Special Planimeter
Wheel at tracer point: l
= 1
Region determines length and path followed by left endpoint
From before: A = l s - 1/2 l l2 Dq
l = 1 Dq = 2p
A = l s - pl2
A little algebra yields
s2 - 4pA = (A - pl2)2/l2
Key Observation
ds 
ds, s
L
(A
- pl2)2/l2