Every field has its own language to speak. And shouting into the field from "outside" that they should change is not polite.

E.g * if you redefine c = n-1 the connection between number of points and dimension is lost. * c ist very often used as a constant Skalar. E.g as the speed of light. Using it as a dimension of a problem is quite unintuitive.

Two points define a line, a polynomial of degree 1. A polynomial with 2 coefficients, ax + b.

Three points give us a quadratic, a polynomial of degree 2 with three coefficients, ax^2 + bx + c.

N points gives us a polynomial of degree N-1 with N coefficients.

Indexing coefficients by their associated power of X seems natural to some.

A(N-1).X^(N-1) + ... A(1).X^1 + A(0).X^0 (where X^0 == 1)

are the N indexed coefficients of a generic polynomial of order N-1.