Editing 1184: Circumference Formula

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==Explanation==
 
==Explanation==
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The {{w|circumference}} C of a {{w|circle}} is 2{{w|pi|π}}''r'', 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>). The comical purpose of this ambiguity is that the formula initially makes an appearance of a mistake and confusion with the formula for the ''{{w|area}}'' of the circle: A = π''r'' <sup>2</sup>. If and only if the reader realizes that the superscript text is a reference to a footnote will they understand that the author has in fact supplied the correct formula. The comic [[1208: Footnote Labyrinths]] is another joke on footnotes.
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The {{w|circumference}} C of a {{w|circle}} is 2{{w|pi|π}}''r'', 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>.
  
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The title text makes a related joke. Randall has used r' (r-{{w|Prime (symbol)|prime}}) and r" (r-prime-prime, typically pronounced as ''r double prime''). Like many symbols, prime has widely differing meanings depending on context. In mathematics prime is often employed to distinguish corresponding components in analogous systems. For example, in a description of a basic physical system, if the velocity of an object is denoted with the variable ''v'', the velocity of that object at time=0 may be denoted with ''v′''. Playing off this use of prime, Randall has selected the radius of {{w|Earth Prime}}, a concept used in speculative fiction with parallel universes and multiple Earths. Earth Prime is our Earth (or at least the Earth from which the protagonists originate).
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The ' and " that follow the r's in the title text should be 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.
  
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However, other disciplines use prime to mean other things. In timekeeping and navigation ' denotes minutes (fractions of hours or degrees, respectively) and " denotes seconds (fractions of minutes). In the United States and some other places not using meters to measure distance, ' denotes feet and " denotes {{w|inches}}. The suggestion of using r' or r" does not cause any mathematical confusion, but using the former to denote the radius of a specific object and the latter to denote a radius using a specific unit of measurement would be highly esoteric. Furthermore, r' and r" can be used in calculus as a method of denoting, respectively, a first derivative and a second derivative. For someone attempting to use the formula and some derivative representing a circle's radius, trouble could result quite easily.
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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>2</sup> These are not intended to indicate the presence of a footn... oh, nevermind.</small>
  
 
==Transcript==
 
==Transcript==
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{{comic discussion}}
 
{{comic discussion}}
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[[Category:Math]]
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[[Category:Geometry]]
 
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[[Category:Footnotes]]
 

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