Cycloid is Best Shape for Arch

Theorem

The optimal shape for an arch is a cycloid.


Proof


This theorem requires a proof.
In particular: ... and of course an elaboration of what "optimal" means would be useful.
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Historical Note

Galileo Galilei was the first to suggest that the cycloid might be a good shape to use for the arches of bridges, but he had no knowledge of the mechanical reasons as to why that should be.


Sources

  • 1937: Eric Temple Bell: Men of Mathematics ... (previous) ... (next): Chapter $\text{V}$: "Greatness and Misery of Man"
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