Making a "Spherical Straight Edge"

During the course of Dr. Polking's classes, it became necessary to construct a device that generated great circles on the sphere. This is a set of directions on the materials, methods for construction and use of such a device. Since a great circle is the spherical equivalent of a line in a plane, the device will be called a straight edge.

Materials

To create a straight edge for a sphere, you will need the following items:

String long enough to encompass the sphere
A brand new pencil
An overhead marker
Rubber bands large enough to encompass the sphere
Scissors

Constructing the Ruler

The first task is to create a length of string 1/4th the distance of a great circle. Unfortunately, the best way to do this is by trial and error:

Wrap a long piece of string around the sphere at the best estimate of a great circle.
Mark the string where it begins to overlap.
Repeat above until the longest length has been obtained.
Fold the string in half and half again and mark it at 1/4, 1/2 and 3/4.
Cut the string at least two inches past the 1/4 mark.

The second task is to construct the straight edge using the string and new pencil. (A new pencil is desirable because the flat eraser will help to keep it from slipping on the sphere.)

Carefully tie the two inches of extra string tightly around the metal end of the new pencil so that the mark on the string is just hidden by the knot.
Check to be sure the distance from the center of the pencil to the 1/4 mark on the string is correct using the left over piece that was marked at 3/4 and 1.
Repeat above until the desired accuracy is obtained.

Using the Straight Edge

To draw a great circle on the sphere, you will need the straight edge, rubber bands and overhead markers. Overhead markers are desirable because they will wash from the sphere easily with water and a rag.

Make a point on the sphere that will serve as the center of the great circle.
Place the eraser of the pencil on this point.
Move the string around the sphere marking the 1/4th distance in six to eight points
Remove the eraser and renew the center point if necessary
Place a rubber band around the sphere so that it rests on the six to eight points
Use the rubber band as the great circle or trace next to it.
Label the center and line so it is obvious they go together.

Note: You may find it easier to use the rubberband as the great circle rather than attempting to trace it.

Created by Boyd E. Hemphill with the help of Karen Flanagan

Return to the discussion of area on the sphere.

Table of Contents.

url: http://math.rice.edu/~pcmi

John C. Polking <polking@rice.edu>

Last modified: Mon May 04 13:14:32 Central Daylight Time 1998

	Return to the discussion of area on the sphere.
	Table of Contents.