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Programmeruser: /* Why \tau Is Better Than \pi */
2021-11-23T01:18:27Z
<p><span dir="auto"><span class="autocomment">Why \tau Is Better Than \pi</span></span></p>
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<td colspan="2" style="background-color: #fff; color: #222; text-align: center;">Revision as of 01:18, 23 November 2021</td>
</tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l5" >Line 5:</td>
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<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>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>.</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>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>.</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td></tr>
<tr><td class='diff-marker'>−</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><del class="diffchange diffchange-inline">uh what about the area of a circle since </del><math>\pi r^2</math> is <del class="diffchange diffchange-inline">clearly </del>simpler than <math>\frac{\tau r^2}{<del class="diffchange diffchange-inline">4</del>}</math> <del class="diffchange diffchange-inline">- mathleticguyyy</del></div></td><td class='diff-marker'>+</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins class="diffchange diffchange-inline">Some may argue that </ins><math>\pi r^2</math> is simpler than <math>\frac{<ins class="diffchange diffchange-inline">1}{2}</ins>\tau r^2<ins class="diffchange diffchange-inline"></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</ins>}{<ins class="diffchange diffchange-inline">2</ins>}</math> <ins class="diffchange diffchange-inline">which is unavoidable.</ins></div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>==Other Uses of Tau==</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>==Other Uses of Tau==</div></td></tr>
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Programmeruser
https://artofproblemsolving.com/wiki/index.php?title=Tau&diff=104656&oldid=prev
Mathleticguyyy at 14:19, 18 March 2019
2019-03-18T14:19:20Z
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<td colspan="2" style="background-color: #fff; color: #222; text-align: center;">Revision as of 14:19, 18 March 2019</td>
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<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>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>.</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>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>.</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td></tr>
<tr><td class='diff-marker'>−</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>uh what about the area of a circle</div></td><td class='diff-marker'>+</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>uh what about the area of a circle <ins class="diffchange diffchange-inline">since </ins><math>\pi r^2</math> is clearly <ins class="diffchange diffchange-inline">simpler </ins>than <math>\frac{\tau r^2}{4}</math> - mathleticguyyy</div></td></tr>
<tr><td class='diff-marker'>−</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><math>\pi r^2</math> is clearly <del class="diffchange diffchange-inline">better </del>than <math>\frac{\tau r^2}{4}</math> - mathleticguyyy</div></td><td colspan="2"> </td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>==Other Uses of Tau==</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>==Other Uses of Tau==</div></td></tr>
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Mathleticguyyy
https://artofproblemsolving.com/wiki/index.php?title=Tau&diff=104655&oldid=prev
Mathleticguyyy at 14:18, 18 March 2019
2019-03-18T14:18:55Z
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<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>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>.</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>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>.</div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;"></ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">uh what about the area of a circle</ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;"><math>\pi r^2</math> is clearly better than <math>\frac{\tau r^2}{4}</math> - mathleticguyyy</ins></div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>==Other Uses of Tau==</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>==Other Uses of Tau==</div></td></tr>
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Mathleticguyyy
https://artofproblemsolving.com/wiki/index.php?title=Tau&diff=60807&oldid=prev
Greenpepper9999 at 21:45, 10 March 2014
2014-03-10T21:45:39Z
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<td colspan="2" style="background-color: #fff; color: #222; text-align: center;">Revision as of 21:45, 10 March 2014</td>
