Old business: I asked,
So, can you construct any circular arc which divides a given disc into areas 1:2 ?-)
The only ones I know are full circles of radius sqrt(1/3) or sqrt(2/3), internally tangent to the propositus. Unlikely new, but interesting: inf ==== k \ k 4 z 1/4
theta (2 z, q ) = theta (-, q ) - 1 / 2 3 2 ==== k = 0 1 -- k z 4 2 inf theta (--, q ) z ==== 4 k ------ \ 2 4 %pi log(q) --------------- = 2 theta (2 z, q ) - sqrt(- ------) %e / k 3 log(q) ==== 2 k = 0
Of equally dubitable novelty: Q: How is Margaret not a gem?