How Al-Biruni Calculated the Circumference of the Earth Using a Mountain in the 11th Century
Can we know the shape of the Earth? or How Al-Biruni Calculated the Circumference of the Earth Using a Mountain in the 11th century As you might recall from my earlier posts, I've used the Sun at local Solar Noon (when the Sun is at its zenith) on the Equinox as a way to know the shape of the Earth. But all we need is some point that is high enough to be seen at some significant distance and Mountain peaks are much easier to experiment with than a moving Sun. If the ground is a flat plane then we can simply triangulate using the mountain peak at different distances and get the SAME answer for the height using simple trigonometry: Figure 1 For example, if the ground was flat , we could find h by simply measuring our angle α at two different distances, where Δ d is the distance between the two observation points using the formula: Δd * tan(α₀) * tan(α₁) h = ---------------------- tan(α₁) - tan(α₀) Can you prove that? This ...