Polar coordinate system
In mathematics, the polar coordinate system is a two-dimensional coordinate system in which each point on a plane is determined by a distance from a reference point and an angle. Grégoire de Saint-Vincent and Bonaventura Cavalieri independently introduced the concepts in the mid-17th century. The actual term polar coordinates has been attributed to Gregorio Fontana and was used by 18th-century Italian writers.
About Polar coordinate system in brief
In mathematics, the polar coordinate system is a two-dimensional coordinate system in which each point on a plane is determined by a distance from a reference point and an angle. Grégoire de Saint-Vincent and Bonaventura Cavalieri independently introduced the concepts in the mid-17th century. The actual term polar coordinates has been attributed to Gregorio Fontana and was used by 18th-century Italian writers. Polar coordinates are most appropriate in any context where the phenomenon being considered is inherently tied to direction and length from a center point in a plane, such as spirals. The concepts of angle and radius were already used by ancient peoples of the first millennium BC. From the 8th century AD onward, astronomers developed methods for approximating and calculating the direction to Mecca —and its distance—from any location on the Earth. In Method of Fluxions, Sir Isaac Newton examined the transformations between polar coordinates and nine other coordinate systems. The term appeared in English in George Peacock’s 1816 translation of Lacroix’s Differential and Integral Calculus. Alexis Clairaut was first to think of polar coordinates in three dimensions, and Leon Euler was the first to actually develop them. The radial coordinate is often denoted by r or r or simply radius, and the angle is called the angular coordinate, polar angle, or azimuth. Angles in polar notation are generally expressed in either degrees or radians. For example, the direction from the pole in the reference direction is usually drawn as a ray from a pole, usually drawn clockwise or clockwise.
The angular coordinate is specified as φ, or t in the ISO standard 31-11 standard for rotations in either counterclockwise orclockwise clockwise orientation. The polar coordinate is used in many mathematical disciplines, including surveying and surveying, while radians are more common in physics and many applied disciplines in mathematics and physics. It is also used in some forms of astronomy, especially in the study of circular and orbital motion, and in the calculation of the length of parabolic arcs. The concept was first used to solve a problem relating to the area within an Archimedean spiral by Blaise Pascal in the 17th century, and was later extended to three dimensions by Isaac Newton in his work The Seventh Manner; For Spirals. In the journal Acta Eruditorum, Jacob Bernoulli used a system with a point on the line, called the pole and polar axis respectively, Coordinates were specified by the distance from the poles and angle from the polar axis. In modern mathematics, polar coordinates are generally written in either radians or degrees, with radians being the most common notation for the two- and three-dimensional versions. The first polar coordinates were used in the 19th century by the French mathematician Jean-Baptiste-Camille Poirier, who used them to describe the shape of the Earth’s poles.
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This page is based on the article Polar coordinate system published in Wikipedia (as of Dec. 04, 2020) and was automatically summarized using artificial intelligence.
