ically ▁established ▁too . ▁On ▁the ▁cur ved ▁surface ▁of ▁the ▁Earth , ▁we ▁can ▁see ▁this ▁effect ▁in ▁long - ha ul ▁air line ▁fl ights ▁where ▁the ▁distance ▁between ▁two ▁points ▁is ▁measured ▁based ▁upon ▁a ▁great ▁circle , ▁rather ▁than ▁the ▁straight ▁line ▁one ▁might ▁plot ▁on ▁a ▁two - dimensional ▁map ▁of ▁the ▁Earth ' s ▁surface . ▁In ▁general , ▁such ▁short est - distance ▁paths ▁are ▁called ▁" ge odes ics ". ▁In ▁E uclidean ▁geometry , ▁the ▁ge odes ic ▁is ▁a ▁straight ▁line , ▁while ▁in ▁non - E uclidean ▁geometry ▁such ▁as ▁on ▁the ▁Earth ' s ▁surface , ▁this ▁is ▁not ▁the ▁case . ▁Indeed , ▁even ▁the ▁short est - distance ▁great ▁circle ▁path ▁is ▁always ▁longer ▁than ▁the ▁E uclidean ▁straight ▁line ▁path ▁which ▁passes ▁through ▁the ▁interior ▁of ▁the ▁Earth . ▁The ▁difference ▁between ▁the ▁straight ▁line ▁path ▁and ▁the ▁short est - distance ▁great ▁circle ▁path ▁is ▁due ▁to ▁the ▁curv ature ▁of ▁the ▁Earth ' s ▁surface . ▁While ▁there ▁is ▁always ▁an ▁effect ▁due ▁to ▁this ▁curv ature , ▁at ▁short ▁distances ▁the ▁effect ▁is ▁small ▁enough ▁to ▁be ▁un not ice able . ▁ ▁On ▁plane ▁maps , ▁great ▁circles ▁of ▁the ▁Earth ▁are ▁mostly ▁not ▁shown ▁as ▁straight ▁lines . ▁Indeed , ▁there ▁is ▁a ▁s eld om - used ▁map ▁projection , ▁namely ▁the ▁g nom onic ▁projection , ▁where ▁all ▁great ▁circles ▁are ▁shown ▁as ▁straight ▁lines , ▁but ▁in ▁this ▁projection ,