A cable hanging between two supports takes on a lovely shape called a **catenary** *(also known as a chainette, alysoid, or funicular curve)*. The mathematical equations that define a catenary are slightly tricky; there's a hyperbolic cosine in there, for instance. Deriving the shape was a famous challenge problem in the 1600's, and it's still stressful enough to be a good exercise in an undergraduate calculus class. *(Galileo got it wrong --- he thought it was a parabola.)*

Whenever I see high wires, loosely spun spiderwebs, dangling chains, or other pendulous curves, I think of catenaries. The other day as I drove past some high-voltage transmission towers I said to my daughter, *"Look at those power lines arcing!"* --- and then suddenly laughed as I realized there's a rather different electrical meaning to the word *" arcing"* ...

TopicScience - TopicLanguage - TopicHumor - TopicPersonalHistory - 2004-10-10

*(correlates: In Memoriam, PoeticCredo, Comments on High Voltage Fiberoptic Cable, ...)*