Planeekäyrän

Planeekäyrän is a Finnish term that translates to "plane curve." It refers to a curve that lies entirely within a single plane, as opposed to a curve in three-dimensional space, which is known as a spatial curve. In geometry, plane curves are fundamental objects of study, and they can be described using various mathematical representations.

These representations include explicit equations, where one variable is expressed as a function of another (e.g., y = f(x)), implicit equations, where the relationship between variables is defined by an equation (e.g., F(x, y) = 0), and parametric equations, where the coordinates of points on the curve are expressed as functions of a parameter (e.g., x = x(t), y = y(t)).

Examples of common plane curves include lines, circles, ellipses, parabolas, and hyperbolas, which are collectively known as conic sections. More complex plane curves can be generated through various mathematical operations and definitions, such as algebraic curves defined by polynomial equations or transcendental curves defined by trigonometric or exponential functions. The study of plane curves involves analyzing their properties like curvature, tangency, intersections, and enclosing areas.