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
.
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