AREA OF THE SPHERICAL SURFACES 

A spherical triangle ABC with area S arises from the intersection of three great circles on a sphere. The total angle at A is 2p  and the area of the sphere is 4pR²; therefore, the area limited by the two circles that intersect at A will be 2·(4pR²/2p)=4R²Â. Thus, if we sum the areas of these double cylinders we will have 

4R²Â+4R²B+4R² =(4pR²-2S)+6S, 

where Â+B+ =p+S/R².

What happens when the radius of the sphere tends to infinity?

Geodesics in spheres

Index

Spheric packaging