▁show ▁that ▁space ▁is ▁expand ing , ▁even ▁if ▁a ▁r uler ▁on ▁earth ▁could ▁not ▁measure ▁it . ▁ ▁The ▁metric ▁expansion ▁of ▁space ▁is ▁described ▁using ▁the ▁mathematics ▁of ▁metric ▁tens ors . ▁The ▁coordinate ▁system ▁we ▁use ▁is ▁called ▁" com oving ▁coordinates ", ▁a ▁type ▁of ▁coordinate ▁system ▁which ▁takes ▁account ▁of ▁time ▁as ▁well ▁as ▁space ▁and ▁the ▁speed ▁of ▁light , ▁and ▁allows ▁us ▁to ▁incorpor ate ▁the ▁effects ▁of ▁both ▁general ▁and ▁special ▁relativ ity . ▁ ▁Example : ▁" Gre at ▁Circle " ▁metric ▁for ▁Earth ' s ▁surface ▁ ▁For ▁example , ▁consider ▁the ▁measurement ▁of ▁distance ▁between ▁two ▁places ▁on ▁the ▁surface ▁of ▁the ▁Earth . ▁This ▁is ▁a ▁simple , ▁familiar ▁example ▁of ▁spher ical ▁geometry . ▁Because ▁the ▁surface ▁of ▁the ▁Earth ▁is ▁two - dimensional , ▁points ▁on ▁the ▁surface ▁of ▁the ▁Earth ▁can ▁be ▁specified ▁by ▁two ▁coordinates ▁– ▁for ▁example , ▁the ▁latitude ▁and ▁longitude . ▁Spec ification ▁of ▁a ▁metric ▁requires ▁that ▁one ▁first ▁specify ▁the ▁coordinates ▁used . ▁In ▁our ▁simple ▁example ▁of ▁the ▁surface ▁of ▁the ▁Earth , ▁we ▁could ▁choose ▁any ▁kind ▁of ▁coordinate ▁system ▁we ▁wish , ▁for ▁example ▁latitude ▁and ▁longitude , ▁or ▁X - Y - Z ▁Cart esian ▁coordinates . ▁Once ▁we ▁have ▁chosen ▁a ▁specific ▁coordinate ▁system , ▁the ▁numerical ▁values ▁of ▁the ▁coordinates ▁of ▁any ▁two ▁points ▁are ▁uniqu ely ▁determined , ▁and ▁based ▁upon ▁the ▁properties ▁of ▁the ▁space ▁being ▁discussed , ▁the ▁appropriate ▁metric ▁is ▁mathemat