Reproducing Eratosthenes' Determination of Earth's Circumference on a Smaller Scale
The balloon was situated on a stool to sit in a stable position and to allow for repositioning so that the center dart cast no shadow, and the shadows of the north and south darts lie along the meridian.
The balloon was positioned so that the center dart casts no shadow and the north and south darts cast shadows that lie along the meridian.
When properly positioned, the rays of light from the Sun are parallel to the center dart. Note the congruence between the shadow angles, and and the respective latitude angles, and .
The measurements of the distances of north and south darts from the center dart and , the darts' shadow lengths and , and the darts' lengths and were necessary in order to find the polar circumference C of the balloon.
This table shows the polar circumferences C obtained using the shadow lengths of the north and south darts (first two columns) and using a cloth measuring tape (third column). Agreement between north/south dart shadow-based circumference measurements and measuring tape-based circumference measurements were within 5% margin of error.
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