Misuse of the term "resonance"

The Electrician said:

You don't quite have it right; your example should be like this:

'Now there are 3 holes on either side of the beam their positions referenced with relative coords to the beam centre point, so that the position of 3rd hole xc is determined by the positions of the first 2 holes;
xa = 2"
xb = 3"
xc = (xa*xb) = (2"*3") = 6"" (inches squared, but it should be just inches)
...

In freshman physics we learn that if the units don't work out as expected at the end of a calculation, you've done something wrong.

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In understand the point about the inches squared, but I think it is not relevant to the argument as my stance is on the multiplying of *any* 2 numbers that have - signs and it's not for describing an area but for generating any shape that requires multiply or divide.

If you are generating a cuved path for CNC use where the curve (or any shape) must be generated equally with mirror symmetry on both sides of the 0 line then I don't have any problem with doing
(-)x2 = (-)x1*(-)y1
or if you prefer
(-)(x2 = x1*y1)
but it's just easier to write it as
-6 = -2*-3

The Electrician said:

...
Suppose:

xa = 2"
xb = -3"

Then what would xc be? Would it be 6, or -6, or zero, or would it be undefined? Where on the beam would the xc hole be?

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In the case of those numbers you would have to use whichever system gives the correct result.

Since we are talking real world coordinate generation where the curve existed on both sides of zero I would offset the entire array to one side of zero, then do the curve generation there then offset it back to it's original location crossing zero. But there are probably other ways to do it depending what the actual task is and what shape needs to be generated and what symmetry is required in the result.