Cornu
Spiral Animation with Rhombus Substitution

The
Spiral of Cornu is named for the French scientist Marie Alfred
Cornu (1841  1902). He studied this curve, also known as a
clothoid or Euler's Spiral, in connection with diffraction. Euler
applied a similar figure while measuring the elasticity of a spring.
The parametric equations for a generalized Cornu spiral are on the
right.
Similar integrals are named for Augustin Jean Fresnel (17881827), one
of the founders of the wave theory of light.


The Spiral of
Cornu, a.k.a. Clothoids "are important curves used in
freeway and railroad construction. For example, a clothoid is
needed to make the gradual transition from a highway; which has zero
curvature, to the midpoint of a freeway exit, which has nonzero
curvature. A clothoid is clearly preferable to a path consisting
of straight lines and circles, for which the curvature is
discontinuous." (!!)
Alfred Gray



Copyright Notice:
This
animation and all images within are under copyright by Cye Waldman and
may not be copied, electronically or otherwise, without his espress
permission.
Dr.
Cye Waldman
cye@att.net
