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Difference between revisions of "Tau"
(→‎Why \tau Is Better Than \pi)
 
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'''Tau''', denoted <math>\tau</math>, is most commonly used as 2<math>\pi</math> (see [[Pi]] if you are part of the minority of the AoPS community which does not know what <math>\pi</math> is). For a convincing proof that <math>\tau</math> is a better circle constant than <math>\pi</math>, see [http://www.tauday.com The Tau Manifesto] by Michael Hartl. This following section will summarize one main point of the Tau Manifesto.
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'''Tau''', denoted <math>\tau</math>, is most commonly used as 2<math>\pi</math> or 2 [[pi]]. Tau is the number of [[radians]] in a circle. For a convincing proof that <math>\tau</math> is a better circle constant than <math>\pi</math>, see [http://www.tauday.com The Tau Manifesto] by Michael Hartl. This following section will summarize one main point of the Tau Manifesto.
  
 
== Why <math>\tau</math> Is Better Than <math>\pi</math>==
 
== Why <math>\tau</math> Is Better Than <math>\pi</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>.
 
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>.
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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.
  
 
==Other Uses of Tau==
 
==Other Uses of Tau==
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*Tau is the 19th letter of the Greek alphabet.
 
*Tau is the 19th letter of the Greek alphabet.
 
*Tau is also an uncommon name for [[Phi]].
 
*Tau is also an uncommon name for [[Phi]].
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==See Also==
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*[http://www.youtube.com/watch?v=jG7vhMMXagQ Vi Hart's "Pi is Still Wrong."]
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*[http://www.youtube.com/watch?v=FtxmFlMLYRI&list=PL5F03A9D6D278C5D9 Vi Hart's "A Song About A Circle Constant".]
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*[http://www.youtube.com/watch?v=3174T-3-59Q Michael Blake's "The Sound of Tau".]
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*[http://www.youtube.com/watch?v=H69YH5TnNXI Michael Hartl's lecture using "The Tau Manifesto".]
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*[http://www.tauday.com Michael Hartl's "The Tau Manifesto".]

Latest revision as of 20:18, 22 November 2021

Tau, denoted $\tau$, is most commonly used as 2$\pi$ or 2 pi. Tau is the number of radians in a circle. For a convincing proof that $\tau$ is a better circle constant than $\pi$, see The Tau Manifesto by Michael Hartl. This following section will summarize one main point of the Tau Manifesto.

Why $\tau$ Is Better Than $\pi$

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$\pi$ radians in a full revolution)? $\tau$ resolves that. One $\tau$ is one revolution. Simple as that. While you have to remember that $\frac{\pi}{8}$ radians is NOT $\frac{1}{8}$ of a revolution, but is equal to $\frac{1}{16}$ of a revolution because of that idiosyncratic factor of 2, $\frac{\tau}{8}$ radians is just $\frac{1}{8}$ of a revolution. Likewise, $\frac{\tau}{3}$ radians is just $\frac{1}{3}$ of a revolution, $9001\tau$ radians is just 9001 revolutions, $123456789\tau$ radians is just 123456789 revolutions, and $x\tau$ radians is $x$ revolutions for any real $x$.

Some may argue that $\pi r^2$ is simpler than $\frac{1}{2}\tau r^2$, but as noted in the Tau Manifesto, many quadratic forms in physics contain a factor of $\frac{1}{2}$ which is unavoidable.

Other Uses of Tau

$\tau$ can have other meanings:

  • Tau is the 19th letter of the Greek alphabet.
  • Tau is also an uncommon name for Phi.

See Also

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