Difference between revisions of "1184: Circumference Formula"

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| number    = 1184
 
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| date      = March 11, 2013
 
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| title    = Circumference Formula
 
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| image    = circumference_formula.png
 
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| titletext = Assume r' refers to the radius of Earth Prime, and r'<nowiki/>' means radius in inches.
 
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}}
 
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==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.
 
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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''). The title text can be explained thusly:
 
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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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However, other disciplines use prime to mean other things. In timekeeping and navigations ' 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}}.
 
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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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<small><sup>2</sup> These are not intended to indicate the presence of a footn... oh, never mind.</small>
 
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==Transcript==
 
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:Circumference of a circle:
 
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:2πr<sup>2</sup>
 
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:<sup>2</sup>The circle's radius
 
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{{comic discussion}}
 
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[[Category:Geometry]]
 

Revision as of 23:50, 4 May 2022

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