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Favorite math theory/rules/law/et cetera.
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Topic: Favorite math theory/rules/law/et cetera. (Read 16926 times)
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Yeong
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Favorite math theory/rules/law/et cetera.
«
on:
March 02, 2011, 05:06:16 pm »
Well, mah favorite math law is L'Hospital's Law.
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squidgetx
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Re: Favorite math theory/rules/law/et cetera.
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Reply #1 on:
March 02, 2011, 06:35:37 pm »
Taylor Series. Just the fact that we can take practically any function and write it as a polynomial is mind-blowing. Not to mention you can use them to prove e^(ix)+1=0, which ties for second for me along with 1+2+3+4...=-1/12
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Re: Favorite math theory/rules/law/et cetera.
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Reply #2 on:
March 02, 2011, 06:39:08 pm »
Both of those are among my favorites, but since I study sequences (both infinite and finite) in my spare time, I think I gotta love things like the Riemann Zeta function... it's also yet another reason to love those Taylor Series ♥
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Re: Favorite math theory/rules/law/et cetera.
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Reply #3 on:
March 02, 2011, 06:41:57 pm »
Quote from: squidgetx on March 02, 2011, 06:35:37 pm
1+2+3+4...=-1/12
Remind me again how this can be even remotely possible? There seems to be no way to get that to work
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Re: Favorite math theory/rules/law/et cetera.
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Reply #4 on:
March 02, 2011, 06:44:07 pm »
Is it 1+2+3+4+... or is it 1-2+3-4+5-6...? I know one of them was proven to be -1/12 and the other to be -1/4
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Re: Favorite math theory/rules/law/et cetera.
«
Reply #5 on:
March 02, 2011, 06:45:08 pm »
My question is, how can 1+2+3+4... ever end up being less than 1?? You are starting with 1 and only adding positive numbers, how can you get negative? It seems mathematically impossible O.o
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Re: Favorite math theory/rules/law/et cetera.
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Reply #6 on:
March 02, 2011, 06:46:02 pm »
Euler's formula forever. It's actually true.
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Re: Favorite math theory/rules/law/et cetera.
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Reply #7 on:
March 02, 2011, 06:47:41 pm »
it seems that Eulers formula only deals with trig and complex numbers
Can i see some sort of mathematical proof or explanation?
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Re: Favorite math theory/rules/law/et cetera.
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Reply #8 on:
March 02, 2011, 06:48:20 pm »
I think you use Ramanujan sums? Yeah, these funky summation systems (Abel, Cesaro, Euler, etc) give you results like 1+1+1+1+... = -1/2, 1-1+1-1+1-... = 1/2, and 1-2+3-4+5-6+... = 1/4.
Let's add a geometry theorem: Given a hexagon that has an incircle, its opposite diagonals meet at a single point. (Brianchon)
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Re: Favorite math theory/rules/law/et cetera.
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Reply #9 on:
March 02, 2011, 06:48:44 pm »
It's here:
http://en.wikipedia.org/wiki/Euler's_formula#Proofs
It makes no sense, but apparently it makes sense O.o
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Re: Favorite math theory/rules/law/et cetera.
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Reply #10 on:
March 02, 2011, 06:52:58 pm »
Okay, after doing some reading, it was not fully explained in the original post that it is not a traditional sum, but in fact a Ramanujan Sum, which is *not* the same
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Re: Favorite math theory/rules/law/et cetera.
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Reply #11 on:
March 02, 2011, 06:53:17 pm »
That is because even math is theoretical
But think of this... when working with mod systems, negatives are really positive. So, say you are working in mod 8... you would count {0,1,2,3,...,6,7,0,1...}...
Now also consider the numbers that are not infinity, but by performing a mathematical operation, you still get that number (so n+a=n, n*a=n, et cetera).
Now say you work in mod r... -1 really equals r-1. Taking all of this into account, working with mod (r) where r is equal to one of the before mentioned "infinite" numbers, the very largest number is in fact -1. No matter how high you count, it has been proven you will never reach these numbers, but in a mod system, -1 means you are just 1 away from that number!
Anywho, that has nothing to do with the proof that 1+2+3+4... is less than 1, but it is still interesting, yes?
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Last Edit: March 02, 2011, 06:53:35 pm by Xeda112358
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Re: Favorite math theory/rules/law/et cetera.
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Reply #12 on:
March 02, 2011, 06:55:50 pm »
1+2+3+4... does not equal -1/12. It eauls -1/12R where R is the symbol denoting a Ramunujan Sum
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Re: Favorite math theory/rules/law/et cetera.
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Reply #13 on:
March 02, 2011, 07:30:35 pm »
∭
∞
-∞
(√(x²+y²+z²)e
-(x²+y²+z²))
)dxdydz =2ㅠ
The reason why is very fun to figure out, but should be rather obvious to some people
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Yeong
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Re: Favorite math theory/rules/law/et cetera.
«
Reply #14 on:
March 02, 2011, 07:32:15 pm »
(d/dx)ln x = 1/x
I know this is basic stuff, but without this, there's no complex d/dx ing!
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Favorite math theory/rules/law/et cetera.