[Rampage]

Happy PI Day!  That's right, it's March 14 today!  Math and science nerds galore!

Post anything related to PI, Euler, etc.  Or did I mention PIES?!?!

NOTE: I'm just bored!

[WMCoolmon]

Great, a math pr0n thread. At least CP will be happy.

[Stunaep]

It's the national Mothertongue day here. So **** PI.

[Tiara]

Its the national End of school - Beginning of a new weekend day over here

[Stunaep]

oh yes, it's the end of school - beginning of the spring break day here.

[Styxx]

* yawns *

[Joey_21]

Here's some c++ programs I've been working on lately... one calculates Bernoulli numbers recursively and the other makes usage of the numbers in stirling's approximation for the logarithm of the gamma function (and applies anti logarithm to get exact gamma function value).

http://denebsystem.250free.com/bernoulli.exe
http://denebsystem.250free.com/lngamma.exe

Edit: Oh ya, just now added the factorial, double factorial, and beta function in there... easy to implement.

[beatspete]

 Nice on styxx.

[Knight Templar]

CP should release PI today. Yes, Procyon Insurgency.  

[CP5670]

This has to be the best thread around in a while. unfortunately, my campaign isn't ready yet though. but soon...

Styxx: That thing is really neat. It must have taken the guy quite a while to do it though...

Anyway, hmm lets see, here is some neat stuff involving pi and bernoulli numbers:



can anyone prove them?

[Joey_21]

Originally posted by CP5670

Which log base is that?

[CP5670]

eh...you know, the usual one, base e

[Joey_21]

Originally posted by CP5670
eh...you know, the usual one, base e

Hmm... weird... I don't get those results when I sum it...

[CP5670]

probably a typo on my part then, one minute...

hmm, it seems to work fine for me if I try it numerically; how are you calculating it?

[Joey_21]

Originally posted by CP5670
probably a typo on my part then, one minute...

hmm, it seems to work fine for me if I try it numerically; how are you calculating it?

Code: [Select]


(java app)

sum = 0;
for (i = 1; i <= 9999999; i++)
sum += (i * Math.log(1 + 1/i) + 1/(2*i) - 1);



[CP5670]

The convergence is quite slow, but with that many terms you should still get quite a few digits. The value I am getting (and an approximate value of the expression on the right) is 0.3696692992460937; what are you getting there?

[Joey_21]

-9999998.30685282

[Goober5000]

I think just plain "log" stands for logarithm base 10.  You're supposed to use "ln" for natural logarithm (base e).  Java ought to have a ln function - if not, use log(...)/log(e).

[Joey_21]

Originally posted by Goober5000
Possibly the program may be using log base 10.  I think you're supposed to use ln for natural logarithm (base e).  Java ought to have an ln function - if not, use log(...)/log(e).

Java's default log is base e.

[CP5670]

-9999998.30685282

oh wait I think I know what is going on; the series is not absolutely convergent, and after some one million terms they start to oscillate between positive and negative values, so that may well be skewing the result. Try something like 50000 terms and see if that works any better.

I think just plain "log" stands for logarithm base 10. You're supposed to use "ln" for natural logarithm (base e). Java ought to have a ln function - if not, use log(...)/log(e).

This is one of the (many) cases of bad notations used in math. It seems that physicists and applied math guys use ln while pure math guys use log. Personally I like log much better; I mean, what the heck is ln supposed to mean when it is called a logarithm, and the e base is about the only one ever used anyway...