How to Ride a Square-Wheeled Tricycle

A catenary is the curve defined by a rope or chain hanging loosely from two supports, like a "U"with a detachable jaw.


A row of inverted catenaries is the kind of surface on which you ride a bicycle vehicle with square wheels.

You can also ride on wheels like this:


on a surface like this:


thusly:

Also:

and:


and don't forget:

or:

Stan Wagon, who developed the wheel variations and is riding it in the photograph above, has several mathematical publications available for purchase; you can also read the Mathematics Magazine article that introduced his catenary wheel (several of the diagrams in this post are taken from that article). Ivars Peterson, who wrote the article for Science News which introduced me to this concept, has also published several mathematical books, which look to be written for curious laypersons.