Difference between revisions of "Tau"
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Have you ever been in geometry class and been asked to graph sine waves with their ridiculous extra factor of 2 in the x-axis? Have you ever thought radian angle measure was hopelessly tainted with the superfluous and yet unavoidable factor of 2 (There are '''''2'''''<math>\pi</math> radians in a full revolution)? <math>\tau</math> resolves that. One <math>\tau</math> is one revolution. Simple as that. While you have to remember that <math>\frac{\pi}{8}</math> radians is '''NOT''' <math>\frac{1}{8}</math> of a revolution, but is equal to <math>\frac{1}{16}</math> of a revolution because of that idiosyncratic factor of 2, <math>\frac{\tau}{8}</math> radians is just <math>\frac{1}{8}</math> of a revolution. Likewise, <math>\frac{\tau}{3}</math> radians is just <math>\frac{1}{3}</math> of a revolution, <math>9001\tau</math> radians is just 9001 revolutions, <math>123456789\tau</math> radians is just 123456789 revolutions, and <math>x\tau</math> radians is <math>x</math> revolutions for any real <math>x</math>. | Have you ever been in geometry class and been asked to graph sine waves with their ridiculous extra factor of 2 in the x-axis? Have you ever thought radian angle measure was hopelessly tainted with the superfluous and yet unavoidable factor of 2 (There are '''''2'''''<math>\pi</math> radians in a full revolution)? <math>\tau</math> resolves that. One <math>\tau</math> is one revolution. Simple as that. While you have to remember that <math>\frac{\pi}{8}</math> radians is '''NOT''' <math>\frac{1}{8}</math> of a revolution, but is equal to <math>\frac{1}{16}</math> of a revolution because of that idiosyncratic factor of 2, <math>\frac{\tau}{8}</math> radians is just <math>\frac{1}{8}</math> of a revolution. Likewise, <math>\frac{\tau}{3}</math> radians is just <math>\frac{1}{3}</math> of a revolution, <math>9001\tau</math> radians is just 9001 revolutions, <math>123456789\tau</math> radians is just 123456789 revolutions, and <math>x\tau</math> radians is <math>x</math> revolutions for any real <math>x</math>. | ||
− | + | Some may argue that <math>\pi r^2</math> is simpler than <math>\frac{1}{2}\tau r^2</math>, but as noted in the [https://tauday.com/tau-manifesto#table-quadratic_forms Tau Manifesto], many quadratic forms in physics contain a factor of <math>\frac{1}{2}</math> which is unavoidable. | |
− | <math>\pi r^2</math> is | ||
==Other Uses of Tau== | ==Other Uses of Tau== |
Latest revision as of 21:18, 22 November 2021
Tau, denoted , is most commonly used as 2
or 2 pi. Tau is the number of radians in a circle. For a convincing proof that
is a better circle constant than
, see The Tau Manifesto by Michael Hartl. This following section will summarize one main point of the Tau Manifesto.
Why
Is Better Than ![$\pi$](//latex.artofproblemsolving.com/f/2/c/f2ca003a7da0de4994b4733e203b74ff52d42553.png)
Have you ever been in geometry class and been asked to graph sine waves with their ridiculous extra factor of 2 in the x-axis? Have you ever thought radian angle measure was hopelessly tainted with the superfluous and yet unavoidable factor of 2 (There are 2 radians in a full revolution)?
resolves that. One
is one revolution. Simple as that. While you have to remember that
radians is NOT
of a revolution, but is equal to
of a revolution because of that idiosyncratic factor of 2,
radians is just
of a revolution. Likewise,
radians is just
of a revolution,
radians is just 9001 revolutions,
radians is just 123456789 revolutions, and
radians is
revolutions for any real
.
Some may argue that is simpler than
, but as noted in the Tau Manifesto, many quadratic forms in physics contain a factor of
which is unavoidable.
Other Uses of Tau
can have other meanings:
- Tau is the 19th letter of the Greek alphabet.
- Tau is also an uncommon name for Phi.