Extended complex plane laboratory

Match a moving plane point to the sphere

One projection ray gives the same point two addresses.

The complex plane is tangent at the south pole. The ray from the north pole through P(z) meets the sphere once, at S(z).

Teacher layers Sphere grid Projection / rotation traces Plane and sphere loci Corresponding points Section planes

Fixed view Model zoom 100%

Drag to rotate the model. The tangent plane, sphere and loci remain one fixed geometric construction.

Teacher cue

On step 03, ask which sphere circle contains N. On step 04, distinguish the displayed rigid rotation from a general Möbius transformation before returning to the general circle theorem.