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While using a piece of jewelry ie a fine chain hanging against a piece of graph paper then placing an origin, axes and scale on the paper I collected the position of the chain as a set of coordinates (x,y).

Entering the data into curve fitting software a perfect fit for a polynomial degree 2 was obtained.

Also fitted the data to a catenary made of exponentials.

My question is what does it mean to say the theoretical curve to model some data is this when you can adjust any polynomial within reason to get the same fit.

Entering the data into curve fitting software a perfect fit for a polynomial degree 2 was obtained.

Also fitted the data to a catenary made of exponentials.

My question is what does it mean to say the theoretical curve to model some data is this when you can adjust any polynomial within reason to get the same fit.

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