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<tr><td class='diff-marker'>−</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>'''Tau''', denoted <math>\tau</math>, is most commonly used as 2<math>\pi</math> <del class="diffchange diffchange-inline">(see </del>[[<del class="diffchange diffchange-inline">Pi</del>]] <del class="diffchange diffchange-inline">if you are part of </del>the <del class="diffchange diffchange-inline">minority </del>of <del class="diffchange diffchange-inline">the AoPS community which does not know what <math>\pi</math> is)</del>. 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.</div></td><td class='diff-marker'>+</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>'''Tau''', denoted <math>\tau</math>, is most commonly used as 2<math>\pi</math> <ins class="diffchange diffchange-inline">or 2 </ins>[[<ins class="diffchange diffchange-inline">pi</ins>]]<ins class="diffchange diffchange-inline">. Tau is </ins>the <ins class="diffchange diffchange-inline">number </ins>of <ins class="diffchange diffchange-inline">[[radians]] in a circle</ins>. 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.</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>== Why <math>\tau</math> Is Better Than <math>\pi</math>==</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>== Why <math>\tau</math> Is Better Than <math>\pi</math>==</div></td></tr>
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Greenpepper9999
https://artofproblemsolving.com/wiki/index.php?title=Tau&diff=53103&oldid=prev
Mathcool2009 at 04:11, 27 June 2013
2013-06-27T04:11:37Z
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<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>*[http://www.youtube.com/watch?v=3174T-3-59Q Michael Blake's "The Sound of Tau".]</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>*[http://www.youtube.com/watch?v=3174T-3-59Q Michael Blake's "The Sound of Tau".]</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>*[http://www.youtube.com/watch?v=H69YH5TnNXI Michael Hartl's lecture using "The Tau Manifesto".]</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>*[http://www.youtube.com/watch?v=H69YH5TnNXI Michael Hartl's lecture using "The Tau Manifesto".]</div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">*[http://www.tauday.com Michael Hartl's "The Tau Manifesto".]</ins></div></td></tr>
</table>
Mathcool2009
https://artofproblemsolving.com/wiki/index.php?title=Tau&diff=53102&oldid=prev
Mathcool2009 at 04:10, 27 June 2013
2013-06-27T04:10:26Z
<p></p>
<table class="diff diff-contentalign-left" data-mw="interface">
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<td colspan="2" style="background-color: #fff; color: #222; text-align: center;">Revision as of 04:10, 27 June 2013</td>
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<td colspan="2" class="diff-lineno">Line 11:</td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>*Tau is the 19th letter of the Greek alphabet.</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>*Tau is the 19th letter of the Greek alphabet.</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>*Tau is also an uncommon name for [[Phi]].</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>*Tau is also an uncommon name for [[Phi]].</div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;"></ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">==See Also==</ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">*[http://www.youtube.com/watch?v=jG7vhMMXagQ Vi Hart's "Pi is Still Wrong."]</ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">*[http://www.youtube.com/watch?v=FtxmFlMLYRI&list=PL5F03A9D6D278C5D9 Vi Hart's "A Song About A Circle Constant".]</ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">*[http://www.youtube.com/watch?v=3174T-3-59Q Michael Blake's "The Sound of Tau".]</ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">*[http://www.youtube.com/watch?v=H69YH5TnNXI Michael Hartl's lecture using "The Tau Manifesto".]</ins></div></td></tr>
</table>
Mathcool2009
https://artofproblemsolving.com/wiki/index.php?title=Tau&diff=53100&oldid=prev
Mathcool2009 at 04:01, 27 June 2013
2013-06-27T04:01:32Z
<p></p>
<table class="diff diff-contentalign-left" data-mw="interface">
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<col class="diff-marker" />
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<td colspan="2" style="background-color: #fff; color: #222; text-align: center;">← Older revision</td>
<td colspan="2" style="background-color: #fff; color: #222; text-align: center;">Revision as of 04:01, 27 June 2013</td>
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<tr><td class='diff-marker'>−</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>'''Tau''' (<math>\tau</math>) can have <del class="diffchange diffchange-inline">multiple </del>meanings:</div></td><td class='diff-marker'>+</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>'''Tau'''<ins class="diffchange diffchange-inline">, denoted <math>\tau</math>, is most commonly used as 2<math>\pi</math> </ins>(<ins class="diffchange diffchange-inline">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.</ins></div></td></tr>
<tr><td class='diff-marker'>−</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>*Tau is <del class="diffchange diffchange-inline">a </del>letter of the Greek alphabet<del class="diffchange diffchange-inline">.</del></div></td><td class='diff-marker'>+</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div> </div></td></tr>
