The Logic Off Topic list

Thoughts from the mind of Lars Vik, 08-11-2001:

>  >The answer may surprise you, and puts a nice upper
>>boundary on the "sensible number of decimals of pi
>>you'll ever need".
>
>But how many decimals do you need? Just interested... You know, nice 
>thing to know when you check up girls or things like that...! It's 
>Wednesday, but still...

Let's suppose the speed of light is 3 * 10^8 m/s (it's actually a bit 
less, but that doesn't matter for the outcome).
So in one year light travels

3 * 10^8 * 60 * 60 * 24 * 365 meters = 9.4608 * 10^15 m = 1 lightyear (approx)

So 1 billion lightyears is times 10^9: 9.4608 * 10^24 m

Expressed in 0.1 mm units (i.e. times 10^4) gives 9.4608 * 10^28.

So the diameter of the proposed circle is 9.4608 * 10^28, where the 
unit is 0.1 mm -- a 29-digit number.  Let's call this number A.

The circumference of a circle is pi*diameter.

Now suppose we knew pi in zero decimal places -- i.e. pi = 3.
Then A*pi = 2.838.. * 10^29

Now we take pi with 1 decimal place: pi=3.1
Then A*pi = 2.932.. * 10^29

Now we take pi with 2 decimal place: pi=3.14
Then A*pi = 2.970.. * 10^29

Ditto, 3 places (3.142) gives 2.97258... * 10^29
With pi=3.1415 we get 2.97211...  * 10^29

So with 0 decimals, we see that the "2" part is OK but the rest is 
wrong (as can be seen from the following calculations which give 
2.9... instead of 2.8...).  With 1 decimal we get 2.9, but the rest 
is still wrong (ditto: it should be 2.97... instead of 2.93... as cab 
be seen from subsequent calculations).

Etcetera: each time we add a decimal in pi, we gain (not 
surprisingly) 1 position of accuracy.
0 decimals: 1 digit of accuracy. 1 decimal: 2 digits of accuracy. 
Etc.  So in order to get 29 digits of accuracy (since our unit was 
already 0.1 mm) we need 28 decimals of pi.  To be on the safe side, 
we simply take 30 decimals and all will be well.  Besides, 30 is 
easier to remember :-).

Now you try to get laid by using this in a bar conversation with 
girls.  Let me know if it works :-).


cheers,
HJ
-- 
     Hendrik Jan Veenstra
     email: mailto:h@...
     www:   http://www.ision.nl/users/h/index.html