This is very similar to Pascal's triangle, except for it goes up two levels instead of 1, and uses a different formula. In fact, it is very closely related to Pascal's triangle, since you can get these numbers as diagonals in Pascal's triangle. basically, Tnext(k) = 2*Tnow(k-1) - Tlast(k) As you can see, Chebyshev Polynomials are extremely common and appear in a large number of places. You can use them to do some kinds of trigonometry much faster, including some related to calculus, you can also find roots of things, and they are also important for other reasons that even I don't completely understand: http://milan.milanovic.org/math/english/fibo/fibo6.html http://en.wikipedia.org/wiki/Chebyshev_polynomials http://www.mathpages.com/home/kmath304.htm http://mathworld.wolfram.com/ChebyshevPolynomialoftheFirstKind.html Mainly, I just remember that Chebyshev Polynomials are Polynomials that represent various trigonometric identities relating to the identity: Cos(A+B) = Cos(A)*Cos(B) - Sin(A)*Sin(B), and Cos(2A) = 2*Cos(A)^2 - 1 Basically you can always express Cos(ax) = P( Cos(x) ), where P() is a Polynomial with Integer Coefficients. Then, you can also turn any power of a trig function into a sum of trig functions of integer coefficients of the trig function's arguement over some number. The way I display the Polynomial Coefficients is that I give constant, x, x^2, x^3, x^4, etc. coefficients. So, when it says 1 0 -8 0 8 in cell #5, that means that Cos(4x) = 1 - 8*Cos(x)^2 + 8*Cos(x)^4
