1184: Circumference Formula

2013-03-12T15:09:48Z

202.108.26.13: /* Explanation */

{{comic
| 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 footnote about ''r'', using 2. This creates a typographical ambiguity, since a superscript 2 can also be an exponent (as in ''x''2). 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'' 2.

As for the title text; ''r'' ′ and ''r'' ″ is {{w|derivative#Lagrange's notation|Lagrange's notation for the derivative}} and the {{w|second derivative}} of ''r'', respectively. Since ′ is the {{w|prime symbol}}, ''r'' ′ is often read out as "r-prime". "Prime" can mean first or original, and "{{w|Earth Prime}}" is a term sometimes used in works of fiction involving parallel universes to refer to ''our'' 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.) The double prime (″) also designates {{w|inches}}.

Also note that primes and double-primes is a popular [citation needed] notation to tell apart the same property of different objects. In this case, 'r' is already used to notate the radius of any circle. To distinguish other radii, one is tempted to add a prime or double-primes, resulting in r' (r prime) which sounds like the radius of Earth Prime and Earth, and r'' (r double-prime) which looks like r inches.

2 These are not intended to indicate the presence of a footn... oh, nevermind.

==Transcript==
:Circumference of a circle:
:2πr2
:2The circle's radius

{{comic discussion}}
[[Category:Math]]

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1184: Circumference Formula