hosted by the Harvey Mudd College Math Department created, authored and ©1999-2010 by Francis Su

The Math Fun Facts App!

List All : List Recent : List Popular
About Math Fun Facts / How to Use
Contributors / Fun Facts Home
© 1999-2010 by Francis Edward Su

From the Fun Fact files, here is a Fun Fact at the Easy level:

# Suspended Rope Trick

 Figure 1

What is the shape of a suspended rope? Is there some function that describes it?

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 x2 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 + x2/2, 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.

Su, Francis E., et al. "Suspended Rope Trick." Math Fun Facts. <http://www.math.hmc.edu/funfacts>.

References:

Keywords:    demonstration
Subjects:    calculus, analysis
Level:    Easy
Fun Fact suggested by:   Michael Moody
Suggestions? Use this form.
4.04
current
rating
Click to rate this Fun Fact...
*   Awesome! I totally dig it!
*   Fun enough to tell a friend!
*   Mildly interesting
*   Not really noteworthy
and see the most popular Facts!
Get the Math Fun Facts
iPhone App!

Want another Math Fun Fact?

For more fun, tour the Mathematics Department at Harvey Mudd College!