$e$ is the unique number $>1$ such that the area in the plane bounded between the three lines $y=0$, $x=1$, $x=e$ and the hyperbola $y=1/x$ is equal to $1$.

$e$ is the unique number $>1$ such that the area in the plane bounded between the three lines $y=0$, $x=1$, $x=e$ and the hyperbola $y=1/x$ is equal to $1$.