Difference between revisions of "Tau"
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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. |
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| + | == Why <math>\tau</math> Is Better Than <math>\pi</math>== | ||
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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>. | ||
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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. | ||
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| + | ==Other Uses of Tau== | ||
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| + | <math>\tau</math> can have other meanings: | ||
| + | *Tau is the 19th letter of the Greek alphabet. | ||
| + | *Tau is also an uncommon name for [[Phi]]. | ||
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| + | ==See Also== | ||
| + | *[http://www.youtube.com/watch?v=jG7vhMMXagQ Vi Hart's "Pi is Still Wrong."] | ||
| + | *[http://www.youtube.com/watch?v=FtxmFlMLYRI&list=PL5F03A9D6D278C5D9 Vi Hart's "A Song About A Circle Constant".] | ||
| + | *[http://www.youtube.com/watch?v=3174T-3-59Q Michael Blake's "The Sound of Tau".] | ||
| + | *[http://www.youtube.com/watch?v=H69YH5TnNXI Michael Hartl's lecture using "The Tau Manifesto".] | ||
| + | *[http://www.tauday.com Michael Hartl's "The Tau Manifesto".] | ||
Latest revision as of 20:18, 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 
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.
