You could try calculating the average distance of each set of points from the curve - perhaps better to look at the root mean square distance. Essentialy the standard deviation of the points from the curve.
You could think left hand expression => right hand expression as left hand expression implies right hand expression
left hand expression <= right hand expression as left hand expression is implied by right hand expression
So left hand expression <=> right hand expression is LHE implies...
Sometimes polish notation is called prefix, reverse polish is post fix and traditional is infix.
I.e. the operator is before, after or between the operands.
Incidentally polish in this context is pronounced as in a person from Poland not as in the stuff to make furniture shine.
It might be worth your while investigating post operator notation (sometimes called polish) in which the operator precedes the operands. No brackets are needed at all. (A variant is reverse polish in which the operator follows the operands. Hewlett Packard calculators used to use this)...
Many years ago I read the Fortran Technical manual fora UNIVAC1108. The routines implemented reduced the angle to 0-90 and then split to four ranges. Then it used a 5th degree polynomial in the square of the angle, different coefficients in each of the four ranges.
The function doesn't have to...
The irreducibility of a/b is assumed by the prover. At a later stage in the proof we show that a and b must have a common factor - there lies the contadiction that is the heart of the proof.
For an homogenous medium all properties are the same at any point (or at least the properties in which you are interested - you have to be certain that any properties that differ have no effect on what you are considering)
Assuming you are referring to a simple pendulum what is it's length, and the error in that measurement? The final calculated value for g will involve both errors .