Arc length, curvature and area

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“Metes and bounds”

Computing arc lengths and areas on elliptic curves is in general very difficult and involves transcendental elliptic functions and elliptic integrals. If y=f(x), then the arc length s of the function plot may be computed as

and the curvature as

where the radius of the osculating circle is r=1/κ when f’’(x)≠0.

To be continued ...