A geodesic still joins most pairs, but if the unique minimizing great-circle arc passes through the deleted north pole, that arc is unavailable; the complementary great-circle arc remains a geodesic, so a geodesic does exist. A length minimizer need not: for points whose shorter arc passes through the missing pole, curves detouring arbitrarily close to it approach the spherical distance but never attain it.
Articles by others on the same topic
There are currently no matching articles.