I wrote something on a Fibonacci number generator. Is the proof a proof?
https://www.scribd.com/document/414774296/Fibonacci-and-Chebyshev-Polynomials
Question
My formulas are: y=(x+a)^2 x=(-y+a)^2 I would like to solve for a where they touch (exact solution). Here is a graph demonstrating what I mean: As you can see, I have attempted to solve for a by making them closer and closer. I think 1.100917368760402698 ≤ a ≤ 1.100917368760402699, but floating point error may have reduced the accuracy of that range, but it should be near those numbers at least. There will also be a negative solution of a , which will be exactly negative I believe.
Sorry, but I can't view that file :(, can you give the link again?
I changed the link to scribd. I've never used it before so I don't know if it works.
thanks
interesting work, anw you can see my post if needed
Nice, I didn't know about that. It works for all cases of k in (1+sqrt(k))^n. Francois Viete invented the binomial function. He did a binomial function with sin(n*theta), and cos(n*theta). I think he probably messed around with vectors in an unconventional way. He is also behind the quadratic formula somewhat.