The closest and nearest call of the circumference of the planet earth to what were determined contemporarily was made by Abu Rayhan Biruni (973-1048) after Eratosthenes( 300 B.C.) close estimates depending on what 'stadia' he was referring too Egyptian or Greek; Abu Rayhan Biruni studied closely the work of famous Indian mathematician named Aryabhata who lived around 500 A,D. Al- Biruni actually calculated the Earth's circumference in a small town on a mountain top of Pind Dadan Khan, District Jhelum, Punjab, presently Pakistan. His method was different from Eratosthenes.
Early Greek philosophers alluded to a spherical Earth, Pythagoras (6th century BC) allegedly originated the idea, but Plato (427–347 BC) did travelled to southern Italy to study Pythagorean mathematics, on returned to Athens he established his school, and taught his students that Earth was a sphere though he offered no justifications. "My conviction is that the earth is a round body in the centre of the heavens, and therefore has no need of air or of any similar force to be a support".
The Alexandrian philosopher Eratosthenes, the famous man who headed the royal library in Alexandria, the greatest and most famous library in history called "temple of the muses" or "museion," from which our modern "museum" is derived. Eratosthenes actually estimated how large the Earth was.
He was told that on midsummer day (June 21) in the town of Syene in southern Egypt (today Aswan, near a huge dam on the river Nile) the noontime Sun was reflected in a deep well, meaning that it was right overhead, at zenith. Eratosthenes himself lived in Alexandria, near the river's mouth, north of Syene, about 5000 stadia north of Syene (the stadium, the size of a sports arena, was a unit of distance used by the Greeks). In Alexandria the Sun on the corresponding date did not quite reach zenith, and vertical objects still threw a short shadow. Eratosthenes established that the direction of the noon Sun differed from the zenith by an angle that was 1/50 of the circle, that is, 7. 2 degrees, and from that he estimated the circumference of the Earth to be 250,000 stadia.
Aristotle (384–322 BC) observed "there are stars seen in Egypt and Cyprus which are not seen in the northerly regions." Earth was a sphere "of no great size, for otherwise the effect of so slight a change of place would not be quickly apparent." (De caelo, 298a2–10). Aristotle provided physical and observational arguments supporting the idea of a spherical Earth in his treatise 'De caelo.'
It has been suggested that seafarers probably provided the first observational evidence that the Earth was not flat, based on observations of the horizon. This argument was put forward by the geographer Strabo (c. 64 BC – 24 AD), who suggested that the spherical shape of the Earth was probably known to seafarers around the Mediterranean Sea since at least the time of Homer, he cited a line from the Odyssey indicating that the poet Homer was already aware of this as early as the 7th or 8th century BC. Strabo cited various phenomena observed at sea as suggesting that the Earth was spherical. He observed that elevated lights or areas of land were visible to sailors at greater distances than those less elevated, and stated that the curvature of the sea was obviously responsible for this.
If you stand on the seashore and watch a ship sailing away, it will gradually disappear from view. But the reason cannot be the distance: if a hill or tower are nearby, and you climb to the top after the ship has completely disappeared, it becomes visible again. Furthermore, if on the shore you watch carefully the way the ship disappears from view, you will notice that the hull vanishes first, while the masts and sails (or the bridge and smokestack) disappear last. It is as if the ship was dropping behind a hill, which in a way is exactly the case, the "hill" being the curve of the Earth's surface.
Claudius Ptolemy (90–168 AD) from Alexandria advanced many arguments for the sphericity of the Earth. Among them was the observation that when sailing towards mountains, they seem to rise from the sea, indicating that they were hidden by the curved surface of the sea. The Greek concept of a spherical earth surrounded by the spheres of planets vehemently supported the works of the classical Indian astronomer and mathematician.
Aryabhatiya (476-550 AD) dealt with the sphericity of the Earth and the motion of the planets. It is unlike a practical manual or a basic set of theoretical proofs like Euclid's Elements. Aryabhatiya is written in verses like all typical Sanskrit works - Aryabhatiya gives fairly basic construction definitions such as "the circle is made by turning..." with the use of a compass implicit. He mentions proportions of triangles with respect to shadows. This could have been applied to the use of shadows on sundials and to find the angle the Earth makes with the sun.
