FROM CONSTRUCTION TO ITERATION
Construct a root, step by step.
Follow the lines and arcs, change the degree, and compare the geometric readout. Enter p and X: setup is automatic, then you advance one iteration at a time. The result is the pth root of X.
Seven V20 protocols and four experimental post-V20 explorations. Adaptive normalization is optimal among the tested dyadic scales according to the gallery conditioning score.
Settings, proofs and manual exploration
Overview
Drag the sphere with a mouse or one finger to rotate it.
Readout in the rectangle
Understanding the domain and checks
Points are computed from line and circle intersections. An independent formula then checks the readout. Browser calculations use about 16 significant digits: a displayed zero error does not prove exact equality. Distant centers and tangencies can reduce accuracy.
On the sphere, a line becomes a circle through the north pole N. Directions at infinity remain distinct in the calculation, even though they map to the same point N. This representation is not a physical protocol with the same construction cost.
FURTHER EXPLORATIONS
From the first figures to stereographic views.
The seven protocols from the paper are available above. These additional demonstrations preserve the earlier constructions and their original conventions.