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That's an interesting factoid I've never thought about before. Here's my guess why it's true.

In a hanging chain, the sum of the forces pulling down (due to gravity/load) and away from the end (due to tension) on a given link must point in a direction exactly opposite the angle of the next chain link toward the end. Else that chain link would rotate until the above is true.

In a stone arch, the sum of the forces pushing down (due to gravity/load) and toward the base (due to compression) on a given stone must point in a direction exactly equal to the next stone toward the base. Else that stone would rotate and the arch would break.




I don't understand much about questions of why in nature. It sounds like you're arguing that it must be as such, but given your explanation is true (and it seems a reasonable proposal), I don't know if it tells me why.




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