If I squish a circle, will the new shape have the same curved loop length as the circumference as the circle?
Lets say I have a Ø27 circle and I alter the same by squishing both sides so I now have an ellipse. Will the circumference of the ellipse equal the circumference of the original circle?
Solution 1:
No. If you squish it all the way to a straight line, the circumference approaches twice the diameter.
The circumference is the 'complete elliptic integral', and is not one of the 'elementary' functions which are polynomials, exponentials, logs, sine, cosine and combinations of those.
The 'incomplete elliptic integral' is the lemgth of an arc of an ellipse.