Consider the Riemann sphere given by 𝑥

2 + 𝑦

2 + (𝑧 −

1

2

)

2

=

1

4

. If (𝑥, 𝑦, 0) is a point

on the complex plane, prove that the stereographic projection (𝛼, 𝛽, 𝛾) is given by:

𝛼 =

𝑥

1+𝑥

2+𝑦2

, 𝛽 =

𝑦

1+𝑥

2+𝑦2

, 𝛾 =

𝑥

2+𝑦

2

1+𝑥

2+𝑦2

.

asked by guest
on Jan 22, 2025 at 9:48 pm



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