Given two points A and B on the surface of the hyperboloid x^2+y^2z^2=1. How to find the shortest distance between them along the surface?
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Using the following formula $$ \cosh(d(A,B))=\frac{q(A,B)}{q(A)^{1/2}q(B)^{1/2}}, $$ where $$ q(A,B)=A^t I_{2,1} B = a_1b_1+a_2b_2a_3b_3 $$ with $I_{2,1}=diag(1,1,1)$. 

