Math Monday: Cardboard Catenary Arches

Science
Math Monday: Cardboard Catenary Arches

By George Hart for the Museum of Mathematics

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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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See all of George Hart’s Math Monday columns

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Gareth Branwyn is a freelance writer and the former Editorial Director of Maker Media. He is the author or editor of over a dozen books on technology, DIY, and geek culture. He is currently a contributor to Boing Boing, Wink Books, and Wink Fun. His free weekly-ish maker tips newsletter can be found at garstipsandtools.com.

View more articles by Gareth Branwyn

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