You are not logged in.
I couldn't understand all of this but I can help you with the last equation:
c1≈2.5
,I think.
And for the integral - it can't be simplified.
Simplified area:
Area = 5.66169988597863380413031960736...
I'm simplifying the AREA...
And here's the proof thingy:
Let ff[x]=(x)
The wanted area won't change if we push it one up. We to this to reduce ff to positive function.
We want S+S1+S3.
(x,y) means point x,y.
so S = INEGRAL - S2.
Now we'll find S1 and S3:
Then
Ready! here is it:
Ha, ha, ha!
I tougth a while and I got very simple geometric solution.
But you must wait a wnile to make a pictures.
But it's useless, because I don't know non-trivial terms for a function to be periodic.
I found something:
Number r is:
1.Rational, if the function
Here's a simple example:
we use the function f(x)=x^2.(picture 1)
f-¹(y) = {sqrt(y) (picture 2) OR -sqrt(y) (picture 3)}
Then the Riemann surface of the function f-¹(y) is the union of the plots(picture 4)
3.(answer): I think I understood what is this.
But how to explain it?
A Riemann surface is a surface-like configuration that covers the complex plane with "sheets.". When we have a functin over the complex plaine C, which is not "single valued":
∃ z1,z2 ∈ C: (z1)=(z2)=y.
What will we get for the inverse function of (z)?
Here's "logical" answer:
-¹(z) =={1-¹(z) OR 2-¹(z)}.
In the general case -¹(z) may be union of k "single valued" functions.
The riemann surface of -¹(z) is the union of the graphs of these functions.
We can use Euclidean plane, too.
3. What is Riemann surface?
2 (answer). As i understood it is just Euclidean plane. Is that right?
2. What is cartesian plane?
I need a function dic(x) that gives 1 when x is rational and 0 when it's irrational.
Please give me some advice.
I think there will exist such.
OK. We have simple alogritm for ax+by. I know it as Euler's reduction algoritm.
The next general case:
ax^2+by=c
I'm starting exploring internet...
1. What is an eliptic curve?
I have a great idea:
Do you want to understand it?
I'm offering to discute the proof from the begining to the end. We'll post what we don't understand.
Are you in?
Thank you very much.
The coeficient for x^2:
(x-a1)(x-a2)(x-a3) =>-a3x^2-a2x^2-a1x^2
-(a1+a2+a3)x^2=+3x^2 =>
a1+a2+a3=-3
a[1]=const
a[2]=F[a[1]]
a[3]=F[a[1],a[2]]
a[4]=F[a[1],a[2],a[3]]