Spirals are classified by the mathematical relationship between the length r of the radius vector, and the vector angle q, which is made with the positive x axis. Most spirals are also infinite, that is they do not have a finite ending point. The line winding away from the nucleus is called the tail. The center, or starting point, of a spiral is known as its origin or nucleus. Like all other geometric shapes, a spiral has certain characteristics which help define it. 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. Unlike the rectangular coordinate system, the polar coordinate system uses the distance and angle from the origin of a point to define its location. For example, the point (4,3) would be located 4 units over on the x axis, and 3 units up on the y axis. In the rectangular coordinate system, each point is defined by its x and y distance from the origin. The polar coordinate system is another way in which points on a graph can be located. The equation for a spiral is typically given in terms of its polar coordinates. Tail -The part of a spiral that winds away from the origin. Spiral of Archimedes -A type of curve defined by the relationship r = aq. Logarithmic spiral -A type of curve defined by the relationship r = e a q. Characteristics of a spiralĪ spiral is a function which relates the distance of a point from the origin to its angle with the positive KEY TERMS Another type of spiral, called a logarithmic spiral, is found in many instances in nature. Some common spirals include the spiral of Archimedes and the hyperbolic spiral. It can be defined by a mathematical function which relates the distance of a point from its origin to the angle at which it is rotated. A spiral is a curve formed by a point revolving around a fixed axis at an ever-increasing distance.

Spiral of archimedes