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This problem is being discussed on the AAMT email discussion list. I have a meter long metal ruler. I push the ends together so that they're only 99cm apart, which means the ruler will bow a bit. How tall is that arc?

The problem we haven't been able to solve is 'what is the shape of the arc'?

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    Doesn't the answer depend on the nature of the material under consideration? I suspect that the answer needs some 'physical' assumptions about the ruler (e.g., [Young's modulus](http://en.wikipedia.org/wiki/Young's_modulus)) and hence a purely mathematical answer may not be available.2011-11-04
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    Why wouldn't [Euler-Bernoulli](https://secure.wikimedia.org/wikipedia/en/wiki/Euler%E2%80%93Bernoulli_beam_equation) apply?2011-11-04
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    You can imagine bending a much longer strip into a variety of shapes - a circle, for example, or where the two "ends" cross at right angles. You can then find a chord which is 99% of the length of the arc it cuts off (intermediate value theorem), and scale to match the problem. So a variety of shapes will be possible. What makes the difference, I think (this may be wrong), is the direction of the forces applied at the end of the arc and stuff like gravity (the answer will be a little different in a horizontal v vertical plane).2011-11-04

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