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Geography and geodesy

Bīrūnī devised a novel method of determining the Earth's radius by means of the observation of the height of a mountain. He carried it out at Nandana in Pind Dadan Khan (present-day Pakistan). He used trigonometry to calculate the radius of the Earth using measurements of the height of a hill and measurement of the dip in the horizon from the top of that hill. His calculated radius for the Earth of 3928.77 miles was 2% higher than the actual mean radius of 3847.80 miles. His estimate was given as 12,803,337 cubits, so the accuracy of his estimate compared to the modern value depends on what conversion is used for cubits. The exact length of a cubit is not clear; with an 18-inch cubit his estimate would be 3,600 miles, whereas with a 22-inch cubit his estimate would be 4,200 miles. One significant problem with this approach is that Al-Biruni was not aware of atmospheric refraction and made no allowance for it. He used a dip angle of 34 arc minutes in his calculations, but refraction can typically alter the measured dip angle by about 1/6, making his calculation only accurate to within about 20% of the true value.

In his Codex Masudicus (1037), Al-Biruni theorized the existence of a landmass along the vast ocean between Asia and Europe, or what is today known as the Americas. He argued for its existence on the basis of his accurate estimations of the Earth's circumference and Afro-Eurasia 's size, which he found spanned only two-fifths of the Earth's circumference, reasoning that the geological processes that gave rise to Eurasia must surely have given rise to lands in the vast ocean between Asia and Europe. He also theorized that at least some of the unknown landmass would lie within the known latitudes which humans could inhabit, and therefore would be inhabited.