Difference between revisions of "1184: Circumference Formula"

Explain xkcd: It's 'cause you're dumb.
Jump to: navigation, search
m (Reverted edits by The author of xkcd (talk) to last revision by Theusaf)
Line 1: Line 1:
{{comic
+
crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap 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| number    = 1184
 
| date      = March 11, 2013
 
| title    = Circumference Formula
 
| image    = circumference_formula.png
 
| titletext = Assume r' refers to the radius of Earth Prime, and r'<nowiki/>' means radius in inches.
 
}}
 
 
 
==Explanation==
 
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 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:
 
 
 
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).
 
 
 
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}}.
 
 
 
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.
 
 
 
<small><sup>2</sup> These are not intended to indicate the presence of a footn... oh, never mind.</small>
 
 
 
==Transcript==
 
:Circumference of a circle:
 
:2πr<sup>2</sup>
 
:<sup>2</sup>The circle's radius
 
 
 
{{comic discussion}}
 
[[Category:Geometry]]
 

Revision as of 22:01, 20 May 2022

crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap 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crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap crap 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