The one calculator

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AuthorTopic: The one calculator
Master
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I wonder if you could come up with a random number generator based on the digits of pi.

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It wouldn't be a very good source of randomness. If you use the digits of pi in order, they're obviously going to be predictable. So you have to use some random method for picking digits, in which case you can just use that as your randomiser and skip the step involving pi.

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Actually, that's a good question. Since all pseudorandom number generators are just a long string of numbers and become predictable if the current location is known, so all presumably depend on some form of random seeding.

Pi has a few other problems, I think. The fact that it has to be calculated, not arbitrarily declared, is one of them. While pi is irrational, I'm not sure if anyone has proved, or even can prove, that it has random and even distribution.

—Alorael, who would rather stick to the tried and true ways of generating "random" numbers. That's not the kind of thing you want to trust to dumb luck.
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http://www.random.org/. Very useful if you need anything random - a string, a hex code, a number in binary, even a bitmap.
IMAGE(http://www.random.org/cgi-bin/randxbm?width=64&height=64)

[ Wednesday, September 07, 2005 22:40: Message edited by: Arancaytar ]

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That bitmap doesn't look very random.

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quote:
Originally written by Laudanum:

That bitmap doesn't look very random.
In what way does it look non-random? It's generated by the same process as the other random numbers on the site, apparently from atmospheric noise. They have an explanation page somewhere.

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At the time I made that post, the right half of the image was white with a couple of regularly-spaced black bands, while the left half looked relatively random. I reloaded the image a couple of times with similar results. It's not happening at the moment, though. I suspect it's not actually the fault of the random bitmap generator, but rather because my browser sucks at displaying images.

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Another explanation would be that entropy has briefly reversed itself. Allegedly, it's not impossible, just infinitely improbable... :P

Hey! When I reloaded this page I saw the face of the Virgin Mary appear in that bitmap! :eek:

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Posts: 8752 | Registered: Wednesday, May 14 2003 07:00
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quote:
Originally written by Laudanum:

It wouldn't be a very good source of randomness. If you use the digits of pi in order, they're obviously going to be predictable. So you have to use some random method for picking digits, in which case you can just use that as your randomiser and skip the step involving pi.
Well, for the purpose of a simple calculator program, pi will do quite nicely. Who do you think will be able to pick up on that if you don't tell them.

And pi has also shown to have an almost perfectly random distribution of all 10 digits, so it is a really good number for that. I s'pose the square root of 2 would work too.

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quote:
Originally written by Benny Boy:

And pi has also shown to have an almost perfectly random distribution of all 10 digits
How many digits of Pi have been calculated to show this? Is it possible to make a prediction for the rest of Pi using only these digits?

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"Polaris leers down from the black vault, winking hideously like an insane watching eye which strives to convey some strange message, yet recalls nothing save that it once had a message to convey." --- HP Lovecraft.
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quote:
Originally written by Arancaytar:

Hey! When I reloaded this page I saw the face of the Virgin Mary appear in that bitmap! :eek:
You may jest, but being a mathematician I challenge you to work out the actual odds of that happening.

As for the bitmap, the first one looked random, but the second one looked rather uniform (on the left side).

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quote:
Originally written by Arancaytar:

quote:
Originally written by Benny Boy:

And pi has also shown to have an almost perfectly random distribution of all 10 digits
How many digits of Pi have been calculated to show this? Is it possible to make a prediction for the rest of Pi using only these digits?

A few million if I remember right. That should be enough to start over again once its done and not me noticed much.

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I remember it being something like 3 billion places

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quote:
Originally written by SupaNik:

quote:
Originally written by Arancaytar:

Hey! When I reloaded this page I saw the face of the Virgin Mary appear in that bitmap! :eek:
You may jest, but being a mathematician I challenge you to work out the actual odds of that happening.

As for the bitmap, the first one looked random, but the second one looked rather uniform (on the left side).

Given the immensely diverse number of patterns one could reasonably recognize as a face, and the even larger number of patterns a superstitious miracle-adherent is ready to declare a face, that's pretty impossible. However, it is possible to calculate the exact odds of one certain picture appearing.

1 : 2 ^ (64*64)

= 1 : 2^4096

[ Saturday, September 10, 2005 00:45: Message edited by: Arancaytar ]

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The Encyclopaedia Ermariana <-- Now a Wiki!
"Polaris leers down from the black vault, winking hideously like an insane watching eye which strives to convey some strange message, yet recalls nothing save that it once had a message to convey." --- HP Lovecraft.
"I single Aran out due to his nasty temperament, and his superior intellect." --- SupaNik
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quote:
Originally written by Eldibs:

I remember it being something like 3 billion places
Pi itself has been calculated to over 1 trillion places.

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With a modern computer processor generating a large number of "random" numbers as fast as it can, a trillion digits will last significantly less than an hour. That's a definite repetition problem.

—Alrael, who doesn't see how that would work better on a calculator. Yes, the processor is much slower, so you go through digits slower, but no calculators have all of pi stored. Most only store around 15 digits. That kind of "random" very quickly gets noticed.
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Mmmmm…pi. Sounds good right now.

I'm with Sullust, Casios are for learners and scholars. And cool people, like me.

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Posts: 830 | Registered: Tuesday, August 20 2002 07:00
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But like I said, this is just a simple calculator program, not the next new big project in programming. I'll bet even 15 digits would fool some people for a while. :P

But anyway, if that's not good, you could use the square root of two, which can be calculated on the fly.

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Sometimes random things don't look as random as they actually are, that is the beauty of it...

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quote:
Originally written by Jeros:

I bet a lot of people who get bored in classes probably do the same thing with their graphing calculators as well. I'm not the only one that does it, am I?
Are you kidding? Anyone who takes a math course at my school and doesn't do that is in a definite minority. Phoenix kept me entertained for hours. Falldown wasn't bad, either. Never got the hang of those FastTunnel-esque games, though.

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My casio couldn't play games...oh well... :(

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That's a good thing, it helps you learn.

*raises fist in the air with a bowed head*

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In Nature's family all are brothers.
Puff and blow and wheeze and hiss;
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You can never frighten me,
One who never fears is FREE!"
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quote:
Originally written by Lady Davida:

quote:
Originally written by Jeros:

I bet a lot of people who get bored in classes probably do the same thing with their graphing calculators as well. I'm not the only one that does it, am I?
Are you kidding? Anyone who takes a math course at my school and doesn't do that is in a definite minority. Phoenix kept me entertained for hours. Falldown wasn't bad, either. Never got the hang of those FastTunnel-esque games, though.

I spent most of the period bent over my calculator too, but I was usually trying to write programs for trigonometric formulas or statistics/probability stuff. Hey, it kept me occupied! :)

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The Encyclopaedia Ermariana <-- Now a Wiki!
"Polaris leers down from the black vault, winking hideously like an insane watching eye which strives to convey some strange message, yet recalls nothing save that it once had a message to convey." --- HP Lovecraft.
"I single Aran out due to his nasty temperament, and his superior intellect." --- SupaNik
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I just managed to make a program that calculates (directly translated from Dutch) The series of Fabernatchi. Doe anybody know it? or should I explain it?

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You mean Fibonacci.
F(0) = 0
F(1) = 1
F(n) = F(n-1) + F(n-2)

I don't think it's all that difficult to program. The only difference perhaps is whether you choose to have F(0) = 0 or 1...

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