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Kenneth Cole
15 March 1998
Eratosthenes didn't have the luxury of knowing about the Equinox and the Equator, but we do. At the Equinox, both Vernal and Fall, the Sun is directly above the Equator. Since the Sun is so far away, 93 million miles, the rays from the Sun follow virtually a direct path to the Earth. Since the rays at the top of the globe and at the bottom of the globe follow a direct path, we can use what we know about parallel lines cut by a transversal to find the central angle of the Earth by measuring the Noon shadow at the Equinox. Look at the sketch below. What term do we use for the Sun's noon angle at Equinox and the central angle of the Earth?
There are more details about the geometric applications of measuring the noon shadow posted on the Web by Maryland Virtual High School.
Noon Shadow Project
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