It seems to me that you project the sphere onto the plane with a stereographic map and solve the minimal circle problem there, and transform back to the sphere. I don't see why a minimal circle in the plane would correspond to a minimal circle on the sphere since the stereographic projection does not preserve areas.

This notebook observes that [Apollonius' problem](https://bl.ocks.org/mbostock/7115f7a0393de96f2fdc) can be transported to the stereographic plane, solved there, and transported back. Since circles are projected to circles both ways, an enclosing circle in the plane will be an enclosing circle on the sphere. You're correct that it doesn't prove that the solution is minimal wrt area (equivalently enclosing circle radius). In fact I mention that if the initial problem covers more that a half-sphere, the method in this notebook often returns the wrong solution (push "dispersion of the centers" to 170).

So it's it correct to say this method only finds av approximate solution and not an exact one?

Since the answer is made over a finite collection (all triplets of circles), I don't think it there is a notion of an _approximate_ solution. Either the answer is correct, or it is wrong. Experimentally, it seems to work in all cases enclosed in a half-sphere, but beyond that it it easy to create examples where it fails.

There are path rendering artefacts at certain positions which can be fixed by adding ``` context.lineJoin = "round"; ```

Here is an example (note the stroke in the top right): https://i.imgur.com/B1exzaA.png

Hm, although I can't reproduce them in Firefox, only in Chrome.

I've already noticed these artifacts in chrome, but had no idea what was causing them (still no idea, I must say), or how to fix them (problem solved, thanks!)