https://www.explainxkcd.com/wiki/api.php?action=feedcontributions&feedformat=atom&user=221.204.199.38explain xkcd - User contributions [en]2026-07-09T14:24:14ZUser contributionsMediaWiki 1.30.0https://www.explainxkcd.com/wiki/index.php?title=1184:_Circumference_Formula&diff=343231184: Circumference Formula2013-04-19T14:38:35Z<p>221.204.199.38: /* Explanation */</p>
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<div>{{comic<br />
| number = 1184<br />
| date = March 11, 2013<br />
| title = Circumference Formula<br />
| image = circumference_formula.png<br />
| titletext = Assume r' refers to the radius of Earth Prime, and r'<nowiki/>' means radius in inches.<br />
}}<br />
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==Explanation==<br />
The {{w|circumference}} C of a {{w|circle}} is 2{{w|pi|π}}''r''<sup>1</sup>, where ''r'' is the {{w|radius}} of the circle. Randall then makes a {{w|Note (typography)|footnote}} about ''r'', using <sup>2</sup>. This creates a typographical ambiguity, since a superscript 2 can also be an exponent (as in ''x''<sup>2</sup>). Randall's formula now looks like a strange hybrid of the correct formula and the formula for the ''{{w|area}}'' of the circle: A = π''r''&thinsp;<sup>2</sup>.<br />
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The ′ and ″ that follows the r's in the title text are the {{w|prime symbol|prime}} and double prime symbols. {{w|Prime (symbol)#Designation of units|Among other things}}, these are often used in mathematics to tell apart corresponding properties of different objects.<br />
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In this case, ''r'' is already used to notate the radius of any circle. ''r''&thinsp;′ ("r-prime") could then be used to notate radii of things that are not circles (like the [http://www.mathsisfun.com/definitions/radius-polygon-.html radius of any regular polygon], or the radius of any {{w|sphere}}). [[Randall]] chooses the radius of {{w|Earth Prime}}.<br />
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"Prime" can mean first or original, and "Earth Prime" is a term sometimes used in works of fiction involving parallel universes to refer to ''our'' Earth (e.g. in {{w|The Long Earth}}), or to a world with a minimum of divergence points from Earth as we know it. (The radius of Earth Prime would thus not differ much from the {{w|radius of the Earth}}; 6&thinsp;371&thinsp;km.)<br />
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As the title text also plays on, another of the uses of the double prime symbol (″) is to designate {{w|inches}}.<br />
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<small><sup>1</sup> This is not intended to indicate the presence of a footn... oh, nevermind.</small><br />
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<small><sup>2</sup> So are these.</small><br />
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==Transcript==<br />
:Circumference of a circle:<br />
:2πr<sup>2</sup><br />
:<sup>2</sup>The circle's radius<br />
<br />
{{comic discussion}}<br />
[[Category:Math]]</div>221.204.199.38