The greek letter is used in math as a geometric constant to represent a half-rotation in radians. The value of is naturally occuring and can be found by dividing the length of a circle’s circumference by the length of its diameter.
The constant also appears in geometric formulas related to the area and length of a circle.
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.
is closely related to the constant (tau). Where represents a half rotation in radians, represents a full rotation. This relationship is expressed below:
The circle constant τ (tau) is a number approximately equal to 6.283. The number is defined as the length of a circle's circumference divided by the length of its radius.