[ Which one do you prefer working with ] Pi or e (1 Viewer)

Forbidden. · Jun 19, 2008

Trebla said:
e = 1 + 1/2! + 1/3! + 1/4! + ............
e = lim _{n ->∞} (1 + 1/n)ⁿ

π = 4 - 4/3 + 4/5 - 4/7 + 4/9 - 4/11 + ..........

Any more?

3unitz said:
pi²/6 = 1 + 1/2² + 1/3² + 1/4² + ...

<3

Wha ... what the fuck? Constants being expressed as sums?
I thought it was peculiar that the sine and cosine function could be expressed as a sum of a Taylor series (whatever it was called).
Damn integration.

Odbe · Jul 7, 2008

I love pi but e is quicker for me to write and less likely to turn out illegible if I'm writing quickly.

marcquelle · Oct 8, 2008

i like pie

and π =

3.1415926535897932384626433832795028841971693993751058209749445923078164062862089986280348253421170679

i learnt it in year 9 maths when it was posted up around the room and was often bored so i learnt pi to 100 places off by heart

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tommykins · Oct 9, 2008

回复: Re: [ Which one do you prefer working with ] Pi or e

still doesn't beat this girl who can recite it to 625 places at our school.

she's called 'pi dude'. haha

tommykins · Oct 9, 2008

回复: Re: 回复: Re: [ Which one do you prefer working with ] Pi or e

Charity F said:
that's... incredibly sad.

tell me about it- was humorous when we decided to use our walkway and write out all the digits though.

sirfeathers · Oct 9, 2008

Pi. Go the Greeks!

tacogym27101990 · Oct 9, 2008

theres some savant dude that recited pi to 20,000 digits on some thing called pi day
took him like 8 hours
he learnt it in 2 weeks aswell

Forbidden. · Oct 9, 2008

Damn can't change poll vote, e is getting more interesting now.

Trebla said:
e = 1 + 1/1! + 1/2! + 1/3! + 1/4! + ............
e = lim _{n ->∞} (1 + 1/n)ⁿ

π = 4 - 4/3 + 4/5 - 4/7 + 4/9 - 4/11 + ..........

Any more?

Guaranteed my bank manager knows that limit you mentioned.

3unitz said:
well thats where some of them come from

tan^-1 x = x - x³/3 + x⁵/5 - x⁷/7 + ...

sub in x = 1, and you'll get a series for pi/4

Now that I am learning Taylor polynomials and series this stuff is actually pretty cool.

bored of sc · Oct 9, 2008

Re: 回复: Re: [ Which one do you prefer working with ] Pi or e

tommykins said:
still doesn't beat this girl who can recite it to 625 places at our school.

That's not sad, that's amazing!

To OP, you should put in a third and a fourth option "Both" and "Neither".

pLuvia · Oct 9, 2008

Pi even goes beyond maths and into the economic world it also is used to be a symbol for inflation

Except that doesn't mean inflation is equal to 3.142 blah blah blah

Other than that, e is so much more useful

tommykins · Oct 9, 2008

e is awesome but i love pi, just the way of writing it is awesome.

Timothy.Siu · Oct 9, 2008

definitely pi, but maybe coz i haven't really learnt e that much yet...but pi is cool, at least u can eat it......

studentcheese · Mar 18, 2009

pi.The use of pi in integration is really elegant. e is annoying. I find it confusing doing differentiation with e.

gcchick · Mar 18, 2009

pi ftmfw.

possessionless · Mar 27, 2009

duckcowhybrid · Mar 27, 2009

Pie.

I don't know. Pi is easier to work with. e is natural, like sex. So I can't decide.

McLoving · Mar 27, 2009

e is elegant

Drongoski · Mar 28, 2009

Certainly e .. it is so rich! Just consider a few below:

$e^{x}\ \ =\ \ \sum_{k=0}^{\infty }\frac{x^{k}}{k!}\ \ =\ \ 1\ +\ \frac{x}{1!}\ +\ \frac{x^{2}}{2!}\ +\ \frac {x^{3} } {3!}\ +\ \frac{x^{4}}{4!}\ + \ \ \cdots \\ \\ \\ sin\ x\ \ =\ \ \frac{x}{1!}\ -\ \frac{x^{3}}{3!}\ +\ \frac{x^{5}}{5!}\ -\ \frac{x^{7}}{7!} \ +\ \ \ \cdots \\ \\ \\ cos\ x\ \ =\ \ \ 1\ -\ \frac{x^{2}}{2!}\ +\ \frac{x^{4}}{4!}\ - \ \frac{x^{6}}{6!}\ +\ \ \ \cdots \\ \\ \\ e^{ix}\ \ =\ \ \sum_{k=0}^{\infty }\frac{(ix)^{k}}{k!}\ \ =\ \ (1\ -\ \frac{x^{2}}{2!}\ +\ \frac{x^{4}}{4!}\ -\ \ \cdots \ )\ \ +\ \ i\ (\ \frac{x}{1!}\ -\ \frac{x^{3}}{3!}\ +\ \frac{x^{5}}{5!}\ -\ \ \cdots )\\ \\ \therefore \ \ e^{ix}\ \ =\ \ \ cos\ x\ \ \ +\ \ \ i\ sin\ x\ \ \ \ =\ \ \ cis\ x \\ \\ \\ e^{i\pi }\ =\ -1\\ \\ (\ cis\ \theta \ )^{n}\ \ =\ \ (e^{i\theta })^{n}\ \ =\ \ e^{in\theta }\ \ =\ \ cis\ n\theta \ \ =\ \ De\ Moivre's\ Theorem\ \\$

Drongoski · Mar 28, 2009

In addition:

$\\ \\ \\ e^{i\theta }\ \ \ =\ \ cos\ \theta \ \ +\ \ i\ sin\ \theta \\ \\ e^{-i\theta }\ \ =\ \ cos\ \theta \ \ -\ \ i\ sin\ \theta \\ \\ \therefore \ \ \ sin\ \theta \ \ =\ \ \frac{e^{i\theta }\ -\ e^{-i\theta }}{2\ i}\\ \\ \ \ \ \ cos\ \theta \ \ =\ \ \frac{e^{i\theta }\ +\ e^{-i\theta }}{2}\\ \\ e\ \ =\ \ 1\ +\ 1\ + \frac{1}{2!}\ +\ \frac{1}{3!}\ +\ \frac{1}{4!}\ +\ \ \cdots \\ \\ \ \lim_{x\to \infty }\ \left (1\ + \ \frac{1}{x} \right )^{x}\ \ =\ \ e$

tommykins · Mar 28, 2009

there are also series' that concern pi .

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[ Which one do you prefer working with ] Pi or e (1 Viewer)

Which one do you like pi or e

Pi

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