Wednesday, January 9, 2013

Catenary out the window

I hung a rope between two trees for my kids to play on the other day, and when I looked out the window later I saw a catenary graph. 

1-DSC04143

The catenary is a curve describing the shape of a in idealized hanging chain, and looks a lot like a parabola (enough so to trick Galileo).  Its equation was determined independently by three people in response to a contest challenge.

I like to think of it as the sum of two exponential functions:
Here’s y = ex and y = e-x
1-Fullscreen capture 192013 95234 AM2-Fullscreen capture 192013 95250 AM
…and their sum
3-Fullscreen capture 192013 95315 AM

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