TIL why you cannot construct a regular heptagon with compass and straight edge. I'll tell you all about it on the next episode of #Un-NaturalNumbers which we record tomorrow. Very excited!

#mathaky
#chebyshevpolynomials

Chebyshev Feature Neural Network for Accurate Function Approximation

dl.begellhouse.com/journals/558...

#NeuralNetworkApproximation #ScientificML #ChebyshevPolynomials

The weird thing here is, for both the Fibonacci and the Pell #MarkovNumbers, L(') proves to be a natural factor of A+(-)B. If one could generalize how this occurs, one would have a very clean explicit expression for Markov Numbers. #Unicity
#ChebyshevPolynomials of the 2nd kind

Alright, this is pretty beautiful. I have gotten the #ChebyshevPolynomials *out* of the equation. They were of magnificent utility while they lasted. Au revoir, #ChebyshevPolynomial... hopefully this will enlighten #MarkovNumber #Unicity somehow. It's a pretty fantastic equation. #MarkovNumbers

Ugh, I am stuck stuck stuck. I have a feeling that if I can re-build identity II to apply to negative subscripts (using Identity I again) I'll get some sort of weird infinite series that may be of utility. Tick, brain! #MarkovNumbers #Unicity #ChebyshevPolynomial #MarkovNumber #ChebyshevPolynomials

(2) Given that there is only one such sequence {z_j}, "c" only appears once on the tree.

Like holy fuck. #MarkovNumbers #MarkovNumber #Chebyshev #ChebyshevPolynomial #ChebyshevPolynomials #Unicity