E

e is the

Geometric interpretation

" A ray through the unit hyperbola x² − y² = 1 at the point (cosh a, sinh a), where a is twice the area between the ray, the hyperbola, and the x-axis. For points on the hyperbola below the x-axis, the area is considered negative" [TODO]

$\cosh(a)$ and $\sinh(a)$ are the $x$ and $y$ coordinates on a unit hyperbola, at the place where the ray subtending an area of $a/2$ intersects the hyperbola. This description is not very clear; see the figure.

In this situation, $e^{a}$ is the sum of $x$ and $y$ coordinates