Question for math geeks

[Orrex]

Given a particular angle, how do you determine the equation of the curve that best "fits" into that angle?

I'm sorry that I don't know the proper terminology, but you can see therefore why I'm having trouble researching the solution for myself. For all I know, it might be terrifically simple but I'm over-thinking it.

For example, if you have a 45° angle, what's the formula for the angle that snuggles into it most comfortably? What's this process called, if indeed it has a name?


A request for anyone who's passionate about the subject: be merciful and not too complainy about my awkward terminology; if I knew a better way to ask the question I would do so, so don't jump on me for a lack of precision, please!


Thanks!