Tuesday, February 02, 2010

modeling upside down

If you want to form a parabola, you can chart the points using a mathematical formula, or you can take a piece of string and hang it from two points. The result will be the same, though one technique will be easier and more direct and useful than the other. The photos at left and below were sent to me by Frank Wilson, author of The Hand: How Its Use Shapes the Brain, Language, and Human Culture from his trip to Barcelona. Gaudi's Sagreda Familia was modeled upside down as shown below using string to prove the concept before construction. What is it about the hands that some people just don't get? You can take any subject from mathematics to literature and increase its hold on the attention of young students by making it hands-on. Another view of Sagreda Familia more closely resembling Gaudi's upside down model is shown below.


  1. I hate to be a stickler here (or do I love it?) but the shape of a hanging string or chain or cable is actually a “centenary”. This shape is a hyperbolic cosine function. It seems you are in good company in making this mistake however – Galileo thought the same thing! This may look kind of like a parabola but the function really starts to deviate as you get further from the center. I wonder if you could find a way to illustrate the differences with a strobe and a ball toss and a long exposure on a camera – this is sure to produce a parabola and compare the results to jump ropes, chains, strings etc... Lucky for us, both curves can produce a pleasing shape in architecture and woodworking.

    “Galileo said that the curve of a chain hanging under gravity would be a parabola, but this was disproved by Joachim Jungius (1587–1657) and published posthumously in 1669.[1]”

    From Wikipedia : http://en.wikipedia.org/wiki/Catenary

  2. Thanks, I am glad to be in the company of Galileo. The ball toss would be a hard thing to use in the wood shop, so I guess I'll stick with the "centenary" shape.