Math Monday: Cardboard Catenary Arches

by George Hart

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?

This article first appeared on Make: Online, June 6, 2011.

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