( ( In ( terms ( of ( the coordinates ) ) ) ) ( ( the metric ) ( ( takes ( ( the form ) ( Thus ( is ( ( the length ) ( of ( ( the ( geodesic circle ) ) ( ( consisting ( of ( ( all points ) ( at ( distance r ) ) ) ) ) ( from p ) ) ) ) ) ) ) ) ) . ) ) )
(ROOT (S (PP (IN In) (NP (NP (NNS terms)) (PP (IN of) (NP (DT the) (NN coordinates))))) (NP (DT the) (NN metric)) (VP (VBZ takes) (SBAR (S (NP (DT the) (NN form)) (ADVP (RB Thus)) (VP (VBZ is) (NP (NP (DT the) (NN length)) (PP (IN of) (NP (NP (DT the) (JJ geodesic) (NN circle)) (VP (VBG consisting) (PP (IN of) (NP (NP (DT all) (NNS points)) (PP (IN at) (NP (NN distance) (NN r))))) (PP (IN from) (NP (NN p))))))))))) (. .)))
In terms of the coordinates the metric takes the form Thus is the length of the geodesic circle consisting of all points at distance r from p .
(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))))))))) (. .)))