The circle constant (tau) is a geometric constant that appears in numerous math formulas relating to circles and angles. The numeric value of is defined as the length of the circumference of a circle divided by the length of its radius and is approximately equal to [1].
In the radian angle system, the circle constant is equal to a full rotation in radians. Measured angles are represented as fractions of the circle constant . For example, shown below are two angles measured using the circle constant.
Here are some traditional geometric formulas in terms of the circle constant.
Calculate the area of a circle given the radius.
Calculate the circumference of a circle given the radius.
Calculate the volume of a sphere given the radius.
Calculate the volume of a cylinder given the radius and height.
The circle constant also appears in advanced applications such as the normal distribution, Fourier transforms, and more.
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Approximate the Circle Constant Example
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No, really, pi is wrong: The Tau ManifestoMichael Hartl