The circle constant (tau) is a number approximately equal to . The number is defined as the length of the circumference of a circle divided by the length of its radius:
The number appears naturally when measuring angles in radians. A full rotation in radians is equal to radians. For reference, a full rotation in degrees is . The signficance of the number tau comes from the fact that the distance required to travel the circumference of a circle is equal to tau multiplied by the radius of the circle.
The constant (pi) is defined as the length of a circle’s circumference divided by the length of its diameter. The constant is directly related to :
While is an adequate constant, has long-term advantages as the better constant. The circle constant makes talking about, teaching and converting the unit of radians easier. For these reasons, this website presents equations and concepts using the circle constant .
Here are some geometry formulas that utilize the constant .
The area of a circle is give by one-half 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.
The volume of a cylinder is equal to PI multiplied by its radius squared and its height.
The volume of a cone is given by one third multiplied by PI, the radius of its base squared, and its height.
The volume of a sphere is given by two-thirds multiplied by the circle constant τ (tau) multiplied by the radius cubed.
Radians are a unit that measure angle using the radius of a circle. One radian is equal to the amount of rotation required to travel the length of one radius along the circumference of the circle.
The Polar Coordinate System describes points in space using an angle and radius relative to the origin.
The unit circle is a unifying idea in mathematics that connects many useful concepts together. This article goes over the basic properties of the circle using interactive examples and explains how they connect to the trigonometric functions and pythagorean theorem.