What does plane curve mean?
Definitions for plane curve
plane curve
This dictionary definitions page includes all the possible meanings, example usage and translations of the word plane curve.
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Wiktionary
plane curvenoun
the locus of points in the Euclidean plane that satisfies some geometric or algebraic definition
Wikipedia
Plane curve
In mathematics, a plane curve is a curve in a plane that may be either a Euclidean plane, an affine plane or a projective plane. The most frequently studied cases are smooth plane curves (including piecewise smooth plane curves), and algebraic plane curves. Plane curves also include the Jordan curves (curves that enclose a region of the plane but need not be smooth) and the graphs of continuous functions.
Wikidata
Plane curve
In mathematics, a plane curve is a curve in a Euclidean plane. The most frequently studied cases are smooth plane curves, and algebraic plane curves. A smooth plane curve is a curve in a real Euclidean plane R² and is a one-dimensional smooth manifold. Equivalently, a smooth plane curve can be given locally by an equation ƒ = 0, where ƒ : R² → R is a smooth function, and the partial derivatives ∂ƒ/∂x and ∂ƒ/∂y are never both 0. In other words, a smooth plane curve is a plane curve which "locally looks like a line" with respect to a smooth change of coordinates. An algebraic plane curve is a curve in an affine or projective plane given by one polynomial equation ƒ = 0 Algebraic curves were studied extensively in the 18th to 20th centuries, leading to a very rich and deep theory. Some founders of the theory are considered to be Isaac Newton and Bernhard Riemann, with main contributors being Niels Henrik Abel, Henri Poincaré, Max Noether, among others. Every algebraic plane curve has a degree, the degree of the defining equation, which is equal, in case of an algebraically closed field, to the number of intersections of the curve with a line in general position. For example, the circle given by the equation x² + y² = 1 has degree 2.²²
Numerology
Chaldean Numerology
The numerical value of plane curve in Chaldean Numerology is: 8
Pythagorean Numerology
The numerical value of plane curve in Pythagorean Numerology is: 9
Translations for plane curve
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"plane curve." Definitions.net. STANDS4 LLC, 2024. Web. 25 Apr. 2024. <https://www.definitions.net/definition/plane+curve>.
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