By George Hart for the Museum of Mathematics
The shape of a hanging chain is called a catenary curve. Each link settles in to an equilibrium angle relative to its neighbors, so if you turn everything over, those angles give a plan for blocks which can rest on each other to make an arch in equilibrium. This suggests a fun construction: making giant arches from separate cardboard blocks.
Edward Ebert gives instructions here on how to hang a chain, measure it, and scale up the measurements to large cardboard blocks. If properly made, the blocks rest stably on each other without tape, glue, or clips to join them.
How high a catenary arch can you make?
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6 thoughts on “Math Monday: Cardboard Catenary Arches”
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“math monday”™ about Catenary curves and no equation? (i’m shocked…shocked)
how about: y = k*cosh(x/k) = (k*(exp(x/k) + exp(-x/k)))/2
i leave it for others to post the Taylor series …yep.
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I would love to have the plans for the catenary arch model. I am a teacher and would like to pass that learning onto my students. Thank you.