What is the proper geometrical name for a a rectangle with a semi-circle at each end? I'm talking about the shape made up of a rectangle with a semi-circle at each end.  Does it have a particular name? Does it begin with e?
Obround, apparently.  I don't know Wiktionary's source.  This definition of obround does not appear in OED, for example.  Googling indicates that this definition is commonly used for machine parts having this shape.
Another shape called " Bermuda Bottle" has meridian curvature proportional to $x$. Also ratio of shell curvatures is $2$ when rotated about minor axis, however minor axis measures only $\approx 0.6 $ times major axis.

EDIT1:

It is is same shape as filled parachutes.

The differential equation of Cornu Spiral by J.M. is not a mathematician is ( $s$ is arc ):

$$ \frac{d\phi}{ds} = s/a $$

and the Bermuda Bottle (not sketched) is

$$\frac{d\phi}{ds} = x/b $$

They are similar in appearance. Clothoid curve has a third order discontinuity at sharpest corners.