11 Jul '06 05:07>
Originally posted by AThousandYoungActually every number possible in present within the digits of pi. Including e in theory.
There is only one number in pi - pi itself.
Originally posted by XanthosNZWhy? Are you sure? Irrationality certainly doesn't require that.
I should clarify:
The digits of pi contain every possible sequence of digits including e to any number of significant digits you wish.
Originally posted by TommyCYes, the number
Why? Are you sure? Irrationality certainly doesn't require that.
Originally posted by TommyCPi is irrational so it therefore contains an infinite number of digits. Pi also does not repeat in any way. Therefore it must contain every finite string somewhere within it.
Why? Are you sure? Irrationality certainly doesn't require that.
Originally posted by XanthosNZSee edit to previous post - you are incorrect, it is not (yet) a fact that pi contains every sequence. In fact, according to wikipedia, it's not known whether the numbers 0 to 9 do occur infintiely in it (an obvious prerequisite for your claim.)
Pi is irrational so it therefore contains an infinite number of digits. Pi also does not repeat in any way. Therefore it must contain every finite string somewhere within it.
EDIT: To emperically prove it you'd have to show that the digits of pi are in fact random. This is pretty much impossible to prove but it can be shown that pi passes every test of randomness you wish to throw at it.
Originally posted by TommyCYes. Just use 0 and 1s in any non-repeating fashion.
Surely it would be easy to construct a non-repeating, irrational number without certain digits in it?
Originally posted by TommyCYou could only construct such a number by instituting rules into the number (9 can never follow 6). If it can be shown that pi is random then obviously such rules do not exist. The fact that spigot algorithm exists for pi is an extremely strong indicator that this is true.
See edit to previous post - you are incorrect, it is not (yet) a fact that pi contains every sequence. In fact, according to wikipedia, it's not known whether the numbers 0 to 9 do occur infintiely in it (an obvious prerequisite for your claim.)
I don't follow your logic, btw. Surely it would be easy to construct a non-repeating, irrational number without certain digits in it?
Originally posted by XanthosNZA mathematical statement is either proven or not. Establishing truth is not an exercise in offering up impressionistic evidence to the subjectivities of a jury; it is a watertight activity. Your previous claims could be reasonably modified by the world "probably", however.
You could only construct such a number by instituting rules into the number (9 can never follow 6). If it can be shown that pi is random then obviously such rules do not exist. The fact that spigot algorithm exists for pi is an extremely strong indicator that this is true.
Originally posted by TommyCI agree. I should have prefaced my statement with a probably. But I can never keep track of what has and hasn't been mathematically proven.
A mathematical statement is either proven or not. Establishing truth is not an exercise in offering up impressionistic evidence to the subjectivities of a jury; it is a watertight activity. Your previous claims could be reasonably modified by the world "probably", however.
Originally posted by XanthosNZMy undergraduate degree was in mathematics and frankly, I couldn't even understand what was meant to be proven or not most of the time, let alone anything more ambitious.
I agree. I should have prefaced my statement with a probably. But I can never keep track of what has and hasn't been mathematically proven.
Originally posted by LinkHyruleThe answer is... a wife
I am your contant companion.
I am your greatest helper or heaviest burden.
I will push you onward or drag you down to failure.
I am completely at your command.
Half of the things you do you might just as well turn over to me and I will be able to do them quickly and correctly.
I am easily managed-you must merely be firm with me.
Show me exactly ho ...[text shortened]... , and I will place the world at your feet.
Be easy with me and I will destroy you.
Who am I?
Originally posted by GammastyleYou cannot measure the diameter and circumference of a circle to arbitrary precision, so that method is out (and in any case, pi is a mathematical constant, not a physical one...so any "real world" way of calculating pi isn't going to work).
Being a non-math guy. How does one calculate pi. Is there a formula?. Do they measure a radius and diameter more and more exact? I don't understand how they keep getting more and more digits. Please explain.