( ( ( The length ) ( of ( ( the ( minor arc ) ) ( of ( a ( great circle ) ) ) ) ) ) ( ( is ( taken ( as ( ( the distance ) ( between ( ( two points ) ( on ( ( a surface ) ( of ( ( a sphere ) ( in ( Riemannian geometry ) ) ) ) ) ) ) ) ) ) ) ) . ) )
(ROOT (S (NP (NP (DT The) (NN length)) (PP (IN of) (NP (NP (DT the) (JJ minor) (NN arc)) (PP (IN of) (NP (DT a) (JJ great) (NN circle)))))) (VP (VBZ is) (VP (VBN taken) (PP (IN as) (NP (NP (DT the) (NN distance)) (PP (IN between) (NP (NP (CD two) (NNS points)) (PP (IN on) (NP (NP (DT a) (NN surface)) (PP (IN of) (NP (NP (DT a) (NN sphere)) (PP (IN in) (NP (NNP Riemannian) (NNP geometry))))))))))))) (. .)))
The length of the minor arc of a great circle is taken as the distance between two points on a surface of a sphere in Riemannian geometry.
(ROOT (S (NP (NNP Distance)) (VP (VBZ is) (NP (NP (DT the) (NN term)) (PP (IN for) (NP (NP (DT the) (NN length)) (PP (IN of) (NP (NP (DT the) (NN route)) (PP (IN between) (NP (CD two) (NNS points))))))))) (. .)))