Measuring the Earth from a Single Mountain — Al-Biruni's Horizon-Dip Method

Eratosthenes measured the Earth using two cities a known distance apart. Around 1020 AD the Persian scholar Al-Biruni did it from one mountain. He knew that from a height the horizon dips slightly below true level, and that the line of sight to the horizon just grazes the curved Earth. Measure the mountain's height and that tiny dip angle, and trigonometry gives the Earth's radius — no long survey across deserts required. His answer came within about one percent of the modern value. This blueprint reproduces his elegant single-site method.