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In mathematics, and more specifically in geometry, parametrization (or parameterization; also parameterisation, parametrisation) is the process of finding parametric equations of a curve, a surface, or, more generally, a manifold or a variety, defined by an implicit equation. The inverse process is called implicitization. [1] "
In addition to curves and surfaces, parametric equations can describe manifolds and algebraic varieties of higher dimension, with the number of parameters being equal to the dimension of the manifold or variety, and the number of equations being equal to the dimension of the space in which the manifold or variety is considered (for curves the ...
The parametrization is regular for the given values of the parameters if the vectors , are linearly independent. The tangent plane at a regular point is the affine plane in R 3 spanned by these vectors and passing through the point r ( u , v ) on the surface determined by the parameters.
Poloidal direction (red arrow) and toroidal direction (blue arrow) A torus of revolution in 3-space can be parametrized as: [2] (,) = (+ ) (,) = (+ ) (,) = . using angular coordinates , [,), representing rotation around the tube and rotation around the torus' axis of revolution, respectively, where the major radius is the distance from the center of the tube to the center of ...
Arc length is the distance between two points along a section of a curve. Determining the length of an irregular arc segment by approximating the arc segment as connected (straight) line segments is also called curve rectification .
is equal to one. This parametrization gives the same value for the curvature, as it amounts to division by r 3 in both the numerator and the denominator in the preceding formula. The same circle can also be defined by the implicit equation F(x, y) = 0 with F(x, y) = x 2 + y 2 – r 2. Then, the formula for the curvature in this case gives
Poison Profits. A HuffPost / WNYC investigation into lead contamination in New York City
If the angle subtended by the chord at the centre is 90°, then ℓ = r √2, where ℓ is the length of the chord, and r is the radius of the circle. If two secants are inscribed in the circle as shown at right, then the measurement of angle A is equal to one half the difference of the measurements of the enclosed arcs (⌢ and ⌢).