This is how he probably estimated the circumference of the Earth. The final two parts of his Sanskrit magnum opus, the Aryabhatiya, which were named the Kalakriya ("reckoning of time") and the Gola ("sphere"), state that the Earth is spherical and that its circumference is 4,967 yojanas, which in modern units is 39,968 km (24,835 mi), close to the value already calculated by Eratosthenes in the 3rd century BC as well as the current equatorial value of 40,075 km (24,901 mi). I think Aryabhatiya greatly influenced Al-Biruni later work.
Bishop Isidore of Seville (560–636) taught in his widely read encyclopaedia, the Etymologies, that the Earth was round.
The Babylonians, Greeks, and Indians all developed elaborate systems of mathematical astronomical study, the pre-Islamic Arabs relied entirely on empirical observations. These observations were based on the rising and setting of particular stars, and this area of astronomical study was known as Anwa. Anwa continued to be developed after Islamization by the Arabs, where Islamic astronomers added mathematical methods to their empirical observations.
According to David King, after the rise of Islam, the religious obligation to determine the qibla and prayer times inspired more progress in astronomy for centuries. Islamic Astronomy into distinct time periods in its assimilation with earlier Hellenistic, Indian, and Sassanid astronomy. The first major Muslim work of astronomy was Zij al-Sindh by al-Khwarizmi in 830. The work contains tables for the movements of the sun, the moon and the five planets known at the time.
This work also marks the turning point in Islamic astronomy. Muslim astronomers had adopted a primarily research approach to the field, translating works of others and learning already discovered knowledge. Al-Khwarizmi's work marked the beginning of nontraditional methods of study and calculations. Muslim scholars who held to the round Earth theory used it for a quintessentially Islamic purpose: to calculate the distance and direction from any given point on the Earth to Mecca.
This determined the Qibla, or Muslim direction of prayer. Caliph Al-Ma'mun in 830 AD commissioned a group of astronomers and geographers to measure the distance from Tadmur to al-Raqqah, in modern Syria. They found the cities to be separated by one degree of latitude and the meridian arc distance between them to be 662⁄3 miles and thus calculated the Earth's circumference to be 24,000 miles.
Alfraganus a Persian astronomer of the 9th century was involved in measuring the diameter of the Earth, he was commissioned by Al-Ma'mun. His estimate given above for a degree (562⁄3 Arabic miles) was much more accurate than the 602⁄3 Roman miles (89.7 km) given by Ptolemy. Christopher Columbus uncritically used Alfraganus's figure as if it were in Roman miles instead of in Arabic miles, in order to prove a smaller size of the Earth than that propounded by Ptolemy. Persian historian al-Biruni studied closely famous Indian mathematicians named Aryabhata who lived around 500 C.E.
Al- Biruni calculated the Earth's circumference at a small town of Pind Dadan Khan, District Jhelum, Punjab, now in Pakistan. Biruni's method was intended to avoid "walking across hot, dusty deserts" for Hajj and the idea came to him when he was on top of a tall mountain in India. From the top of the mountain, he sighted the angle to the horizon which, along with the mountain's height (which he calculated beforehand), allowed him to calculate the curvature of the Earth.He also made use of algebra to formulate trigonometric equations and used the astrolabe to measure angles.
Biruni's Method for calculation of Earth's radius:
Abu Rayhan Biruni (973-1048) used a new method to accurately compute the Earth's circumference, by which he arrived at a value that was close to modern values for 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. 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.
John J. O'Connor and Edmund F. Robertson write in the MacTutor History of Mathematics archive:
"Important contributions to geodesy and geography were also made by Biruni. He introduced techniques to measure the earth and distances on it using triangulation. He found the radius of the earth to be 6339.6 km, a value not obtained in the West until the 16th century. His Masudic canon contains a table giving the coordinates of six hundred places, almost all of which he had direct knowledge."
A terrestrial globe (Kura-i-ard) was among the presents sent by the Persian Muslim astronomer Jamal-al-Din to Kubla Khan in 1267. It was made of wood on which "seven parts of water are represented in green, three parts of land in white, with rivers, lakes etc."Ho Peng Yoke remarks that "it did not seem to have any general appeal to the Chinese in those days".