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Curve. A parabola, one of the simplest curves, after (straight) lines. In mathematics, a curve (also called a curved line in older texts) is an object similar to a line, but that does not have to be straight . Intuitively, a curve may be thought of as the trace left by a moving point.
Curvature. A migrating wild-type Dictyostelium discoideum cell whose boundary is colored by curvature. Scale bar: 5 μm. In mathematics, curvature is any of several strongly related concepts in geometry that intuitively measure the amount by which a curve deviates from being a straight line or by which a surface deviates from being a plane.
In mathematics, a parabola is a plane curve which is mirror-symmetrical and is approximately U-shaped. It fits several superficially different mathematical descriptions, which can all be proved to define exactly the same curves.
Tangent line to a space curve. In mathematics, a tangent vector is a vector that is tangent to a curve or surface at a given point. Tangent vectors are described in the differential geometry of curves in the context of curves in R n. More generally, tangent vectors are elements of a tangent space of a differentiable manifold.
Each curve in this example is a locus defined as the conchoid of the point P and the line l.In this example, P is 8 cm from l. In geometry, a locus (plural: loci) (Latin word for "place", "location") is a set of all points (commonly, a line, a line segment, a curve or a surface), whose location satisfies or is determined by one or more specified conditions.
In mathematics, a plane curve is a curve in a plane that may be 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 ...
An algebraic curve in the Euclidean plane is the set of the points whose coordinates are the solutions of a bivariate polynomial equation p ( x, y) = 0. This equation is often called the implicit equation of the curve, in contrast to the curves that are the graph of a function defining explicitly y as a function of x .
Slope: = = In mathematics, the slope or gradient of a line is a number that describes the direction and steepness of the line. Often denoted by the letter m, slope is calculated as the ratio of the vertical change to the horizontal change ("rise over run") between two distinct points on the line, giving the same number for any choice of points.