abu rayhan biruni (976–1048) first described a polar equi-azimuthal equidistant projection of the celestial sphere. he was regarded as the most skilled when it came to mapping cities and measuring the distances between them, which he did for many cities in the middle east and the indian subcontinent. he often combined astronomical readings and mathematical equations, in order to develop methods of pin-pointing locations by recording degrees of latitude and longitude. he also developed similar techniques when it came to measuring the heights of mountains, depths of the valleys, and expanse of the horizon. he also discussed human geography and the planetary habitability of the earth. he also calculated the latitude of kath, khwarezm, using the maximum altitude of the sun, and solved a complex geodesic equation in order to accurately compute the earth's circumference, which was close to modern values of the earth's circumference. his estimate of 6,339.9 km for the earth radius was only 16.8 km less than the modern value of 6,356.7 km. in contrast to his predecessors, who measured the earth's circumference by sighting the sun simultaneously from two different locations, al-biruni developed a new method of using trigonometric calculations, based on the angle between a plain and mountain top, which yielded more accurate measurements of the earth's circumference, and made it possible for it to be measured by a single person from a single location.