Circumference Formula
Circumference Formula
Circumference of a circle: 2πr 2 2 The circle's radius

The circumference C of a circle is 2 π r , where r is the 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 ). The comical purpose of this ambiguity is that the formula initially makes an appearance of a mistake and confusion with the formula for the area of the circle: A = π r 2 . 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- 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 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 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.
2 These are not intended to indicate the presence of a footn... oh, never mind.
Circumference of a circle: 2πr 2 2 The circle's radius
