Editing 1184: Circumference Formula
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==Explanation== | ==Explanation== | ||
− | The {{w|circumference}} C of a {{w|circle}} is 2{{w|pi|π}}''r'', where ''r'' is the {{w|radius}} of the circle. | + | 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'' <sup>2</sup>. |
− | The title text | + | 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. |
− | + | In this case, ''r'' is already used to notate the radius of any circle. ''r'' ′ ("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}}. | |
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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}}; 6 371 km.) | ||
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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}}. | ||
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+ | <small><sup>1</sup> This is not intended to indicate the presence of a footn... oh, nevermind.</small> | ||
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+ | <small><sup>2</sup> So are these.</small> | ||
==Transcript== | ==Transcript== | ||
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{{comic discussion}} | {{comic discussion}} | ||
− | + | [[Category:Math]] | |
− | [[Category: | ||
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