Abu Abdullah Muhammad ibn Musa Al-Khwarizmi, a Persian scholar, mathematician, astronomer father of algebra, algorithms and trigonometry.
Al-Khwarizmi c. 813–833 CE in his 'Compendious book on calculation by completion, balancing showed how to solve linear and quadratic equations by completing the square, reduction" and "balancing, transposing terms to the other side of an equation and cancelling them.
He has been described as the father of algebra, the word al-jabr meaning "completion" or "rejoining").
His book, the Compendious Book on Calculation by Completion and Balancing, translated into Latin by Robert of Chester in 1145, was the major textbook used by European universities until the sixteenth century.
Latin translations of his 'Algorithmo de Numero Indorum' introduced Indian numerals and decimals to the Western world in the 12th century.
Al Khwarizmi advanced further the work of Brahmagupta, the great Indian mathematician, and gave us what rules the world today, algorithms. Latinization of his name gave rise to the terms algorism and algorithm, a term used universally, but of whose origin few are aware today.
He corrected the latitudes, longitudes of many cities given by Ptolemy. He also wrote about the astrolabe and sundials.
He also made a significant, seminal contribution to trigonometry by producing accurate sine and cosine tables, and the first table of tangents.
He measured the distance from Palmyra to Raqqa in Syria, thereby calculating the Earth's circumference to be within 5-15% of the value we know today.
The first person to measure the Earth's circumference was the Indian mathematician, Aryabhata in his treatise Aryabhatiya in 525 A.D. He measured it to be 1050 Indian yojana units, 24,835 miles, correct to within 0.2%, . Aryabhata also calculated a value for pi that equates to 3.1416, gave us the zero and an understanding of eclipses.
Nevertheless the Eastern stalwarts were aware by the use of their primitive instruments that the Earth was spherical, it revolved around the Sun centuries before Galileo was imprisoned by the Catholic inquisition in 1633 for promulgating their heliocentric model of the universe .
Astronomical, astrological studies of Naseredin Tusi
Muhammad ibn Muhammad ibn al-Hasan al-Tūsī / Nasir al-Din al-Tusi
( 18 February 1201 – 26 June 1274)was born in the city of Tus, Khorasan (northeastern Iran) in the year 1201. He commenced his studies at Hamadan/Ecbatan and Tus . Then he relocated to Nishapur to study philosophy under Farid al-Din Damad and mathematics from Mohammed Hasib.
Nasir al-Din al-Tusi researched and wrote on subjects of math, engineering, prose, and mysticism.
He had persuaded the Mongol king of Iran, Halagu Khan to let him build a Rasadkhunay/Observatory at Maraghay in East Azerbaijan, cleverly informing the king that his astrological calculations would further Mongol military victories.
He drew the planetary positions, movements using Maraghey as the meridean, improving on Ptolemey's charts..
He was the creator of trigonometry as a separate mathematical discipline. He devised formulas for the spherical right angled triangles, binomial co-efficients, that Blaise Pascal later worked with.
He devised the Tusi couple, a term coined by Edward Kennedy. He demonstrated, when a smaller circle rotates inside a larger circle of twice it's diameter, a point on the circumference of the smaller circle apparently moves back and forth in a straight line along a diameter of the larger circle.
His work replaced Ptolemy's geocentricism, i.e the Earth is the center around which the Sun, planets revolve with Heliocentrism, i.e the Sun is in the center and the Earth revolves around it.
These were translated by Byzantine workers and made their way to the hands of Nicolaus Copernicus. Copernicus' De revolutionbus, Mercury model and theory of trepidation are thus extensions of the original work of Naseredin Tusi.