A curve is a continuous and smooth flowing line without any sharp turns or angles, often representing a mathematical function or path in geometry and calculus. It can be described in various forms such as parametric, implicit, or explicit equations, and is fundamental in understanding the behavior of functions and shapes in both two and three dimensions.

Curve

continuous and smooth flowing line

sharp turns or angles

A mathematical function is a relation that uniquely associates each element of a set with exactly one element of another set, often expressed as f(x) = y, where x is the input and y is the output. Functions are fundamental in mathematics as they describe the dependence of one quantity on another, allowing for precise modeling of real-world phenomena and abstract concepts.

mathematical function

path in geometry

Path in calculus

Parametric equations express a set of related quantities as explicit functions of an independent parameter, often simplifying the representation of curves and surfaces in mathematics and physics. They allow for more flexible and comprehensive modeling of geometric figures, enabling the analysis of complex shapes that are difficult to describe with standard Cartesian equations.

Parametric Equations

Implicit equations

explicit equations

understanding the behavior of functions

Understanding the behavior of shapes

Two dimensions

three dimensions

Curves and Surfaces

Introduction to Functions and Graphs

Introduction to Parametric Equations: The Basics

Relevant Degrees

Log in to see lessons