Stereographic projection preserves circles and angles. That is, the image of a circle on the sphere is a circle in the plane […]. We will outline two proofs of the fact that stereographic projection preserves circles, one algebraic and one geometric.
I also ran across a math stackexchange thread talks about a proof that “Stereographic projection maps circles of the unit sphere, which do not contain the north pole, to circles in the complex plane”.
Further I notices the mathematical wikipedia page for the projection states it without the weird map terminology simply as “It maps circles on the sphere to circles or lines on the plane”.
I really don’t see any qualifiers anywhere, to the best of my understanding this holds in general for all circles. With the one exception that circles through the point opposite the center turn into lines (infinitely large circles for simplicity).
I couldn’t find the video I was thinking about, which is a bummer.
I did find one written argument (uiuc - Stereographic Projection)
And one video proof youtube - Stereographic Projection Circle to Circle Proof.
I also ran across a math stackexchange thread talks about a proof that “Stereographic projection maps circles of the unit sphere, which do not contain the north pole, to circles in the complex plane”.
Further I notices the mathematical wikipedia page for the projection states it without the weird map terminology simply as “It maps circles on the sphere to circles or lines on the plane”.
I really don’t see any qualifiers anywhere, to the best of my understanding this holds in general for all circles. With the one exception that circles through the point opposite the center turn into lines (infinitely large circles for simplicity).