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That video was weird. On the subject of pi, you can youtube and find videos of people who have memorized like 600-2000 digits of pi.
I remember 16 :PQuote:
Originally Posted by Dianeva
I love how fast Steve runs in relation to the other kids.
I now feel like I know everything there is to know about pi.
Nothing says 'legit' like cultists in orange robes and traffic cone hats.
I know 97 digits.
I know pi to infinite accuracy so suck on that.
BSQuote:
Originally Posted by Xei
4/1 - 4/3 + 4/5 - 4/7 + 4/9 - 4/11 + etc. for however long you like. ;V
I double like your post, Xei, because in my time zone you posted at 3:14.
Shame that, I actually posted it at exactly pi o'clock but the forum's not accurate enough to show it. :(
I didn't know there was a taylor series for pi... cool :PQuote:
Originally Posted by Xei
That's not a Taylor series. Just a standard convergent series. A Taylor series will be a power series.
Last time I checked it looked like one.Quote:
Originally Posted by PhilosopherStoned
Sorry my mistake. They look similar.
It is interesting nonetheless.
Well if you think about it, there must be a series for pi of some form or other, otherwise how would it ever be calculated? A decimal is a kind of series after all.
You were not far off with the Taylor series thing though actually. The above is basically the simplest expression for pi, and it comes from putting x = 1 in the Taylor series of arctanx, and as tan(pi/4) gives 1, the resultant series gives you pi/4; then of course all you need to do is multiply it all by 4 to get pi.
sweetness :), I'm not a major math geek but I love this stuff. The formulas for calculating stuff
that everybody just does on the calculator. Like Sine/Cosine/Tangent ( taylor series ) and square
roots ( something similar to long division ). Can't get enough of it :P
Do you know if there's a formula for the inverse trig functions?
Yeah I know just what you mean, it's pretty awesome when you realise that all of those functions you've been using are just 'infinite polynomials'. It's kind of a watershed moment actually; if you like that kind of stuff then to be honest you'd probably like the stuff that's covered from degree level onwards: there's a dramatic shift in flavour from the basic application stuff you do at school (application of algebra, calculus, etc; essentially just 'doing questions' with the tools you've learned), to much more abstract concepts and the study of objects in their own right, such as Taylor series.
And sorry, when I said arctan I was probably using a notation you're not familiar with; it simply means 'inverse tangent', so the answer to your question is 'yes'. arccos and arcsin are here:
Taylor series - Wikipedia, the free encyclopedia
These are all found by a standard method which I'm guessing you know about already.
I am familiar with arctan, I just said inverse trig functions to sum up arctan, arcsin, and arccos.Quote:
Originally Posted by Xei
Ah okay, cool beans. At school it's normally just written tan^-1.
yeah I've seen it written all different ways. arctan, tan^-1, inverse tangent, atan.