So it does not start at the beginning? You may as well print any list of random numbers on it, since Pi is infinite and must have that sequence in it at some point.

And I thought this was a measuring tape, graduated in units (inches, cm) on one side, and pies (pork, apple, scotch) on the other. That way, you could find out the circumference of anything by measuring the diameter or radius, and similarly you could find the diameter of anything by directly measuring the circumference. Great for calculating the volume of pork required to fill a certain size of crust.

//since Pi is infinite and must have that sequence in it at some point.// Not provable to be true, but possibly provable to be untrue for certain sequences. (refers to Kurt Gödel) Some infinities are of course greater than others - see also Cantor's "the cardinality of the continuum"

Anyway, the whole joy of the idea is that the sequences actually HAVE been derived from the Pi sequence and are not speculative strings.

[mitxela]
// You may as well print any list of random numbers on it, since Pi is infinite and must have that sequence in it at some point.

That's actually not proven. (And the claim is becoming something of a pet peeve of mine over the years - we're launching into the same discussion at the very beginning of the "Bricks of Pi" conversation, so let me not repeat it here.)

I agree that even a trained mathematician is very unlikely to look at that number sequence and see anything but a long random string of digits, though.

[xenzag]
// As the sequence is infinite, no two rolls of tape will ever be exactly the same.

They can't *all* be the same - but if the infinite sequence of pi ends up containing all finite sequences of numbers, there will be an infinite number of pairs of rolls with the exact same sequence on them. The company probably won't get around to printing them before the end of the universe, but...

I'm constantly interested in the idea of an achievable product that nevertheless skirts the parameters of contradiction.

I refer to these in other work that I do in various terms such as: The Minor Dilemmas presented by Dualities of Reciprocity with a particular focus on the Cohesion of the Sticky Strands.

From wikipedia: "....calculations that have determined over 1 trillion digits of Pi, no simple base-10 pattern in the digits has ever been found."

If each roll of tape had a string of 1,000 digits and the printing machinery was co-ordinated and computer linked so that no string was repeated, then you could make whatever number of rolls you get when you divide a trillion by a thousand, with a certified guarantee that each roll was unique.

//how big a segment of pi would you have to have in order to determine that it is indeed a "piece of pi" ?// To be a proper piece, it has to go right from the centre to the crust. Given the crumblability of pastry and the squodgability of filling, I am guessing that there might be a limit at about 10°, though experiments are clearly required.

If you are talking numbers, surely by definition it is the other way round, a single digit is demonstrably "part of pi". Similarly two. The task of demonstrating becomes harder as the number of digits increases.

//calculations that have determined over 1 trillion digits of Pi, no simple base-10 pattern in the digits has ever been found//

hmmm, has anyone ever looked at how the sequence of prime numbers occurs within the decimal points of pi? That is probably a stupid question because I can't find any hits using those words in any order but I wonder if there would be a pattern...

...and while I'm asking stupid questions, why is 1 not a prime number? It should be a prime number. It's like the primest number.

WIKI: //...a prime number is a number which has exactly two divisors: 1 and itself.// Well it can't have exactly 2 divisors, it only has the same one, twice.
Perhaps we should lobby for a different definition, something like a "Pr1me number is a number that when divided by any number other than itself and 1 gives a positive integer result"...

It just seems a bit arbitrary to me. I read about generations of math buffs trying to find patterns in the prime number sequence but have those same attempts been made without assuming that the number one is excluded?

One is the loneliest prime number that you'll never do. Two can be as bad as one, as it's the substitute first prime number for the number one.