Last I knew, a secant in geometry is different from a secant function in trigonometry. Either way, that still doesn't explain how you came to your conclusion. I'm looking for the step-by-step process that you used to justify this statement.
Because in order to match the predictions of RET, a secant curve is what would be required.

We want to find y as a function of x. Using high school mathematics, we have the following relationships:
x = rθ
y + r = r / cos θ
Now all we need to do is relate the two:
y = (r / cos θ) - r
y = r * [sec (x/r) - 1]
I guess we talk about different things. I talk about blue line in this drawing. What you talk about?

And The light doesn't actually curve like blue line, it goes like red line, because else you would get very fast ascent in the end of the path but you don't. You get steady elevation, so the light would travel in your EA like red line, not like blue. But in both cases you o up from A to b and down from B to A.
We are talking about the same thing, then. Do you understand the difference between gradient and curvature? One corresponds to the first derivative of a function, the other to the second derivative. The blue line has opposite gradient if you go in the opposite direction, but the same curvature.
Why were you banned?
Irrelevant.
Yeah, like you've never made an irrelevant post or avoided a question.
Please stop derailing the thread.