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September 28th, 2018, 09:00 AM   #1
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Find ellipse sector line length?



So if I know a and b of the ellipse and also the angle of it.
How can I calculate the curved line from the point of b to the point of a?

I want the length of the curved line. For example:
In a circle you can calculate the circle sector by
knowing the angle and the radius..

If possible using a, b and the angle of the ellipse.
How can you calculate the same thing for an ellipse?
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September 28th, 2018, 10:06 AM   #2
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Very easy...according to the Master:

Ellipse -- from Wolfram MathWorld
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September 28th, 2018, 01:15 PM   #3
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So is it r1 + r2 = 2a that I should use to get the length of the curved line?

I don't find the article clear about what gives me the curved lines length?
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October 17th, 2018, 02:14 PM   #4
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There is no simple formula for arc length for an ellipse. The calculation leads to what are called Elliptic integrals, which are non-elementary. Google it and you will likely find more than you want to know.
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