Re: Patterns in pi, copyright law, and philosophy

shepherdm...@xxxxxxxxx wrote (in part):

3. Whether pi itself can appear "in" pi.

Peter Webb wrote (in part):

No.

Pi has an infinite representation as a decimal.

The only way that pi can appear in pi is if

pi = 3.14159265.... (finite number of digits) ...
314159265358 ... (infinite decimal expansion of pi)

On the other hand, it is by no means obvious (to me),
and probably not known, whether pi can appear in pi
in any of the follwing ways (where each appearance of
* represents any of the ten digits 0, 1, ..., 9, with
all the choices being independent of the other choices
for *):

pi = (finite number of digits) ... 3010401050902060...

pi = (finite number of digits) ... 301004000100005000009...

pi = (finite number of digits) ... 3*1*4*1*5*9*2*6...

pi = (finite number of digits) ... 3**1**4**1**5**9**2**6...

pi = (finite number of digits) ... 321345175119132176...

The last one has pi containing, in a simple way, both
pi and the sequence of prime numbers.

Dave L. Renfro
.

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