strings (Already Cut to Length), Pulley Measuring Tool, Chalkboard Compass (Pencil with String and Chalk Attached), Compass Standard (Flat Cardboard with Circle Drawn on it to Set the Compass to the Proper Diameter), Note Card with Calculated Values, and Lab Coat.

In the first part of this experiment take the compass and set it to the proper diameter using the compass standard.  Now take a piece of string and place it on the circle drawn on the standard and cut it so that the ends meet.  This string when measured with the pulley measuring tool should be 5 and 3/16 revolutions long.  Now use the compass on the chalk globe to mark a circle, and then cut a string to fit this circle.  Even though made with the same diameter compass this string should only measure 4 and 12/16 revolutions long.  Now do the same procedure on the piece of inner tube cut from the inside radius of the tube.  This string should only measure 4 and 5/16 revolutions long.  This demonstrates that even though drawn with the same compass radius the total circumference distance will be different depending on whether the surface is flat or spherical, and whether the spherical surface is an inner or outer radius.  Take the inner tube piece and one/half of the grapefruit and try to flatten them.  This shows that a spherical surface cannot be flattened unless the object is torn or stretched in some manner.

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