@realisenothing
Yep, solvability of a polynomial equation is related to a certain group theoretic property. The symmetric group S_n has this property iff n < 5.
(And A_60 fails to have this property as it is structurally pretty much the same as S_5.)
Last edited by glittergal96; 25 Dec 2015 at 9:55 AM.
So, to be more explicit about the geometric series approach to that summation:
where
is the geometric series in the unit disk (which is easy to differentiate).
This gives us the rational function expression for S.
An Identity that comes from the proof of Euler's Partition Theorem:
In other words...
Don't ask me about the radius of convergence, I have no idea.
If I am a conic section, then my e = ∞
Just so we don't have this discussion in the future, my definition of the natural numbers includes 0.
Radius of convergence will just be 1.
A must know for the Ext 2 student:
Fundamental Theorem of Algebra
This has appeared elsewhere on this forum before:
Expressions for the Golden Ratio
If you square the first 9 numbers with only 1's in them:
If I am a conic section, then my e = ∞
Just so we don't have this discussion in the future, my definition of the natural numbers includes 0.
Very famous result on what e actually is:
Still famous but not as famous result on what e is, esp amongst HSC students:
Tbh isn't the first statement really just a Taylor series?
If I am a conic section, then my e = ∞
Just so we don't have this discussion in the future, my definition of the natural numbers includes 0.
987654321 is divisible by 9
987654312 is divisible by 8 (this particular one gives 123456789 btw)
987654213 is divisible by 7
987653214 is divisible by 6
987643215 is divisible by 5
987543216 is divisible by 4
986543217 is divisible by 3
976543218 is divisible by 2
876543219 is divisible by 1
0123456789 * 2 = 246913578 (a permutation of 0123456789)
And likewise up to 100; excluding multiples of 3
There is approximately a 50% chance of two people sharing the same birthday in a room of 23 people
~ First in Drama 2015 ~
If I am a conic section, then my e = ∞
Just so we don't have this discussion in the future, my definition of the natural numbers includes 0.
Certainly not a pure mathematician, but Cauchy's Integral Formula stands out for me.
Then I moved to stats.
That's not a bad thing, there are unsolved problems in stats applicable to the real world such as p-values, error values, correlation vs. causation, interpolation of data, etc.
Most of these are relevant to the sciences, as statistical methods are required for collecting any information. Even the medical fields and the humanities require it.
But I digress.
If I am a conic section, then my e = ∞
Just so we don't have this discussion in the future, my definition of the natural numbers includes 0.
There is a lot of highly theoretical mathematics here.
Does anyone have more real-world mathematical statements?
(The birthday problem was a good one)
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