A word with meaning smoothly connecting two known things
Let's say we have two facts known:
Fact A: When there is no cat, there are 10 mice.
Fact B: When there is 10 cats, there is no mouse.
Suppose now I got a new result:
New result: When there is n cats, then there are 10 - n mice.
So this new result generalizes the two known facts.
My question is: Is there any verb to describe that the new result does nicely connect the two known facts smoothly, like "The new result 'verb' the Fact A and the Fact B"?
It's like the so-called "polynomial interpolation", I mean drawing a continuous line between two known points, but somehow the word "interpolate" has no such "connection" meaning.
You already have it. The equation generalizes the earlier data. If you are concerned specifically with the mathematical quality of smoothness, it is a property of your generalized model. You chose a smooth, well behaved expression as a generalization. You may also be trying to get at the exactness of the fit (a yes/no proposition) or the goodness of a fit (graded with a formal metric such as least squares method). But these aren't matters of smoothness. The idea of smoothness doesn't connect a model to it's data sample.
Generalization is the process of identifying the parts of a whole, as belonging to the whole. The parts, completely unrelated may be brought together as a group, belonging to the whole by establishing a common relation between them.
Wikipedia: generalization - https://en.wikipedia.org/wiki/Generalization
In the second chapter of the Springer book Advanced Mathematical Thinking, Tommy Dreyfus defines generalization as the derivation or induction from something particular to something general by looking at the common things and expanding their domains of validity.
Posted on August 21, 2016 by Mohammed Kaabar
American Mathematical Society blog - https://blogs.ams.org/mathgradblog/2016/08/21/role-generalization-advanced-mathematical-thinking/
If the main idea is to expand the domain for which you can model and predict results, use generalize. If the main idea is to point out a construct that allows a set of happenings to be understood as separate instances of a single phenomenon, then the process is called abstraction.
5 : to consider apart from application to or association with a particular instance
Merriam Webster: Abstract - https://www.merriam-webster.com/dictionary/abstract
With the cats and mice, you already had the notion that there should be some smooth relationship, so use generalize because the abstraction had already been done.