Pi (was: Re: TU-58)
cisin at xenosoft.com
Thu Dec 3 12:08:10 CST 2015
>> I tried measuring a whole bunch of circles, and I can't find any rational reason why dividing the circumference by the diameter never came out even! :-)
On Thu, 3 Dec 2015, Tapley, Mark wrote:
> Howzabout: go to Fort Smith, NT, Canada (or thereabouts, 60° N)
> Walk or swim as appropriate, measuring distance, due East until you get back to Fort Smith. You got back, so it must have been a circle, yes?
> Walk or swim to the N. pole, measuring distance again.
> Compute ratio of distances.
> I think both Pythagoras and Eratosthenes would be thrilled at the result.
Thanks to Riemann for removing the IRRATIONALITY of
imposing a Euclidean structure!
Now, for the fun geometric calculations:
What latitude would give you a value of PI of 3.0?
(the distance [on a great circle] to the pole would
be 1/6 (1/(2*PI)) the circumference of your circle)
And, of course, "a spherical chicken in a vacuum",
we'll assume that the earth were a perfect sphere.
Can I get crowd-funding for the expedition?
We could put a plaque there!
("Distance to the pole is x,
distance due east all the way back to here is 6x,
therefore, right here, PI is 3.0")
(I think that Ethan Dicks has been to the southern one)
Another calculation that has been bothering me, . . .
For a message of length of N bits, it will presumably
occur somewhere in PI. Rather than store the entire
message, we could, instead, store the number of bits
offset into PI where that message first occurs.
Acknowledging that PI is random, as far as we are concerned,
what would the AVERAGE offset be as a function of N?
OB_CC: What were the early significant projects of calculating PI?
Grumpy Ol' Fred cisin at xenosoft.com
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