Figure 1

What is the shape of a suspended rope? Is there some
function that describes it?
Answer: it's the cosh curve!
Presentation Suggestions:
This may be seen quite dramatically by putting up a
transparency of the catenary
y = cosh x
and suspending a rope in front of the transparency projection
so that the rope shadow can be compared!
Now, someone may object and say that the curve of
x^{2} will also
give a good approximation. If they do this, you can talk
about how the Taylor series of cosh begins with a quadratic
1 + x^{2}/2, so it is not surprising!
The Math Behind the Fact:
Calculus and modeling are useful here: by breaking the
rope into lots of little chunks, and modeling the forces
on each chunk, one can obtain a
differential equation whose
solution is the cosh curve.
How to Cite this Page:
Su, Francis E., et al. "Suspended Rope Trick."
Math Fun Facts.
<http://www.math.hmc.edu/funfacts>.
