# Find the angle that lets you make a bendy pipe

Mathematics Asked by John Porter on December 13, 2020

I have a pipe with $$n$$ segments of equal length. I move the farthest end nearer than the combined length to make the pipe bend. How do I find the angle between each segment with only the combined length (straight length), the distance between each end, and the number of segments?

1. $$theta$$ is the angle to solve for
2. $$l$$ is segment length
3. $$n$$ is the number of segments
4. $$dx$$ is how the distance between ends

With only two segments I would use the law of cosines:$$dx^2=2*l^2 – 2*l^2*cos theta$$

You have to assume all the angles between the segments are the same or the problem is underdetermined. In that case all the bends lie on the arc of a circle. A figure with four segments is below. $$BG$$ is your $$dx$$, $$n=4$$, and $$l approx 3.6$$ as drawn. All the triangles are isosceles. If angle $$DAB=theta, GAB=4theta, GB=2rsin(2theta),l=BD=2rsin(theta/2)$$. You need to use $$l, GB$$ to get $$r, theta$$

Answered by Ross Millikan on December 13, 2020

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