So why was trigonometric substitution useful in our find the length of
the arc problem...Because it makes the math very easy:
source: Wikipedia, 'Trigonometric substitution', Russian language page.
* * *
Went back to the cubic spline problem, wondering what clamped beginning and
endpoints would be. The clamp is defined by specifying the slope we want at the
two points.
Gemini suggested I use the slopes in the current middle points, thus staying faithful to
the movement of the data...
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