I believe the following 4 questions I have, are all related to eachother.
Question 1: Of course I've been using constants, variables and parameters for a long time, but I sometimes get confused with the definition. It seems to me that these terms are used very loosely.
Let's say we have a second degree polynomial e.g. $ax² + bx + c$. I've heard people say $a, b, c$ are both constants and parameters.
I understand they are parameters, since they allow us to have a 'family' of second degree polynomials. What I mean by that is that if e.g. $c$ is incremented by one, it becomes a different function, since the graph of the function would be shifted up by one.
Why do people call them constants as well though? AFAIK, constants are fixed, e.g. $\pi, e, \varphi$. They would be the same value in any given context, and never change. The parameters $a, b, c$ however, never change with respect to the function, but they represent multiple values, unlike $\pi$.
Question 2: To make things even more confusing, there's also contrast between unknown and known variables. Are known variables the same thing as parameters? If they are known, why don't we just throw in the real value of the variable?
Question 3: If we have $ax + 3$, how does one know if a represents a variable like x, so it's a function that can take two inputs, or if it's a parameter? Should the context provide this information?
In the pythagoream theorem, are $a$, $b$ and $c$ constants, variables or parameters? If they are variables, then why are they represented by the letters a, b, c instead of x, y, z? I've read a, b and c are commonly used as known variables.