

That's impossible! A simple mathematical paradox - acangiano
http://math-blog.com/2008/05/11/thats-impossible/

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slapshot
Not at all a paradox. A paradox would require two inconsistent things to be
simultaneously true.

This is just an answer that's counter-intuitive. It's entirely consistent, but
surprising.

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acangiano
From wikipedia: "A paradox can be an apparently true statement or group of
statements that leads to a contradiction _or a situation which defies
intuition_ ; or it can be, seemingly opposite, an apparent contradiction that
actually expresses a non-dual truth (cf. Koan). Typically, either the
statements in question do not really imply the contradiction, the puzzling
result is not really a contradiction, or the premises themselves are not all
really true or cannot all be true together. [...] A veridical paradox produces
a result that appears absurd but is demonstrated to be true nevertheless.
Thus, the paradox of Frederic's birthday in The Pirates of Penzance
establishes the surprising fact that a person's fifth birthday is the day he
turns twenty, if born on a leap day. Likewise, Arrow's impossibility theorem
involves behaviour of voting systems that is surprising but true."

But yes, it's a puzzle with a counterintuitive result.

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mixmax
Like the birthday paradox: <http://en.wikipedia.org/wiki/Birthday_paradox>

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acangiano
Exactly. Arguably that's the etymological meaning of the term. (It comes from
Greek, "para" which means "contrary to" and "doxa" which is "opinion").

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smanek
Oh, one of the neater mathematical 'paradoxes' I've seen is finding the sum of
a divergent series (obviously you can't treat infinity this way ... but it's a
fun trick).

(excuse the notation, I'm doing this with plain ASCII characters ...):

Let the sum of the geometric series 1 + 2 + 4 + 8 + 16 + ... be called (=) S.

Now multiply both sides by 2: 2S = 2 + 4 + 8 + 16 + 32 + ....

Now subtract the second equation from the first: S - 2S = (1 + 2 + 4 + 16 +
...) - (2 + 4 + 8 + 16 + 32 + ...)

Notice that all the terms except for the '1' cancel out on the right: -S = 1

And simplify: S = -1

Therefore: 1 + 2 + 4 + 8 + 16 + ... = -1

;-)

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KiwiNige
The extra 16cm of Radius is lots compared to a golf ball, and nothing compared
to earth. I have to scale these in my mind to be able to compare the two, and
the relative gap is what I expected. But I'm still surprised that the gap is
exactly the same in both.

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tectonic
See also the fascinating Benford's Law:
<http://en.wikipedia.org/wiki/Benford's_law>

