Circles and PiEratosthenes

Here you can see the well in Swenet as well as the obelisk in Alexandria. The sun rays fall directly into the well, but hit the obelisk at an angle and cast a shadow.

Eratosthenes measured that the angle of the shadow was 7.2°. This is the same as the central angle of the arc from Alexandria to Swenet, because they are angles.

Now we can use the equation for arc length that we derived above:

arc lengthcircumference=°360°

If we rearrange this, we find that the circumference of the Earth is

circumference=360°7.2°×800 km=km

Finally, we know that the circumference of a circle is C=2πr, so the radius of Earth is

rEarth=40000km2π≈6400km.

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Circles and PiEratosthenes