PARAMETRIC CURVE Meaning and
Definition
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A parametric curve refers to a mathematical representation of a curve in a coordinate system, where the position of each point on the curve is determined by one or more parameters. Unlike the more commonly known Cartesian coordinate system where points are described by their x and y coordinates, a parametric curve assigns a separate parameter for each coordinate.
In simple terms, a parametric curve describes how the x and y (and possibly other) coordinates of points on the curve vary as a function of a parameter. This parameter is typically denoted as t, and as it varies within a specific range, the curve is traced out.
The parameter t provides a way to move along the curve and determine the positions of points at specific values of t. The x and y coordinates of a point on the parametric curve are obtained by substituting the corresponding values of t into separate functions, which often take the form of equations. These functions provide the necessary information to calculate the position of each point on the curve.
Parametric curves are commonly used to describe complex shapes, such as curves, spirals, and other intricate patterns. They allow for great flexibility in defining curves and enable precise control over the shape and behavior of the curve.
Due to their versatility, parametric curves find applications in various fields including computer graphics, engineering, physics, and mathematics. They provide a powerful tool for representing and manipulating curves in a way that is often more intuitive and convenient than traditional Cartesian coordinates.
Etymology of PARAMETRIC CURVE
The term "parametric curve" combines two words: "parametric" and "curve".
The word "parametric" is derived from the Greek word "parametros", which means "to have a reference to" or "to have a parameter". It is formed by combining the prefix "para-" (meaning "beside" or "alongside") and the word "metros" (meaning "measure"). In mathematics, "parametric" refers to the use of parameters or variables to express the coordinates of a point in terms of one or more independent variables.
The word "curve" originates from the Latin word "curvus", meaning "bent" or "crooked". It refers to a line or path that is not straight and follows a continuous bend or curvature. In mathematics, a curve is a one-dimensional object that can be represented using equations or parametric equations.
