This can even be used to define the hyperbolic functions geometrically, and many authors do the same with the trigonometric functions. Sine and hyperbolic sine are odd, whereas cosine and hyperbolic cosine are even. But sine and cosine are periodic functions, unlike the hyperbolic counterparts.
Excel has built-in functions for sine and cosine, the two core trigonometric functions, and for hyperbolic sine and hyperbolic cosine, their hyperbolic counterparts. It also has built-in functions for ...
I also know that the hyperbolic functions parametrize the unit hyperbola $ (\cosh a, \sinh a)$ and that $\frac {a} {2}$ corresponds to the area of the region bounded by the hyperbola, the rays from the origin, and the point $ (\cosh a, \sinh a)$.
geometry - What is the relevance of hyperbolic sine and cosine? What is ...
Working in the hyperbolic plane, let an $n$-gon be a finite sequence of points $ [a_0,...,a_n=a_0]$. Say that two $n$ -gons $ [...a_i...], [...b_i...]$ are quasisimilar iff
triangles - A notion of similarity in hyperbolic geometry - Mathematics ...
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 becomes these,...
A hyperbolic rotation is a rotation because of its effect on hyperbolic angles! Like the fact circular angles relate to the area of a (circular) wedge, hyperbolic angle is related to the area of a hyperbolic wedge:
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 hyperbolic metric on the unit disk or the upper half-plane, where you will compute that a hyperbolic circle has area that grows exponentially with the radius.