Abu Rayhan Al-Biruni (973-1048), a polymath scholar from the Khwarezm region (present-day Uzbekistan), is one of the greatest scientific minds in history. He notably developed an ingenious method to measure the Earth's radius, without leaving the ground, with remarkable precision for his time.
Al-Biruni's measurement method
Around 1020, during a stay in the Indus valley (present-day Pakistan), Al-Biruni devised an elegant geometric method to determine the Earth's radius. He first measured the height of a mountain using two observation points and trigonometry. Then, from the summit, he measured the horizon dip angle (the angle between the horizontal line and the line of sight toward the visible horizon).
Knowing the mountain height (h) and the dip angle (θ), he applied the geometric relation linking these quantities to the Earth's radius (R): R = h × cos(θ) / (1 - cos(θ)). This formula follows directly from the geometry of a circle and its tangent.
Al-Biruni obtained a value of about 6,339.6 km for the Earth's radius, remarkably close to the modern average value of 6,371 km (an error of less than 0.5%). This measurement is all the more impressive as it was achieved without modern optical instruments, using only astrolabes and trigonometric calculations.
The comparison with Eratosthenes
Nearly thirteen centuries earlier, the Greek Eratosthenes (c. 276-194 BC) had estimated the Earth's circumference by comparing the sun's shadow at Syene (Aswan) and Alexandria. His method, based on measuring an arc of a meridian, had given a remarkably accurate value. Al-Biruni's method is different: it does not require traveling a long distance nor comparing simultaneous observations in two places. It relies solely on the local measurement of a mountain and the horizon angle, making it simpler to implement and independent of distance errors between two cities.
These two complementary approaches illustrate the maturity of ancient and medieval geodesy, and confirm that the sphericity and dimensions of the Earth were established and scientifically measured knowledge well before the modern era.
The convergence with the Quran
The Quran contains verses that, read attentively, evoke the shape of the Earth. Verse 30 of Surah An-Naziat is often cited in this regard:
"And the earth, moreover, hath He extended [dahaha]." (79:30)
The Arabic verb dahaha (دحا) gave rise to the noun dahya (دحية), which designates the ostrich egg. Some Muslim scholars and modern commentators see in it an allusion to the geoid shape of the Earth, slightly flattened at the poles, comparable to an egg. Honesty requires noting, however, that the dominant classical exegesis understands dahaha as "to spread out, flatten, make habitable," and the "egg-shaped" interpretation is debated and a minority view. The convergence must therefore be presented with caution.
Another verse, in Surah Az-Zumar, offers an interesting linguistic support. It uses the verb kawwara (يكوّر), which literally means "to wrap, to wind like a turban":
"He created the heavens and the earth in truth. He wraps the night over the day and wraps the day over the night." (39:5)
The choice of the verb kawwara — the same used for winding a turban around the head — suggests a circular wrapping of the night around the day, consistent with a spherical terrestrial surface. Here again, classical exegesis reads in this verse above all the regular alternation of day and night; the sphericity argument rests on the semantic value of the verb rather than on the primary meaning retained by commentators. It should therefore be presented as a possible reading, not as an exegetical certainty.
The value of Al-Biruni's example lies above all in demonstrating that Islamic civilization produced, as early as the 11th century, rigorous geometric science that measured the sphericity of the Earth — a knowledge the Quran evokes suggestively, without describing it explicitly in a single unambiguous verse.