PDA

View Full Version : Irrational numbers

chriscurtis
2008-Oct-15, 10:14 AM
This is Pi, e and the square root of two expressed algebraically in integers (for the first time). Where you see this sign "^", think "to the power of" 2^2 is 4, 3^2 is nine, 10^3 is 1000, etc

This is how to express Pi as four integers.

3 + (3816789261729072800164555526354 / 720^11)

This is the number e

2 + (19362094715027164800860196706377/ 720 ^11)

This is the square root of 2

1 + (11165592542028177935665256318230/ 720^11)

HenrikOlsen
2008-Oct-15, 10:32 AM
You are wrong.
3 + (3816789261729072800164555526354 / 720^11) =
3.141592653589793238462643383279501445144073468572 ...
Pi=
3.141592653589793238462643383279502884197169399375 ...

Once again you're mistaking a number's limited precision representation in a computer for the mathematical reality.

Stop doing this.

chriscurtis
2008-Oct-15, 10:33 AM
Explain in mathematics

chriscurtis
2008-Oct-15, 10:34 AM
PS My calculator program can handle these numbers. It has to, the large ones are slight variances on primes. (I.e. these were done by hand, brother)

chriscurtis
2008-Oct-15, 10:46 AM
You are wrong.
3 + (3816789261729072800164555526354 / 720^11) =
3.141592653589793238462643383279501445144073468572 ...
Pi=
3.141592653589793238462643383279502884197169399375 ...

Once again you're mistaking a number's limited precision representation in a computer for the mathematical reality.

Stop doing this.

I think you'll find that it looks wrong because THAT is the answer you would get with a computer not the real PI :) Did you look at the two numbers you put side by side before you posted? The difference is a floating error on YOUR part.

Yippee ki yay...

agingjb
2008-Oct-15, 10:57 AM
Pi and e are transcendental.

chriscurtis
2008-Oct-15, 10:59 AM
These numbers came from a reverse look up and were then checked if that helps? Pay attention Mr Danish, you might just learn something (even if something is or looks wrong). It even says that in the good book apparently, though I drink blood not holy water ;)

chriscurtis
2008-Oct-15, 11:01 AM
well done, the transcendental proofs apply to one dimensional conditions, both these transcendental numbers have 2D structure.

So, wheel out the actual mathematical reasoning, instead of leaning on the expressions of those who actually did some work back in the day. You might learn something as well

HenrikOlsen
2008-Oct-16, 12:29 PM
I think you'll find that it looks wrong because THAT is the answer you would get with a computer not the real PI :) Did you look at the two numbers you put side by side before you posted? The difference is a floating error on YOUR part.

Yippee ki yay...
Nope.

I'm well aware that the calculation I made had limited precision, but I also know how to control the precision with which I calculate and can therefore see which part of the result is influenced by rounding errors.

Division of two integers is a stable operation, with rounding errors that are easily controlled (you simply continue your long division until you have sufficient precicion) in the last few digits only, the number I wrote to be the result of your calculation was calculated to 200 places, it differs from the actual value of Pi in the 34rd digit, well within the precision with which I calculated the number.

BTW, do you still believe 49 is prime?

Pay attention Mr Danish, you might just learn something (even if something is or looks wrong). It even says that in the good book apparently, though I drink blood not holy water ;)
Incidentally, you'd do well to refrain from name calling if you want to be considered mistaken rather than deliberately trolling.

It even says that in the good book apparently, though I drink blood not holy water ;)
Slightly more relevant to this discussion, the good book also says Pi is 3 which is another example of limited precision calculation, in this case the value you get when calculating to one digits precision.

Limited
2008-Oct-16, 02:43 PM
You are wrong.
3 + (3816789261729072800164555526354 / 720^11) =
3.141592653589793238462643383279501445144073468572 ...
Pi=
3.141592653589793238462643383279502884197169399375 ...

Once again you\'re mistaking a number\'s limited precision representation in a computer for the mathematical reality.

Stop doing this.

The particular combination of computer and software I used to check this stopped precisely at the point where the two numbers above become different, so that seems like a screaming red flag.

I think you\'ll find that it looks wrong because THAT is the answer you would get with a computer not the real PI :) Did you look at the two numbers you put side by side before you posted? The difference is a floating error on YOUR part.

