explain xkcd: It's 'cause you're dumb.
The circumference C of a circle is 2πr, 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 x2). Randall's formula now looks like a strange hybrid of the correct formula and the formula for the area of the circle: A = πr 2.
The ′ and ″ that follows the r's in the title text are the prime and double prime symbols. Among other things, these are often used in mathematics to tell apart corresponding properties of different objects.
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 radius of any regular polygon, or the radius of any sphere). Randall chooses the radius of Earth Prime.
"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 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 radius of the Earth; 6 371 km.)
As the title text also plays on, another of the uses of the double prime symbol (″) is to designate inches.
2 These are not intended to indicate the presence of a footn... oh, nevermind.
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- Circumference of a circle:
- 2The circle's radius
- Tau x Radius, superscript 2
- Leaves one wondering what the superscript 1 refers. 22.214.171.124 (talk) (please sign your comments with ~~~~)
- It's 2πr2, not τr2. —126.96.36.199 05:37, 11 March 2013 (UTC)
- You're missing the point. τ == 2π and is considered better than using π by some people 188.8.131.52 (talk) (please sign your comments with ~~~~)
- Only for very loose definitions of "better." 184.108.40.206 14:59, 11 March 2013 (UTC)
- Whoa! Never heard about that before, but after 2 hrs or so, I think I'm getting convinced! Check this site out: http://tauday.com/ What do you think? –St.nerol (talk) 18:06, 11 March 2013 (UTC)
- I think tau is pointless. Using tau what then happens to Euler's famous formula, the most beautiful equation of them all? Pi shows up in so many different ways and places in mathematics. Tau appears pretty much only in the formula for a circle's circumference. Why bother needlessly proliferating symbols? J Milstein (talk) 18:17, 11 March 2013 (UTC)
- RE: Euler's Identity: e^(tau*i) - 1 = 0 --Max Nanasy (talk) 18:27, 11 March 2013 (UTC)
- Ok, that works J Milstein (talk) 17:05, 13 March 2013 (UTC)
- Why not just e^(tau*i) = 1. Do you routinely do 2 + 2 - 4 = 0?220.127.116.11 20:31, 13 March 2013 (UTC)
- --Max Nanasy (talk) 00:35, 14 March 2013 (UTC)
- I think Euler only did that because he disliked negative numbers. It really is less a deal than people make of it.18.104.22.168 03:02, 15 March 2013 (UTC)
- Also, it uses the five most important constants in mathematics: e, π (or τ), i, 1, and 0. Curtmack (talk) 20:33, 30 April 2013 (UTC)
- The tau manifesto fairly well convinced me that all occurances of π in mathematics utimately trace back from the formula C = 2πr. If so, π naturally enter calculations as 2π. Can anyone find a counterexample to this thesis? –St.nerol (talk) 00:29, 14 March 2013 (UTC)
- How could there be a counter-example? I think it is true. In complex analysis, it really should be 2π, and thus Gaussian integrals. And then number theory applications. Even this neat result really stems from trig identities, so it really is a result for 2π. 22.214.171.124 02:59, 15 March 2013 (UTC)
- From what I understand, the thesis from the tau-proponents is that 2*pi is the fundamental natural constant, and that virtually every time that pi shows up without the factor 2, there originally was a factor two that was cancelled out. –St.nerol (talk) 01:53, 12 March 2013 (UTC)
Not completely sure Earth Prime is from Sliders, but it's true it's the only one named exactly that ... -- Hkmaly (talk) 09:54, 11 March 2013 (UTC)
There's also a Prime Earth now. Just so DC can screw with us. Hogtree Octovish (talk) 10:40, 11 March 2013 (UTC)
I still don't get it.126.96.36.199 12:41, 11 March 2013 (UTC)
- If you don't get it, you don't need to get it J Milstein (talk) 18:07, 11 March 2013 (UTC)
Well, that was lame. --188.8.131.52 17:19, 11 March 2013 (UTC)
This comic illustrates the strategy of "The Unconsummated Asterisk", from the essay "Mathmanship" by Nicholas Vanserg (available at ).
The other side of the asterisk gambit is to use a superscript as a key to a real footnote. The knowledge‐seeker reads that S is – 36.714 calories and thinks "Gee what a whale of a lot of calories" until he reads to the bottom of the page, finds footnote 14 and says "oh."
For bonus points, Randall could have used also "Pi-Throwing":
For example every schoolboy knows what π stands for so you can hold him at bay by heaving some entirely different kind of π into the equation. The poor fellow will automatically multiply by 3.1416, then begin wondering how a π got into the act anyhow, and finally discover that all the while π was osmotic pressure. If you are careful not to warn him, this one is good for a delay of about an hour and a half.
) 19:01, 11 March 2013 (UTC)
- Another good one is π as a symbol for profit in financial discussions. -DrGaellon (talk | contribs) 23:23, 25 March 2013 (UTC)
I believe the current description of prime as denoting derivatives is true but irrelevant. Since the area and circumference refers to geometry (not really calculus), it's more likely that the title text is referring to the common use of primes in geometry. For example, there might be two or more parallel lines that are denoted by x, x′, x′′, etc. Wikipedia also notes another geometric use of prime: "if a point is represented by the Cartesian coordinates (x, y), then that point rotated, translated or reflected might be represented as (x′, y′)." S (talk) 23:32, 11 March 2013 (UTC)
that is so wrong, i feel my mind corrupted now. -- Anarcat (talk) 23:57, 11 March 2013 (UTC)
This explanation was hillarious -- where is the up-vote button ?? Spongebog (talk)
- +1 Smperron (talk) 16:33, 13 March 2013 (UTC)
So, where's todays comic? How many times has Randal been late?184.108.40.206 16:15, 13 March 2013 (UTC)
- Today's comic was posted just a few minutes ago. I'm anxiously awaiting its explanation as it picks on a programming language I'm not familiar with (possibly SQL). Smperron (talk) 16:33, 13 March 2013 (UTC)
It uses pseudocode. The new one is about sorting algorithms in general, not any particular language. 220.127.116.11 17:00, 13 March 2013 (UTC)
Perhaps it's just me, but did no one see the "square the circle" gag...? --18.104.22.168
09:24, 14 March 2013 (UTC) No one but you saw the square-the-circle gag, because it's not there. For it to be there, it would require this: (2πr)² J Milstein
) 15:31, 14 March 2013 (UTC)