A circle is a basic geometric shape that is used throughout mathematics. The shape plays an important role in trigonometry and the polar coordinate system. Formally, a circle is defined as a shape where every point along its perimeter is an equal distance from its center.
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Radius The radius is the distance from the center of the circle to any point along the perimeter of the circle. 

Circumference The circumference, denoted with the variable , is the length around the perimeter of the circle. 

Diameter The diameter is the distance between any two points along the perimeter of the circle that passes through the center of the circle. 

Area The area of a circle is the amount of twodimensional space that fits inside the perimeter of the circle. 
The concept of a circle appears throughout math and its applications. There are two important circle constants that, when present in math equations and formulas, usually mean a circle is involved. The constants are (pi) and (tau). This website favors the circle constant (tau) over (pi). The circle constant is defined by the geometry of any circle as shown below:
Here are the basic geometric formulas relating to the circle.
The area of a circle is give by onehalf multiplied by τ (tau) mutliplied by the radius of the circle squared.
The circumference of a circle is given the constant τ (tau) multpilied by the radius of the circle, where τ = 2π.
Here are the equations that form the shape of the circle in the cartesian coordinate system and the polar coordinate system.
The standard form of a circle is given by the radius and center point of the circle.
The general form of the equation of a circle is given in terms of coeffecients.
This webbook covers the fundamentals of trigonometry using the radian angle system and the geometry of the circle. The definitions of the trigonometric functions are extended using the geometry of the circle. The applications of trigonometry are also discussed.
The Polar Coordinate System describes points in space using an angle and radius relative to the origin.
The greek letter π (pi) is a geometric constant approximately equal to 3.1456. The numeric value is equal to the length of any circle's circumference divided by its diameter.
The circle constant τ (tau) is a geometric constant approximately equal to 6.283. The numeric value is defined as the length of any circle's circumference divided by the length of its radius.
The Cartesian Coordinate System describes space of one, two, and three dimensions. Each point in space is represented by its distance relative to the origin of the system.