By contrast, in hyperbolic space, a circle of a fixed radius packs in more surface area than its flat or positively-curved counterpart; you can see this explicitly, for example, by putting a …

I heard teachers say [cosh x] instead of saying "hyperbolic cosine of x". I also heard [sinch x] for "hyperboic sine of x". Is this correct? How would you pronounce tanh x? Instead of saying "

At the moment it seems more math-related to me, but if the moderators feel it belongs elsewhere please feel free to migrate it. I'm working on a project where I have limited computational …

The hyperbolic trigonometric functions are very similar to the standard trigonometric function. Do similar functions exist that trace parabolas (because it is another conic section) when set up as …

When dealing with manifolds, volume forms are often conflated with measures. Here, the volume form on the upper half plane is |y|−2dxdy | y | 2 d x d y, so the measure of a Borel set is its …

8 I'm trying to understand the classification of PDEs into the categories elliptic, hyperbolic, and parabolic. Frustratingly, most of the discussions I've found are "definition by examples.'' I think …

For example, trig functions are periodic but hyperbolic functions are not periodic. $\sin (x)$ and $\cos (x)$ are bounded but $\sinh (x)$ and $\cosh (x)$ are not bounded.

Apr 30, 2020 · Why are the Partial Differential Equations so named? i.e, elliptical, hyperbolic, and parabolic. I do know the condition at which a general second order partial differential equation …

Dec 20, 2014 · Hyperbolic functions describe the same thing but can also be used to solve problem that can't be solved by Euclidean Geometry (where circular functions are …

Oct 2, 2018 · The hyperbolic functions are defined as the even and odd parts of $\exp x$ so $\exp\pm x=\cosh x\pm\sinh x$, in analogy with $\exp\pm ix=\cos x\pm i\sin x$. Rearranging …