Parametric equations are a set of equations that describe the relationship between two variables in a system. In these equations, one variable is typically represented as a function of another variable, and both variables are expressed as independent parameters.
Parametric equations are often used in physics, engineering, and other scientific disciplines to describe the motion or behavior of a system. They are also useful for graphing complex curves and surfaces.
Unlike standard equations, which typically have one variable on each side of the equal sign, parametric equations have multiple variables on one side and a set of parameters on the other. This allows for a more flexible representation of a system's behavior.
The origin of parametric equations can be traced back to the 17th century, when French mathematician René Descartes introduced the Cartesian coordinate system. This system, which uses two perpendicular axes to represent points in a plane, laid the groundwork for the development of parametric equations.
Parametric equations are used in a wide range of real-world applications, such as designing roller coasters, modeling projectile motion, and predicting the behavior of electronic circuits. They are also used in computer graphics and animation to create realistic images and animations.