Islamic Scientific Heritage@IslamicSH_
✨In the 11th century, the famous Muslim polymath Al-Biruni figured out the Earth's radius using nothing more than a mountain and a bit of trigonometry. 📐
The insight was brilliant:
Stand on a mountain, and the horizon dips below the horizontal. That dip isn't an optical illusion; it's a geometric signal. It creates a right triangle where the mountain's height (h) and the Earth's radius (R) are the only variables.
Measuring the mountain's height without climbing down:
He used a simple trigonometric trick: from two points on the plain, he measured the angle to the peak. Knowing the distance between those points, he calculated the mountain's height with a formula surveyors still use today:
H = D / (cot A1 – cot A2)
From the peak, he measured the dip angle to the horizon: α = 34′ (just over half a degree):
R = h * cos(α) / (1 - cos(α))
How did he compute the cosine of such a tiny angle?
Without modern calculators, he used a sophisticated technique: he started with the known value of cos(60°) and used the half-angle formula to work his way down to the required value for his 34′ angle.
He calculated the Earth's radius as 6,340 km. The modern value is 6,371 km.
An error of less than 1%. In 1030 CE.
