The calculations of Muslim astronomers were so accurate that in the 9th century they reckoned the Earth's circumference to be 40,253.4km - less than 200km out. The scholar al-Idrisi took a globe depicting the world to the court of King Roger of Sicily in 1139.

The system of numbering in use all round the world is probably Indian in origin but the style of the numerals is Arabic and first appears in print in the work of the Muslim mathematicians al-Khwarizmi and al-Kindi around 825. Algebra was named after al-Khwarizmi's book, Al-Jabr wa-al-Muqabilah, much of whose contents are still in use. The work of Muslim maths scholars was imported into Europe 300 years later by the Italian mathematician Fibonacci. Algorithms and much of the theory of trigonometry came from the Muslim world. And Al-Kindi's discovery of frequency analysis rendered all the codes of the ancient world soluble and created the basis of modern cryptology.

In 850, al-Farghani wrote Kitab fi Jawani (meaning "A compendium of the science of stars"). The book primarily gave a summary of Ptolemic cosmography. However, it also corrected Ptolemy based on findings of earlier Arab astronomers. Al-Farghani gave revised values for the obliquity of the ecliptic, the precessional movement of the apogees of the sun and the moon, and the circumference of the earth. The book was widely circulated through the Muslim world, and even translated into Latin.[17]
An illustration from al-Biruni's astronomical works, explains the different phases of the moon.

The period when a distinctive Islamic system of astronomy flourished. The period began as the Muslim astronomers began questioning the framework of the Ptolemaic system of astronomy. These criticisms, however, remained within the geocentric framework and followed Ptolemy's astronomical paradigm; one historian described their work as "a reformist project intended to consolidate Ptolemaic astronomy by bringing it into line with its own principles."[18]

Between 1025 and 1028, Ibn al-Haytham wrote his Al-Shukuk ala Batlamyus (meaning "Doubts on Ptolemy"). While maintaining the physical reality of the geocentric model, he criticized elements of the Ptolemic models. Many astronomers took up the challenge posed in this work, namely to develop alternate models that resolved these difficulties. In 1070, Abu Ubayd al-Juzjani published the Tarik al-Aflak. In his work, he indicated the so-called "equant" problem of the Ptolemic model. Al-Juzjani even proposed a solution for the problem. In Al-Andalus, the anonymous work al-Istidrak ala Batlamyus (meaning "Recapitulation regarding Ptolemy"), included a list of objections to the Ptolemic astronomy.

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