# Thread: Are the notes wrong?

1. ## Are the notes wrong?

I've highlighted parts of the image I'm concerned with:

In other words, they want a cubic polynomial, i.e. $\displaystyle P_3$, and if they say that a given polynomial's degree is $\displaystyle n+1$, they must choose $\displaystyle n=2$ so that $\displaystyle n+1=3$.

Perhaps they should have written the degree of the poly is $\displaystyle n$, not $\displaystyle n+1$?

Something here seems inconsistent to me.

2. There doesn't seem to be any inconsistency. You need to use the zeros of the (n+1)th degree Chebshev polynomial in order to get an n'th degree polynomial approximation for a given function f(x).

Notice that a polynomial of degree n has n+1 coefficients (because of the constant term). You need to sample f(x) at n+1 points in order to get sufficient data to determine these coefficients. At the very simplest level, you need to sample the function at 2 points in order to get a straight line (i.e. degree 1) approximation for it.

3. Thanks. I sort of figured this a while after posting, but your post confirmed my thoughts.