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Paper folding activity

Show the students this model of Eratosthenes' problem.

Eratosthenes needs to know what the central angle of
the earth is when there is a shadow at Alexandria (and a sun angle) and
no shadow at Syene (sun angle is 0). Eratosthenes can measure the sun angle
at Alexandria, but how does he find the central angle? It's time to discover
Eratosthenes' insight. You are going to make a paper model of this situation.

Take a piece of paper and make a fold lengthwise (to reduce
the width of the paper.) Carefully tear off that strip. Every student should
have a sheet of paper with a different width.

Draw a diagonal line on your paper. Label the angles
C and SA.

Cut the paper along the diagnal so that you have two pieces.
Now compare angle SA with Angle C by placing one angle on top of the other.

What do you notice? (They are equal.)

Is that true for others in the class? Since every student
had a different width paper (after they cut off the original strip), every
student should have had different size angles SA and C. What can we conclude
about the sun angle and the central angle when there is no shadow at Syene?
(They are equal and it doesn't matter what the angle is.) Confirm the result
with this Javasketchpad
sketch. (Be patient. It takes a while to load. Drag Syene to change
the angles. You should notice that angle SA (sun angle at Alexandria) and
C (central angle) are always equal.

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