<tr><td class='diff-marker'>−</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><del class="diffchange diffchange-inline">*[[Tau--constant]] is sometimes used as 2[[Pi]]</del>.</div></td><td class='diff-marker'>+</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins class="diffchange diffchange-inline">== Why </ins><math>\tau</math> <ins class="diffchange diffchange-inline">Is Better Than <math>\pi</math>==</ins></div></td></tr>
<tr><td class='diff-marker'>−</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>*Tau is also an <del class="diffchange diffchange-inline">archaic </del>name for [[Phi]].</div></td><td class='diff-marker'>+</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div> </div></td></tr>
<tr><td class='diff-marker'>−</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><del class="diffchange diffchange-inline">{{disambig}}</del></div></td><td class='diff-marker'>+</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins class="diffchange diffchange-inline">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</ins>)<ins class="diffchange diffchange-inline">? <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>.</ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div> </div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins class="diffchange diffchange-inline">==Other Uses of Tau==</ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div> </div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div> </div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins class="diffchange diffchange-inline"><math>\tau</math> </ins>can have <ins class="diffchange diffchange-inline">other </ins>meanings:</div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>*Tau is <ins class="diffchange diffchange-inline">the 19th </ins>letter of the Greek alphabet.</div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>*Tau is also an <ins class="diffchange diffchange-inline">uncommon </ins>name for [[Phi]].</div></td></tr>
</table>
Mathcool2009
https://artofproblemsolving.com/wiki/index.php?title=Tau&diff=53099&oldid=prev
Mathcool2009 at 03:40, 27 June 2013
2013-06-27T03:40:39Z
<p></p>
<table class="diff diff-contentalign-left" data-mw="interface">
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<col class="diff-marker" />
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<td colspan="2" style="background-color: #fff; color: #222; text-align: center;">← Older revision</td>
<td colspan="2" style="background-color: #fff; color: #222; text-align: center;">Revision as of 03:40, 27 June 2013</td>
</tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l1" >Line 1:</td>
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<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>'''Tau''' (<math>\tau</math>) can have multiple meanings:</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>'''Tau''' (<math>\tau</math>) can have multiple meanings:</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>*Tau is a letter of the Greek alphabet.</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>*Tau is a letter of the Greek alphabet.</div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">*[[Tau--constant]] is sometimes used as 2[[Pi]].</ins></div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>*Tau is also an archaic name for [[Phi]].</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>*Tau is also an archaic name for [[Phi]].</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>{{disambig}}</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>{{disambig}}</div></td></tr>
</table>
Mathcool2009
https://artofproblemsolving.com/wiki/index.php?title=Tau&diff=18843&oldid=prev
Temperal: creation
2007-10-26T18:53:12Z
<p>creation</p>
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<td colspan="2" style="background-color: #fff; color: #222; text-align: center;">Revision as of 18:53, 26 October 2007</td>
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<tr><td class='diff-marker'>−</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><del class="diffchange diffchange-inline">#REDIRECT </del>[[Phi]]</div></td><td class='diff-marker'>+</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins class="diffchange diffchange-inline">'''Tau''' (<math>\tau</math>) can have multiple meanings:</ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins class="diffchange diffchange-inline">*Tau is a letter of the Greek alphabet.</ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins class="diffchange diffchange-inline">*Tau is also an archaic name for </ins>[[Phi]]<ins class="diffchange diffchange-inline">.</ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins class="diffchange diffchange-inline">{{disambig}}</ins></div></td></tr>
</table>
Temperal
https://artofproblemsolving.com/wiki/index.php?title=Tau&diff=16505&oldid=prev
Temperal: Redirecting to Phi
2007-09-22T20:47:36Z
<p>Redirecting to <a href="/wiki/index.php/Phi" title="Phi">Phi</a></p>
<p><b>New page</b></p><div>#REDIRECT [[Phi]]</div>
Temperal