A connection between mathematical and literary terms.
In old-fashioned high school math classes "back in the day", we learned about the conic sections, the ellipse, the parabola, and the hyperbola, in a very "classical" way. ( A circle is a special case of an ellipse.)
One way to distinguish among the three is a ratio called the eccentricity. Each of these three types of curves can be described as follows:
There is a fixed point F called the focus and a fixed line D called the directrix with the following property: if we take any point P on the curve, then the ratio
e = (distance from P to F) / (distance from P to D)
is a constant. It has the same value for every point P on the curve. This constant "e" is called the eccentricity of the curve.
If e > 1, the curve is a hyperbola. If e = 1, the curve is a parabola If e < 1, the curve is an ellipse.
On the other hand.....
Hyperbole refers to exaggeration, which in a sense is an "excess" ( e > 1)
A parable is a story in which one thing stands for another, just as the numerator and denominator are equal to each other when e = 1. (In fact, in the Latin Bible, the word that appears in the New Testament is "parabola!")
An elliptical sentence is one that is vague or ambiguous because it "lacks" something ( e < 1).
These Greek prefixes cut across different areas of learning!
I once was talking with a friend about exercise equipment. I knew very little about "elliptical machines", and I asked him what that term referred to. I assumed the machine had a belt in the shape of an ellipse, but he said that he was not aware of that being the case. So he joked, "Maybe it's a machine with parts missing!"
I responded, "In which case, all the advertising for them would be hyperbolic claims about elliptical machines!"
Yeah, he is a math nerd like me.
(Maybe I should have posted this under "Greek Language" rather than English! lol)
And then there's elliptic curve cryptography (I don't claim to understand it), based on curves whose equations (Weierstrass equation) are "related to" equations of ellipses!
If you consider the angle of the cut plane with the axis of the cone, with a uniform probability of any angle, you expect to see ellipses and hyperbolæ, because circles and parabolæ are only produced at 1 specific angle.
This exactly maps to orbital solutions for the "two-body problem" in classical celestial mechanics.
Min total energy for an orbit, E = E_{min} is < 0, (bound orbit) => circular orbit
Neg total energy E_{min} < E < 0 (bound orbit) => elliptical orbit
0 total energy E = 0 (not bound) => parabolic orbit (goes to infinity and has no kinetic energy)
positive total energy E > 0 (free) => hyperbolic orbit (goes to infinity and has extra kinetic energy)
In high school, I learned about moderm physics (statistical mechanics, special relativity, basic quantum theory), the simplex method (The Theory of Games and Economic Behavior by Morgenstern & Van Neumann), 2 yrs of college math (3 sem calc + 1 of ord diff equations), 1 yr of engineering physics (Halliday & Resnick).
