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## Main Question or Discussion Point

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

(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