I guess if you redefine the real pi to be some decimal approximation thereof, that would be good enough for government work, but you\'re not the first person to do that.

These numbers came from a reverse look up and were then checked if that helps? Pay attention Mr Danish, you might just learn something (even if something is or looks wrong). It even says that in the good book apparently, though I drink blood not holy water ;)

I believe you, Mr Danish could learn something wrong from your post.

Cougar
2008-Oct-16, 03:39 PM
Pay attention... you might just learn something...

This is such a common internet condescension. And a real turn-off.

[click]

nauthiz
2008-Oct-16, 04:01 PM
I think you'll find that it looks wrong because THAT is the answer you would get with a computer not the real PI :) Did you look at the two numbers you put side by side before you posted? The difference is a floating error on YOUR part.
How do you know? Did you calculate pi out to that precision by hand?

Every source I've found on Google that expands pi out to at least 48 places agrees with HenrikOlsen's number, btw.

Ivan Viehoff
2008-Oct-16, 04:27 PM
Explain in mathematics
You don't deserve this. But, for the benefit of our other readers who might be interested by it, here is the simple demonstration of the irrationality of the square root of 2 that has been known since the time of Pythagoras. In fact it works for any prime number p, so I will show it in the more general form.

Suppose the square root of prime number p is rational.
Let a/b be the square root of p expressed in least terms where a and b are integers.
so a^2 = p b^2
So (by the definition of "prime") a is divisible by p.
Let a = p c (where c is, by the definition of "divisible", an integer)
so p^2 c^2 = p b^2
so p c ^2 = b^2
so b is divisible by p also. Which contradicts the initial premises that a/b was in least terms. By reductio ad absurdam, the square root of p is irrational.

You purport to overturn long established proofs of the irrationality of certain numbers by exhibiting rational numbers, without even attempting to prove they fulfill the function you claim for it. Why should anyone take any notice of you?

In the case of the square root of 2, in fact we can see immediately that the number you exhibit cannot fulfill that function. Let us convert the mixed number you exhibit into a vulgar fraction, retaining the denominator you show. It is will remain true that the denominator ends with 11 zeroes, but the numerator will end with only 1 zero, because 1 +b/c = (c+b)/c. So when you square it, the numerator will end with 2 zeroes, but the denominator with 22 zeroes. So it cannot possibly cancel out to be the integer 2. Your credibility is utterly lost, who can be bothered looking at the other ones?

Pass the sick bag, Alice.

If you don't like the referred (more difficult) proofs of the irrationality of e and pi, frankly that's your problem.
http://pirate.shu.edu/~wachsmut/ira/infinity/irrat_nm.html

Sadly, there are hundreds of people out there bothering the world with purported demonstrations of mathematical things that cannot possibly be true. Sadly, they are rarely capable of understanding, or else unwilling to accept, an explanation of the error in their demonstration. Nor indeed are they happy with a claim that the result they purport to overturn is in fact proven, so they are wasting their time. Since understanding their error often requires Galois theory or Algebraic number theory, or some other difficult area, they typically don't like a recommendation that they take such courses (for which they have often been rejected). Like you, they often say don't refer me to the sources, prove it in front of me. Or they babble meaningless nonsense, like "the transcendental proofs apply to one dimensional conditions, both these transcendental numbers have 2D structure". They often blame some conspiracy to suppress them. Which is why no further correspondence will be entered into.

spratleyj
2008-Oct-18, 12:28 AM
Is this another piece of shenanigans?

mugaliens
2008-Oct-18, 04:41 PM
Slightly more relevant to this discussion, the good book also says Pi is 3 which is another example of limited precision calculation, in this case the value you get when calculating to one digits precision.

Must have been that time, a few thousand years ago, when the quantum black hole filament passed near Earth thereby distorting the spacetime continuum just so...

Seriously, Chris, I think Henrik's right. Furthermore, why express it in so many digits when four digits will do?

tdvance
2008-Oct-18, 05:51 PM
"Originally Posted by HenrikOlsen View Post
Slightly more relevant to this discussion, the good book also says Pi is 3 which is another example of limited precision calculation, in this case the value you get when calculating to one digits precision."

not directly--it says something like--there was a bowl 10 cubits across and 30 cubits round.