Please help. Imposing a metric to preserve distance

[whattttt]

If we use the mapping
(r,phi)---->(x,y)=
(2tan(r/2)cos(phi),
2tan(r/2)sin(phi))
Which metric do we have to impose on R^2 in order that the mapping preserves distance. Any help would be greatly appreciated. Thank you very much

 

[tiny-tim]

hi whattttt!

(have a phi: φ )

tell us what you think, and we'll comment

 

[whattttt]

Nice