Moderators: gmalivuk, Prelates, Moderators General
wing wrote:I'm sorry... But that was THE funniest thing I've ever read on the interbutts.
mathmagic wrote:That... is really odd. Theoretically, that shouldn't happen since pi is irrational (ie. can't be expressed as a fraction), so saying that:
(94613256)*pi = 297236310
Is implying that:
pi = ^{297236310}/_{94613256}
Which is obviously not true. It just must be a very, very, *very* good approximation of pi; such a good approximation that both Google AND my TI-83 both just round up to 1 when you divide that fraction by pi. I'm guessing it's accurate enough to pi to have the same value as the amount of digits that the calculator/Google can store.
$ perl
use Math::BigFloat;
$pi = new Math::BigFloat "3.141592653589793238462643383279502884197169399";
print $pi*94613256/2, "\n";
__END__
148618154.9909052133288675624294648629676
Some of us exist to find out what can and can't be done.
Others exist to hold the beer.
Given floating point roundoff, it doesn't have to be that good an approximation.
quintopia wrote:I think the question wasn't answered and I want to know too. What fraction of integers x have pi*x with at least 9 zeros after the decimal?
Some of us exist to find out what can and can't be done.
Others exist to hold the beer.
mathmagic wrote:pi = ^{297236310}/_{94613256}
Which is obviously not true. It just must be a very, very, *very* good approximation of pi; such a good approximation that both Google AND my TI-83 both just round up to 1 when you divide that fraction by pi.
Cosmologicon wrote:There's about a 2% chance that if you do what the OP did you'll get as close to a whole number. If your calculator only has 9 display digits, though, then it's impossible for it to display a number in the billions as anything but a whole number. If it shows 11 digits, it should not have displayed it as a whole number. So, I don't really get what happened.... Does the OP's calculator display exactly 10 digits?
Some of us exist to find out what can and can't be done.
Others exist to hold the beer.
Cosmologicon wrote:Does the OP's calculator display exactly 10 digits?
wing wrote:I'm sorry... But that was THE funniest thing I've ever read on the interbutts.
It might be a very very *very* good approximation in absolute terms, but compared with some others it's not so hot. 245850922/78256779 is about 2.5 million times better, and it's shorter.
Twasbrillig wrote:Cosmologicon wrote:Does the OP's calculator display exactly 10 digits?
Yes, and does my new avatar throw you off by THAT much, Cosmo?
Cosmologicon wrote:Twasbrillig wrote:Cosmologicon wrote:Does the OP's calculator display exactly 10 digits?
Yes, and does my new avatar throw you off by THAT much, Cosmo?
What? Anyway, if your calculator only displays 10 digits, then any random number with 9 digits left of the decimal that you choose to display has a 1-in-10 chance of appearing as an integer. So, I wouldn't go buying lottery tickets thinking it's your lucky day.
wing wrote:I'm sorry... But that was THE funniest thing I've ever read on the interbutts.
mosc wrote:How did you LEARN, exactly, to suck?
Twasbrillig wrote:Also, I was previously referring to how you called me "OP", even though we've had so many discussions on the fora in the past...
Some of us exist to find out what can and can't be done.
Others exist to hold the beer.
btilly wrote:OP means Original Poster. As in the person who started the thread.
In this discussion you're the OP.
I want to be!Steroid wrote:Don't want to be.bigglesworth wrote:If your economic reality is a choice, then why are you not as rich as Bill Gates?
22/7 wrote:btilly wrote:OP means Original Poster. As in the person who started the thread.
In this discussion you're the OP.
Yes, but OP tends to get used when you're not thinking of someone specifically, but rather the initial idea presented in the thread. If I'm actually fairly familiar with the person, I'll refer to them using their handle (or some kind of shortened version of it) rather than calling them OP.
Some of us exist to find out what can and can't be done.
Others exist to hold the beer.
LoopQuantumGravity wrote:394372834342725903069943709807632345074473102456264
-----------------------------------------------------------------------
125532772013612015195543173729505082616186012726141
Gives Pi correct to 102 decimals .
shill wrote:LoopQuantumGravity wrote:394372834342725903069943709807632345074473102456264
-----------------------------------------------------------------------
125532772013612015195543173729505082616186012726141
Gives Pi correct to 102 decimals .
This one should be correct to 103 decimals:
314159265358979323846264338327950288419716939937510582097494459230781640628620899862803482534211706798
-----------------------------------------------------------------------------------------------------------------------------------------------
100000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
(Please don't shoot me.)
I want to be!Steroid wrote:Don't want to be.bigglesworth wrote:If your economic reality is a choice, then why are you not as rich as Bill Gates?
LoopQuantumGravity wrote:394372834342725903069943709807632345074473102456264
-----------------------------------------------------------------------
125532772013612015195543173729505082616186012726141
Gives Pi correct to 102 decimals .
0.662790697674...
= 0 + 1/(1 + 1/(1 + 1/(1 + 1/28)))
= 0 + 1/(1 + 1/(1 + 1/(29/28)))
= 0 + 1/(1 + 1/(1 + 28/29))
= 0 + 1/(1 + 1/(57/29))
= 0 + 1/(1 + 29/57)
= 0 + 1/(86/57)
= 0 + 57/86
= 57/86
Some of us exist to find out what can and can't be done.
Others exist to hold the beer.
22/7 wrote:shill wrote:LoopQuantumGravity wrote:394372834342725903069943709807632345074473102456264
-----------------------------------------------------------------------
125532772013612015195543173729505082616186012726141
Gives Pi correct to 102 decimals .
