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Answer by PrincessEev for What is the arc-length parameterization of an ellipse?

So, the standard parameterization of the ellipse$$\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1$$is given by$$r(t) = (a \cos t , b \sin t) \quad t \in [0,2\pi)$$The arc-length parameterization is given...

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Answer by Ethan Bolker for What is the arc-length parameterization of an...

No.You have stumbled on a well known difficult problem.In integral calculus, an elliptic integral is one of a number ofrelated functions defined as the value of certain integrals, whichwere first...

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What is the arc-length parameterization of an ellipse?

I know the typical parameterization of an ellipse is (a cos(t), b sin(t)). However, this is not an arc-length parameterization and I can't make the usual techniques for getting an arc-length...

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