Hanging Mardi Gras Beads
Scroll through the pics of Mardi Gras beads, cut and hung from a meter stick. Check the box for a power function (including absolute value in order to ensure symmetry about the y-axis) and/or a hyperbolic cosine function, which forms a catenary curve. Drag the related points on the x-y plane, adjusting the equations accordingly.
- Which curve fits the beads better?
- Does the "better" curve depend on which pic you land on?
- For the power function, which power tends to fit best? Does that answer depend on which pic you land on? Play with the various other options that are presented in the graphics window.
- Historically, which function has been deemed to best model a hanging ideal cable, ideally acted upon by no forces other than gravity?
- Who is credited with proving this?