![]() Cavalieri first used polar coordinates to solve a problem relating to the area within an Archimedean spiral. Saint-Vincent wrote about them privately in 1625 and published his work in 1647, while Cavalieri published his in 1635 with a corrected version appearing in 1653. Grégoire de Saint-Vincent and Bonaventura Cavalieri independently introduced the concepts in the mid-seventeenth century. The full history of the subject is described in Harvard professor Julian Lowell Coolidge's Origin of Polar Coordinates. There are various accounts of the introduction of polar coordinates as part of a formal coordinate system. Around 1025 CE, he was the first to describe a polar equi- azimuthal equidistant projection of the celestial sphere. ![]() The Persian geographer, Abū Rayhĝn Bīrūnī (973-1048), developed ideas which are seen as an anticipation of the polar coordinate system. In the 9th century CE, the Persian mathematician, Habash al-Hasib al-Marwazi, employed spherical trigonometry and map projection methods in order to convert polar coordinates to a different coordinate system centred on a specific point on the sphere, in this the Qibla, the direction to Mecca. ![]() The Greek work, however, did not extend to a full coordinate system. In On Spirals, Archimedes describes the Archimedean spiral, a function whose radius depends on the angle. The astronomer Hipparchus (190-120 BCE) created a table of chord functions giving the length of the chord for each angle, and there are references to his using polar coordinates in establishing stellar positions. The concepts of angle and radius were already used by ancient peoples of the 1st millennium BCE. See also: History of trigonometric functions ![]()
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