Rotation of the sphere as a complex transformation
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I'm trying to solve the following problem:
Show that the rotation $(y,z,x)$ of the sphere around $(t,t,t)$ corresponds to the transformation $M(z)=ifrac{z+1}{z-1}$ under the stereographic projection.
I know I should use the Riemann sphere, but my book doesn't go deep into the details of the spherical representation.
complex-analysis
asked Dec 10 '18 at 22:00
IchVerlorenIchVerloren
969
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add a comment |
$begingroup$
I'm trying to solve the following problem:
Show that the rotation $(y,z,x)$ of the sphere around $(t,t,t)$ corresponds to the transformation $M(z)=ifrac{z+1}{z-1}$ under the stereographic projection.
I know I should use the Riemann sphere, but my book doesn't go deep into the details of the spherical representation.
complex-analysis
asked Dec 10 '18 at 22:00
IchVerlorenIchVerloren
969
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$begingroup$
What does your book cover? Using the Riemann Sphere is correct, but it would be nice to show a bit of context for the problem
$endgroup$
– Brevan Ellefsen
Dec 11 '18 at 10:28
add a comment |
$begingroup$
I'm trying to solve the following problem:
Show that the rotation $(y,z,x)$ of the sphere around $(t,t,t)$ corresponds to the transformation $M(z)=ifrac{z+1}{z-1}$ under the stereographic projection.
I know I should use the Riemann sphere, but my book doesn't go deep into the details of the spherical representation.
complex-analysis
asked Dec 10 '18 at 22:00
IchVerlorenIchVerloren
969
$endgroup$
I'm trying to solve the following problem:
Show that the rotation $(y,z,x)$ of the sphere around $(t,t,t)$ corresponds to the transformation $M(z)=ifrac{z+1}{z-1}$ under the stereographic projection.
I know I should use the Riemann sphere, but my book doesn't go deep into the details of the spherical representation.
complex-analysis
complex-analysis
asked Dec 10 '18 at 22:00
IchVerlorenIchVerloren
969
asked Dec 10 '18 at 22:00
IchVerlorenIchVerloren
969
asked Dec 10 '18 at 22:00
IchVerlorenIchVerloren
969
asked Dec 10 '18 at 22:00
IchVerlorenIchVerloren
969
asked Dec 10 '18 at 22:00
IchVerlorenIchVerloren
969
969
$begingroup$
What does your book cover? Using the Riemann Sphere is correct, but it would be nice to show a bit of context for the problem
$endgroup$
– Brevan Ellefsen
Dec 11 '18 at 10:28
add a comment |
$begingroup$
What does your book cover? Using the Riemann Sphere is correct, but it would be nice to show a bit of context for the problem
$endgroup$
– Brevan Ellefsen
Dec 11 '18 at 10:28
$begingroup$
What does your book cover? Using the Riemann Sphere is correct, but it would be nice to show a bit of context for the problem
$endgroup$
– Brevan Ellefsen
Dec 11 '18 at 10:28
$begingroup$
What does your book cover? Using the Riemann Sphere is correct, but it would be nice to show a bit of context for the problem
$endgroup$
– Brevan Ellefsen
Dec 11 '18 at 10:28
add a comment |
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$begingroup$
What does your book cover? Using the Riemann Sphere is correct, but it would be nice to show a bit of context for the problem
$endgroup$
– Brevan Ellefsen
Dec 11 '18 at 10:28