The term interpolation is usually used in mathematical functions when determining a function for given values, which makes perfect sense. I don't see how that applies for strings, what is being interpolated? Am I missing something obvious?
Why is string interpolation named the way it is?
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Interpolation in mathematics is simply working out the things between two points(a). For example, cubic spline fitting over a series of points will give you a curve of some description (I consider a straight line to be a degenerate curve here so don't bother pointing out that some formulae generate such a beast) between each set of points, even though you have no actual data there.
Contrast this with extrapolation which will give you data beyond the endpoints. An example of that is seeing that, based on history, the stock market indices rise at
xpercent per annum so, in a hundred years, will be much higher than they are now.So it's a short step to the most likely explanation as to why variable substitution within strings is called interpolation, since you're changing things within the bounds of the data:
(a) The actual roots of the word are Latin
inter + polare, those translating to "within" and "polish" (in the sense of modify or improve). See here for more detail.