Here's something my fellow mathnerds may find interesting. This works rather well and fast. At n=3 you get 3.14159245757.

\pi=\sum_{n=0}^{\infty}\left(\frac{4}{8n+1}-\frac{2}{8n+4}-\frac{1}{8n+5}-\frac{1}{8n+6}\right)\cdot\left(\frac{1}{16}\right )^{n}

ah yes, the equation that gives the nth hex digit of pi! Quite amazing and rather accidental if I remember correctly.

I'm a pretty big fan of pi calculation techniques myself :)

who has the most base10 digits memorized if you count digits to the right of the decimal point? I've only got 25 of those digits memorized at the moment, certainly someone has more memorized than that.

35 dp :/

Here's a series that converges even faster - it adds 8 digits of accuracy for each increment of n:


\frac 1 \pi = \frac {\sqrt 8} {9801} \sum _{n=0} ^ \infty \frac{ (4n)! (1103+26390n)} {(n!)^4 396^{4n}}


Using Excel, I get the following values:

For n = 0: 3.14159273
Then adding n = 1: 3.141592654

I have absolutely no idea why this works.

I believe that may be one of Ramanujan's concoctions.

I believe that may be one of Ramanujan's concoctions.

Right - I cribbed it from here:

Pi (http://www.jimloy.com/geometry/pi.htm)

I thought so. It's amzing how anyone could come up with something like that. Shows you what a genius he was. Too bad he died in his early 30's.

calculating pi gives me sort of a buyers remorse. I am excited at the anticipation of calculating many decimal places to this mysterious number and the math involved but ultimately I'm disappointed because the result is largely useless to me.
I keep wondering if there's some use of my computing resources that would provide a more personally useful result than calculating pi or even participating in any of the distributed computing projects.

I keep wondering if there's some use of my computing resources that would provide a more personally useful result than calculating pi or even participating in any of the distributed computing projects.

You're right, in that knowing Pi past a few decimal places is for most practical applications pretty useless. Perhaps getting a bit off topic here, but I think some of the distributed computing project like SETI@home (http://setiathome.berkeley.edu/) are interesting, and potentially important.

I totally agree that seti@home and other various distributed computing projects are interesting and can probably produce important results. I run the "world community grid" projects on my machine when I'm at work and using their electricity & AC.
However, what would really be interesting is if I could use my cpu cycles on something that benefits me directly.
The problem is that I can't think of a problem that requires more time to compute than for me to gather the data while simultaneously being hard enough that I'm too slow and easy enough that the computer will return a result in a useful amount of time.
Do you see what I'm getting at?

Mr.galuctus please solve my question PLEASE and do give me a way to contact you cause I am a mathfreak

What question?

Hi mr.galactus

Mr.galctus
Please answer my question

Are you just being wacky? I don't know what you're talking about.

The question that is in my profile... its about trig func.

You mean the derivative of a\cdot{sin({\omega}t)?

If so, that's basic chain rule.

The derivative of sin(u) is cos(u)

The derivative of wt is w

Therefore, the derivative is awsin({\theta}t)

Take the derivative of the outside and multiply it by the derivative of the inside.

The outside is \underbrace{a\cdot{sin(u)}}_{\text{derivative is a\cdot{cos(u)}}} and the inside is u=\underbrace{wt}_{\text{derivative is w}}

So, we have awcos(wt). See?

Thanks a lot for the information... I needed it the most because my exams are approaching:)

I hope that helps. The chain rule is a biggy in calculus. Know it well.

For instance, suppose you wanted the derivative of sin(3x+2)

The derivative of sin(u) is cos(u)

But u=3x+2. You take the derivative of that too and multiply by cos(u)

So we have 3cos(3x+2). See how that works?

BTW, please rate my answer if you found it helpful.

While you're at it galactus, can you answer the question that's on the post-it note on my monitor? I mean, seriously, I've been waiting for weeks and you haven't responded yet! ;)

Ha Ha. Touche':)

When using a slide rule, try 22/7.

When using a slide rule, try 22/7.

A slide rule?! Now there's some practical advice! What value do you recommend we use for pi when doing calculations on an abacus?;)

Actually, I do value the simplicity of the slide rule, and the discipline it drove in keeping your powers of 10 straight. But I suspect you and I may be only two people on this forum who have had the pleasure of suffering through Chem and Physics exams having to do calculations with a slide rule!

I can't give advice re: using an abacus, but I had a lot of experience using the slide rule while obtaining my BSEE at Penn State.