A circle may also be defined algebraically, as the set of solutions to an equation of the form:
where is the center of the circle.
The distance around the circle, or circumference, is given by:
The area inside the circle is calculated using the formula:
This can be easily derived from the area of an ellipse. For an ellipse with major and minor axis and respectively, the area is . Setting the major an minor axis equal to each other give the formula for a circle.
A circle is a conic section, the intersection of a plane with a cone such that the plane is perpendicular to the axis of the cone.
Circles can readily be constructed by using a fixed distance between a pencil point and the center. A compass is a tool for doing this easily.
A circle with is called the unit circle, and is used extensively in trigonometry.