Good morning,
I have a problem with understanding my homework. I have to write a program that computes a circumference of a parametric curve(it is really not important what curve it is), firstly by computing N points of the curve and comuting distances between them, to do this, I have to write a function ApproximateCircumference(Write real function ApproximateCircumference of integer parameter N, that computes circumference of polygon with N sides with vertexes equal to parameter t=(N-1)*2pi/N, t is the parameter in the parametric curve). Easy one.
The second task is, to write a function that computes lagrangean polynomial(interpolation) of k-1th order from k points. Also easy.
But the last task is, to write a function BetterCircumference that computes the circumference by extrapolates ApproximateCircumference(N/2^(k-1)) as function of x=1/N^2 in point x=0 where N would be equal to infinity.
I don't know how, I don't know what the third task means, I suppose I should use the Lagrangean polynomial, but how? What does that x=1/N^2 mean? N is constant, it is number of points/sides of a polygon in the first task...
I was asking for circumference.
As you say `circumference' of a polygon (instead of `perimeter') it makes me think that you would put arcs between the points.
After a second reading it seems:
_ Compute arc length with the polygonal approximation.
_ Change the number of points.
Now you've got a function s(N),
a) interpolate with a polynomial.
b) Instead of a polynomial, use a rational approximation. (¿?)