

Pi explained - shawndumas
http://upload.wikimedia.org/wikipedia/commons/2/2a/Pi-unrolled-720.gif

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ianterrell
Pi is the wrong constant.

That animation looks great, but it's misleading: the fundamental measurement
of the circle is the radius, not the diameter.

Measured with a unit radius, we'd see 2*pi for a full "turn" of the wheel.
Twice pi, or tau, is the magic number.

See <http://tauday.com/> for details.

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superchink
Random speculation: Maybe pi was chosen because the symbol for tau (τ) is hard
to distinguish from a ‘T’ when hand-written?

BTW, I don't mean to take anything away from your comment; that link was
awesome.

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VMG
When π was "invented" it could have been 2 x 3.141. The author makes a case
for tau because it is too late to redefine π

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sgentle
I only really understood bezier curves after I saw a similar Wikipedia
animation:
[http://en.wikipedia.org/wiki/B%C3%A9zier_curve#Constructing_...](http://en.wikipedia.org/wiki/B%C3%A9zier_curve#Constructing_B.C3.A9zier_curves)

It's amazing just how much seeing something move makes a difference.

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petercooper
You can also calculate pi by throwing frozen hot dogs:
[http://www.wikihow.com/Calculate-Pi-by-Throwing-Frozen-
Hot-D...](http://www.wikihow.com/Calculate-Pi-by-Throwing-Frozen-Hot-Dogs)

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yannis
Or you can see how ants calculate it in "The accuracy of Buffon’s needle: a
rule of thumb used by ants to estimate area" at
<http://beheco.oxfordjournals.org/content/12/6/655.full.pdf>

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hugh3
While I doubt this would actually explain pi to anyone who didn't already
understand it, it is nonetheless kinda neat.

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mtinkerhess
It could help someone who's just learning about pi to grok it more easily.

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m_myers
Next question: Is it possible for a piece of string to be pi units long? How
do transcendental numbers translate to the real world?

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fexl
Just as difficult a question: Is it possible for piece of string to be 2 units
long?

In the real world, you always run into limits on how finely you can measure
things before you run into quandaries about number theory.

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joejohnson
I think something could be two units long. Two is discrete, and at a
microscopic level, things can be exactly discrete values (i.e. two
angstroms...). I think asking if something could be exactly pi long is a
different question.

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ars
Actually, no they can't. At a quantum level things do not have definitive
sizes. They have sort of "clouds", where the center of the cloud is more
likely to be their size, and the edges are less likely - but still possible.

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nitrogen
So a string of 24 carbon atoms is not 2 dozen carbon atoms long? Unit=dozen
carbon atoms, length=2?

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ars
No. A carbon atom does not have a fixed size.

And especially when you attach atoms together the spacing between them varies
depending on the strength and type of the bond.

Additionally, molecules are constantly in motion (heat) - one of the motions
is changing the size of the spacing between them.

But even if you froze it to absolute zero (which is impossible), it doesn't
matter, the size is not determinate, it's only probabilistic.

So a real physical object can never have a fixed size.

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benatkin
Another diagram that gets the number for pi wrong:
<http://www.physicsforums.com/showthread.php?t=452917>

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ctdonath
How about some animations relating that to calculation of pi via assorted
algorithms? esp. the "pick a digit" one?

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tokenadult
"The Amazing Number π" by Peter Borwein,

[http://www.nieuwarchief.nl/serie5/deel01/sep2000/pdf/borwein...](http://www.nieuwarchief.nl/serie5/deel01/sep2000/pdf/borwein.pdf)

one of the leading researchers on π, has a history of investigation of the
number and formulas for calculating π to increasingly accurate place-value
approximations.

A very interesting secondary school textbook in English from Kerala, India

[http://www.education.kerala.gov.in/englishmedium/mathseng/te...](http://www.education.kerala.gov.in/englishmedium/mathseng/text10.PDF)

shows the same visual representation of π on the number in section 3.1 of
chapter 3.

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tschill
Kinda neat. But I was always more intrigued by the Monte Carlo approximation
for thinking about pi. <http://www.eveandersson.com/pi/monte-carlo-demo>.
Although it does take alot of iterations to converge to a decent estimate of
pi.

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evanrmurphy
An animation is worth a thousand incantations.

