3 ms·
And here it is, proof in one picture: https://i.ibb.co/kxjDbWP/a.png https://i.ibb.co/kxjDbWP/a.png Pure classical geometry (I think?) The integral over the
by perihelions 3y ago
And here it is, proof in one picture:
https://i.ibb.co/kxjDbWP/a.png https://i.ibb.co/kxjDbWP/a.png
Pure classical geometry (I think?)
The integral over the circle can be rewritten as an integral of a sum of two terms over a semicircle – the term for the local point, plus the term for the mirrored point on the other semicircle. This sum-term is an everywhere-monotonic function of the radius of the circle (in the proof diagram: XA + XB > XC + XD).
(XAQB, XCRD, and XC¹QD¹ are constructed as parallelograms. XC¹RD¹ doesn't mean anything; it's just a construction whose perimeter compares easily against the other two).