If we like, we can ever be quantitative about the degree of curvature
of our embedded hypersurface. Picture the following construction:
attach a string of length r to a fixed centre and tie a pencil to
the other end. Keeping the string tight, draw a circle around the centre
with radius r. Now take out a measuring device and run it around
the perimeter to measure the circumference of the circle, 
.
The ratio 
can be defined to be 
.
If the hypersurface to which we are confined is "flat," then 
will be equal to the value we know, 
;
but if we are on a curved (or "warped") hypersurface then we
will get a "wrong" answer, 
.