This one should be correct to 103 decimals:
314159265358979323846264338327950288419716939937510582097494459230781640628620899862803482534211706798
-----------------------------------------------------------------------------------------------------------------------------------------------
100000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
(Please don't shoot me.)
That's actually *EXACTLY* what I thought when I saw the "accurate to 102 decimals" thing.
22/7 wrote:shill wrote:LoopQuantumGravity wrote:394372834342725903069943709807632345074473102456264
-----------------------------------------------------------------------
125532772013612015195543173729505082616186012726141
Gives Pi correct to 102 decimals .
This one should be correct to 103 decimals:
314159265358979323846264338327950288419716939937510582097494459230781640628620899862803482534211706798
-----------------------------------------------------------------------------------------------------------------------------------------------
100000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
(Please don't shoot me.)
That's actually *EXACTLY* what I thought when I saw the "accurate to 102 decimals" thing.
mosc wrote:How did you LEARN, exactly, to suck?
SimonM wrote:Look how many more numbers you'd have to remember though!
btilly wrote:22/7 wrote:btilly wrote:OP means Original Poster. As in the person who started the thread.
In this discussion you're the OP.
Yes, but OP tends to get used when you're not thinking of someone specifically, but rather the initial idea presented in the thread. If I'm actually fairly familiar with the person, I'll refer to them using their handle (or some kind of shortened version of it) rather than calling them OP.
That differs widely by person. Speaking personally, I'll often call someone I know well OP if my intent is to refer back in some way to what the discussion started off being about.
Why would I do that? Because even though I know the original poster, I don't assume that all of the people I am addressing know the original poster, or are paying close enough attention to realize that this was the person who started the conversation.
wing wrote:I'm sorry... But that was THE funniest thing I've ever read on the interbutts.
gmalivuk wrote:SimonM wrote:Look how many more numbers you'd have to remember though!
Not really. The continued fraction one requires remembering
394372834342725903069943709807632345074473102456264/125532772013612015195543173729505082616186012726141
and then computing. Whereas just remembering the digits outright requires remembering
3.14159265358979323846264338327950288419716939937510582097494459230781640628620899862803482534211706798
#! /usr/bin/ruby
i = ARGV.map {|x| x.to_i}.reverse
n = 1
m = 0
i.each do |x|
# Flip numerator and denominator
n, m = m, n
# Add x
n += x*m
end
puts "#{n}/#{m}"
Some of us exist to find out what can and can't be done.
Others exist to hold the beer.
Twasbrillig wrote:btilly wrote:I'll often call someone I know well OP if my intent is to refer back in some way to what the discussion started off being about.
Why would I do that? Because even though I know the original poster, I don't assume that all of the people I am addressing know the original poster, or are paying close enough attention to realize that this was the person who started the conversation.
We try to talk to each other on a more personal level on the fora, Registered User #17229... I mean btilly. It's just a courtesy thing.
Cosmologicon wrote:Twasbrillig wrote:btilly wrote:I'll often call someone I know well OP if my intent is to refer back in some way to what the discussion started off being about.
Why would I do that? Because even though I know the original poster, I don't assume that all of the people I am addressing know the original poster, or are paying close enough attention to realize that this was the person who started the conversation.
We try to talk to each other on a more personal level on the fora, Registered User #17229... I mean btilly. It's just a courtesy thing.
It must be an unspoken rule. This is the first I've heard of it. I didn't mean to hurt your feelings.
Cosmologicon wrote:It might be a very very *very* good approximation in absolute terms, but compared with some others it's not so hot. 245850922/78256779 is about 2.5 million times better, and it's shorter.
J Spade wrote:Well, π • π^{-1} = 1
…Sorry.
Some of us exist to find out what can and can't be done.
Others exist to hold the beer.
mathmagic wrote:Given floating point roundoff, it doesn't have to be that good an approximation.
I just have no idea how many digits Google or my calculator actually hold. I figured Google would hold enough to not have to round...
btilly wrote:J Spade wrote:Well, π • π^{-1} = 1
…Sorry.
That wasn't worth apologizing for. Compare with
I + π = no more π
Now that is apology-worthy!
Yakk wrote:mathmagic wrote:Given floating point roundoff, it doesn't have to be that good an approximation.
I just have no idea how many digits Google or my calculator actually hold. I figured Google would hold enough to not have to round...
... this is a joke, right?
mathmagic wrote:Yakk wrote:mathmagic wrote:Given floating point roundoff, it doesn't have to be that good an approximation.
I just have no idea how many digits Google or my calculator actually hold. I figured Google would hold enough to not have to round...
... this is a joke, right?
In what way?
I figured that if an approximation such as the OP's approximation was accurate to x decimal places, I figured that it would have to be a pretty good approximation for Google to just read the answer out as pi. I didn't realize that Google's memory allocation only allowed for n decimal places, where n < x.
If it's a crime to not know off-hand the amount of decimal places that Google stores, then I'm guilty as charged.
mosc wrote:How did you LEARN, exactly, to suck?
SimonM wrote:I think its because it sounded like "Google would hold enough to never have to round..."
mathmagic wrote:I'm guessing it's accurate enough to pi to have the same value as the amount of digits that the calculator/Google can store.
That... is really odd. Theoretically, that shouldn't happen since pi is irrational (ie. can't be expressed as a fraction), so saying that:
(94613256)*pi = 297236310
Is implying that:
pi = ^{297236310}/_{94613256}
Which is obviously not true. It just must be a very, very, *very* good approximation of pi; such a good approximation that both Google AND my TI-83 both just round up to 1 when you divide that fraction by pi. I'm guessing it's accurate enough to pi to have the same value as the amount of digits that the calculator/Google can store.