Why are parametric eqautions bad?

Answer 1

In mathematics, parametric equations of a curve express the coordinates of the points of the curve as functions of a variable, called a parameter.[1][2] For example,

are parametric equations for the unit circle, where t is the parameter. Together, these equations are called a parametric representation of the curve.

A common example occurs in kinematics, where the trajectory of a point is usually represented by a parametric equation with time as the parameter.

The notion of parametric equation has been generalized to surfaces, 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 dimension is one and one parameter is used, for surfaces dimension two and two parameters, etc.).

The parameter typically is designated t because often the parametric equations represent a physical process in time. However, the parameter may represent some other physical quantity such as a geometric variable, or may merely be selected arbitrarily for convenience. Moreover, more than one set of parametric equations may specify the same curve.