Determining the Earth’s Circumference
Eratosthenes – He was a geographer/mathematician that lived around 200 B.C.
He made the first measurement of the distance around the earth longitudinally using
geometry
In doing this he made two assumptions:
1. The earth is spherical (round ball shape)
2. The suns rays that strike the earth are parallel to each other
He noticed that on one day of the year a well in Syene did not have a shadow at noon (90
degrees to the earth) but at the same time a tower in Alexandria did cast a shadow
We will call the angle cast by the
tower angle (a).
The entire distance around the earth is the circumference (C) and the distance between
the well and the tower is fraction of that distance (c).
The angle created on the inside of the earth (a’). This angle is a fraction of 360 degrees
(the degrees in a circle such as earth). This angle is equal to angle a through concept of
alternate interior angles (the two interior angles created by parallel lines are equal).
With this information the following equation can be created
C (circumference of the earth)
_______________________
c (distance from Alexandria to Syene)
360 degrees (degrees in a circle)
=
__________________________
a (angle by tower in Alexandria)