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# What is tau?

## Answer

###### Wiki User

###### March 19, 2013 4:09AM

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.