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# What is tau?

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Tau (τ) is the circumference of a circle divided by the radius, which is equal to 6.28318530718...

Pi (π) is half of tau (3.14159265359...). Pi is defined as the circumference of a circle divided by the diameter (which was easier to measure in the time of Archimedes, but circles are defined by their radius, not their diameter).

Tau is a more natural circle constant because we define circles in terms of their radius and measure around their circumference in radians. In other words, 2/3 of the distance around a circle is 2τ/3 radians.

Whenever 2π pops up in equations, it usually comes from something going completely around a circle. It's often useful to substitute τ to simplify these equations. Tau has many purposes such as the Fourier transform and the nth root of unity and there are many more examples where tau can easily replace pi and make the equation much shorter and save time.

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