Spiral

A spiral is a function which relates the distance of a point from the origin to its angle with the positive x axis. The equation for a spiral is typically given in terms of its polar coordinates. The polar coordinate system is another way in which points on a graph can be located. In the rectangular coordinate system, each point is defined by its x and y distance from the origin. For example, the point (4,3) would be located 4 units over on the x axis, and 3 units up on the y axis. Unlike the rectangular coordinate system, the polar coordinate system uses the distance and angle from the origin of a point to define its location. The common notation for this system is (r, θ) where r represents the length of a ray drawn from the origin to the point, and θ represents the angle which this ray makes with the x axis. This ray is often known as a vector.

Like all other geometric shapes, a spiral has certain characteristics which help define it. The center, or starting point, of a spiral is known as its origin or nucleus. The line winding away from the nucleus is called the tail. Most spirals are also infinite, that is they do not have a finite ending point.