Eratosthenes'
most amazing
discovery:
the "sun" angle is the same as the central angle!!!
One day while in his library in
Alexandria
Eratosthenes read that in the frontier outpost town of Syene at noon on
June 21st, vertical sticks cast no shadow while a reflection of the sun
could be seen at the bottom of the well. Being the scientist that he
was,
he wanted to know if the same thing happened in Alexandria. He
discovered
that there were shadows there.
Java Sketchpad
version
But how does knowing this help in
measuring
the central angle? Eratosthenes used a little geometry to come up with
his insight. This discovery makes possible the use of the measure of
the
central angle (along with the distance between the two towns) to
determine
the circumference of the earth.
Eratosthenes knew that the sun
was far
enough away so that its rays are parallel. In the diagram above note
that
there is no shadow at Syene while there is a shadow in Alexandria. Then
he realized the sun angle had to equal the central angle. See the
Paper
Folding Activity.
But what
happens if
there IS a shadow at both sites? Below is a model (created with the
Geometer's
Sketchpad) of the problem. Notice that neither sun angle A at
Alexandria
nor angle S at Syene equals the central angle.
activity
sheet.
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