Neat Math

[jpub]

The fourth root of (9^2+(19^2/22)) is Pi. Or close enough that my calculator only detects a difference in the 9th decimal place.
That's wild.
...

Yeah, I'm a nerd.--
Christopher Angel, aka JPublic
The Works of Christopher Angel
"Camaraderie, adventure, and steel on steel. The stuff of legend! Right, Boo?"

[zero sum mgame]

That is -very- cool. How in the world did you figure it out?
I've got something similar...assuming I remember the math right.
1
[sigma](-1^x-1)/(2x-1) approaches Pi/4 as x goes to infinity.
infinity
...that looks really bad. If I'm dredging things out of my brain correctly, that's an infinite series that generates the following fractions.
1/1 - 1/3 + 1/5 - 1/7 + 1/9 - 1/11...

Greetings, fellow nerd.

[Epsilon]

----------------
Epsilon
Nerds...

[jpub]

Actually, I came up with it independently from xkcd. I spend a lot of time screwing around with the calculator.
--
Christopher Angel, aka JPublic
The Works of Christopher Angel
"Camaraderie, adventure, and steel on steel. The stuff of legend! Right, Boo?"

[jpub]

speaking of which, if anyone knows a good shortcut for 'e', let me know.--
Christopher Angel, aka JPublic
The Works of Christopher Angel
"Camaraderie, adventure, and steel on steel. The stuff of legend! Right, Boo?"

[TheTwisted1]

The fraction 271801/99990 = 2.7182818281828 is a good approximation for e ~= 2.71828182845904
Further, if you want to compute e to any accuracy, a good series for e is Sigma{n=0 to inf}[1/n!] = 1+1+1/2+1/6+1/24+1/120+1/720+
(derived from the Maclauren series for e^x: Sigma{n=0 to inf}[x^n/n!] = 1+x+x^2/2+x^3/6+x^4/24+x^5/120+ , which actually converges for all x)
Lastly, e can be defined as the limit as n -> inf of (1+1/n)^n, though that converges too slowly to make a good estimate (n=10000 gives 2.718145936).
--The Twisted One"Welcome to Fanboy Hell. You will be spending eternity here, in a small room with Jar-Jar Binks and Dobby the house-elf."
"If you
wish to converse with me, define your
terms."

--Voltaire

[jpub]

I know the mathematical derviation technique, I've gone through the proofs as part of the math classes attached to my Engineering degree.
Neat tricks to come up with irrational numbers on a regular calculator amuse me.
www.jstor.org/view/002557...02p0376s/0
Gives a really neat link on how to come up with those fractions.
I particularly like the forumla for pi above because it's simple, easy to derive with a relatively simple calculator, and it's elegant.
I was hoping someone knew of a similar one for e.--
Christopher Angel, aka JPublic
The Works of Christopher Angel
"Camaraderie, adventure, and steel on steel. The stuff of legend! Right, Boo?"