Q: How do you create great parametric equations?

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Some curves are easier to describe and perform calculations on if using parametric equations

I looked all over the internet and could not find a parametric equation for this shape. You can look at the link below to find the regular cartesian equation. If you are good at parametric equations you could probably convert this into parametric form. I am not so good at parametric equations.

It might be easier to calculate using numeric values directly if the equation is really simple.

Frequently you have to solve complex sets of equations with many variables of different units. It is impractical to use numeric values because it makes the solving process obscure and therefore prone to bugs. It is easier to solve parametric equations down to the point where you have a relatively simple equation and then put in numeric values with their respective units. Plus, you can reuse the parametric equations easily and track how did you solve them any time later.

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Some curves are easier to describe and perform calculations on if using parametric equations

I looked all over the internet and could not find a parametric equation for this shape. You can look at the link below to find the regular cartesian equation. If you are good at parametric equations you could probably convert this into parametric form. I am not so good at parametric equations.

Parametric equations are a way of expressing the points of a curve as the function of a set parameter. Any game that displays modern scaling graphics using a form of parametric equation.

It might be easier to calculate using numeric values directly if the equation is really simple.

Frequently you have to solve complex sets of equations with many variables of different units. It is impractical to use numeric values because it makes the solving process obscure and therefore prone to bugs. It is easier to solve parametric equations down to the point where you have a relatively simple equation and then put in numeric values with their respective units. Plus, you can reuse the parametric equations easily and track how did you solve them any time later.

A parametric cubic curve is a cubic curve made up of two equations. For example an x(t) part, and a y(t) part. They may also be known as 'Bezier' curves. Parametric equations are generally controlled by a 't' value. A google search of 'parametric cubic' may also give you some more information.

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Parametric equations not only give a more general solution to a problem, but they also display the relationship between the parameters, thus providing a better understanding of the what the solution suggests.

Actually, there really are not any. In mechanics, in order to understand problems, everything is broken up into components in order to better understand what is going on. Parametric equations allow physicists to examine individual forces within a problem. Most prefer parametric equations to numeric values.Without a table or graph, you might forget what an equation represents.

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.

Parametric statistics is a branch of statistics that assumes data come from a type of probability distribution and makes inferences about the parameters of the distribution. See related link.

The chain rule.