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117 views

Diametrically opposite points go to diametrically opposite points under stereographic projection

I asked this question before here but I didn’t get a proper answer. So here I am stating it more clearly : Suppose $P_1$ and $P_2$ are two diametrically opposite points of a circle $C$ in the ...
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0answers
119 views

Change in angle between curves due to stereographic projection

Suppose I have say two curves on the complex plane intersecting at a point $P$. Then is the angle between those curves at $P$ same as the angle between their spherical images on the Riemann Sphere (by ...
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1answer
265 views

Transformation under rotation of Riemann sphere

Suppose the Riemann sphere $S$ is rotated by the angle $\phi$ round the diameter whose end points have $a,-1/\bar{a} $ (which have antipodal preimages) as stereographic projections. Suppose moreover, ...
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2answers
499 views

Radius of the inverse image of a circle under stereographic projection

I need to find the radius of the circle on the Riemann sphere $S$ whose stereographic projection is $C(a;r)$, i.e. the circle with centre $a$ and radius $r$ in the complex plane. I have observed ...