PARAMETRIC EQUATIONS Meaning and
Definition
-
Parametric equations refer to a mathematical representation of a curve or a set of coordinates in terms of one or more parameters. These equations express the coordinates of a point on a curve in relation to a parameter, typically denoted as t. The values of the parameter determine the position of the point along the curve.
In parametric equations, the x and y coordinates of a point are given as separate functions of the parameter. The x-coordinate is expressed as a function of t, denoted as x(t), and the y-coordinate is expressed as a separate function of t, denoted as y(t). The relationship between x and y can be defined by various mathematical expressions or equations.
The use of parametric equations provides a flexible and powerful tool in representing curves or objects that cannot be easily described by a single equation. It allows for the description of complex shapes, such as curves with changing slopes or curves that intersect themselves. Parametric equations are commonly used in various fields such as physics, engineering, computer graphics, and mathematics.
When graphing parametric equations, the plot of the curve is obtained by varying the parameter over a specific range and calculating the corresponding coordinates. This representation allows for the visualization of the curve's behavior and characteristics. Parametric equations offer a versatile approach in representing curves or coordinates in mathematical and scientific contexts.
Etymology of PARAMETRIC EQUATIONS
The word "parametric" originates from the Greek word "παραμετρικός" (parametrikos), which is a combination of "παρά" (para) meaning "beside" or "beyond" and "μέτρον" (metron) meaning "measure".
The term "equation" has Latin roots and comes from the word "aequatio", which means "equalizing" or "making equal".
Therefore, "parametric equations" refer to a set of equations that express a set of quantities as functions of one or more independent parameters, often represented through variables such as "t" or "θ" in order to provide an alternative method to describe mathematical relationships. The word "parametric" emphasizes the presence of additional parameters that help define the relationship between the quantities being studied.
