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Dataframe may refer to: A tabular data structure common to many data processing libraries: pandas (software) § DataFrames; The Dataframe API in Apache Spark; Data frames in the R programming language; Frame (networking)
The three coordinates (ρ, φ, z) of a point P are defined as: The radial distance ρ is the Euclidean distance from the z-axis to the point P.; The azimuth φ is the angle between the reference direction on the chosen plane and the line from the origin to the projection of P on the plane.
Hipparchus. The concepts of angle and radius were already used by ancient peoples of the first millennium BC.The Greek astronomer and astrologer Hipparchus (190–120 BC) 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. [2]
The real polar of a subset of is the set: := { : , } and the real prepolar of a subset of is the set: := { : , }.. As with the absolute prepolar, the real prepolar is usually called the real polar and is also denoted by . [2] It's important to note that some authors (e.g. [Schaefer 1999]) define "polar" to mean "real polar" (rather than "absolute polar", as is done in this article) and ...
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The elliptic curve E : 4Y 2 Z = X 3 − XZ 2 in blue, and its polar curve (E) : 4Y 2 = 2.7X 2 − 2XZ − 0.9Z 2 for the point Q = (0.9, 0) in red. The black lines show the tangents to E at the intersection points of E and its first polar with respect to Q meeting at Q.
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