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Meridians and Parallels on a Unit Sphere

1

$begingroup$

Let $S$ be the unit sphere in $Bbb R^3$ with centre $(0, 0, 0)$

$sigma(u, v) = (cos v/cosh u,sin v/cosh u,tanh u)$

is a parametrization of $S$ minus the north and south poles.

Show that meridians and parallels on $S$ correspond under $sigma$ to perpendicular straight lines in the plane with coordinates $(u, v)$.

surfaces curves parametrization

share|cite|improve this question

edited Apr 1 at 18:30

Robert Lewis

49.1k23168

asked Apr 1 at 18:26

Samir SachakSamir Sachak

61

$endgroup$

• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  $begingroup$
  What are your thoughts on this question ?
  $endgroup$
  – Yves Daoust
  Apr 1 at 18:57
  

  
  
  
  

add a comment | 

1

$begingroup$

Let $S$ be the unit sphere in $Bbb R^3$ with centre $(0, 0, 0)$

$sigma(u, v) = (cos v/cosh u,sin v/cosh u,tanh u)$

is a parametrization of $S$ minus the north and south poles.

Show that meridians and parallels on $S$ correspond under $sigma$ to perpendicular straight lines in the plane with coordinates $(u, v)$.

surfaces curves parametrization

share|cite|improve this question

edited Apr 1 at 18:30

Robert Lewis

49.1k23168

asked Apr 1 at 18:26

Samir SachakSamir Sachak

61

$endgroup$

• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  $begingroup$
  What are your thoughts on this question ?
  $endgroup$
  – Yves Daoust
  Apr 1 at 18:57
  

  
  
  
  

add a comment | 

$begingroup$

Let $S$ be the unit sphere in $Bbb R^3$ with centre $(0, 0, 0)$

$sigma(u, v) = (cos v/cosh u,sin v/cosh u,tanh u)$

is a parametrization of $S$ minus the north and south poles.

Show that meridians and parallels on $S$ correspond under $sigma$ to perpendicular straight lines in the plane with coordinates $(u, v)$.

surfaces curves parametrization

share|cite|improve this question

edited Apr 1 at 18:30

Robert Lewis

49.1k23168

asked Apr 1 at 18:26

Samir SachakSamir Sachak

61

$endgroup$

share|cite|improve this question

edited Apr 1 at 18:30

Robert Lewis

49.1k23168

asked Apr 1 at 18:26

Samir SachakSamir Sachak

61

share|cite|improve this question

edited Apr 1 at 18:30

Robert Lewis

49.1k23168

asked Apr 1 at 18:26

Samir SachakSamir Sachak

61

edited Apr 1 at 18:30

Robert Lewis

49.1k23168

edited Apr 1 at 18:30

Robert Lewis

49.1k23168

asked Apr 1 at 18:26

Samir SachakSamir Sachak

61

asked Apr 1 at 18:26

Samir SachakSamir Sachak

61