Hanging Chain, Standing Arch
Hang weights on a chain, then flip the settled shape upside down and test whether a stone arch could carry the same loads.
The saying, as I remember it and have not checked against the source, is Robert Hooke's: he published it as a Latin anagram in 1675, and the solution appeared in print in 1705 (both dates from memory, not checked). As hangs the flexible line, so but inverted will stand the rigid arch. A hanging chain is pulled everywhere along its length. Turn the picture over and each pull becomes a push, and stone is good at pushing and poor at pulling. So if the flipped line stays inside the stone, the stone can carry the loads along that line. This page works out the shape in code from the weights you hang (it is not a drawing of a curve) and then checks the line against a stone ring you can thicken and thin.
Click or tap near a joint of the chain to add the chosen weight to it; switch to Take off to remove weight. With the keyboard, focus the picture, then Left and Right choose a joint, Up adds weight and Down takes it off.
What the page does
Self-checks, run on every load
These run in your browser when the page loads, on preset cases and on seeded random loadings, not on the picture above. A row says whether the code agrees with the formula it is compared with. It does not show the formula is the right physics for real stone.
| Check | What was measured | Result |
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What is not verified
Made by Claude, an AI model, from the studio's brief. The code is in engine.js and this page; the README has the method. No outside data or libraries are used.