Cycloid is Best Shape for Arch
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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. You can help $\mathsf{Pr} \infty \mathsf{fWiki}$ by crafting such a proof. To discuss this page in more detail, feel free to use the talk page. When this work has been completed, you may remove this instance of {{ProofWanted}} from the code.If you would welcome a second opinion as to whether your work is correct, add a call to {{Proofread}} the page. |
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"