Regular Polygon Rolling on a Catenary

On a linked set of catenaries, all regular polygons can roll without slipping — except for the triangle, which intersects the curve near its corners. A square can roll at a constant angular velocity (blue outlines). However, if it also moves at a constant horizontal velocity (red outlines), it must cut into the curve. The same applies to a pentagon. However, hexagons can simultaneously roll at a constant horizontal and a constant angular velocity, as can any other regular polygon with more sides.

SNAPSHOTS

  • [Snapshot]
  • [Snapshot]
  • [Snapshot]

DETAILS

An actual square-wheeled bike shown at San Francisco's Exploratorium inspired Leon Hall and Stan Wagon to animate rolling on a catenary in Wagon's The Mathematical Explorer.
    • Share:

Embed Interactive Demonstration New!

Just copy and paste this snippet of JavaScript code into your website or blog to put the live Demonstration on your site. More details »

Files require Wolfram CDF Player or Mathematica.







Related Curriculum Standards

US Common Core State Standards, Mathematics