▁fiction ▁writers ▁Category : American ▁male ▁short ▁story ▁writers ▁Category : Pe ople ▁from ▁Pr inc eton , ▁Indiana ▁Category : 2 0 th - century ▁American ▁bi ograph ers ▁Category : 2 0 th - century ▁American ▁short ▁story ▁writers ▁Category : American ▁male ▁non - f iction ▁writers <0x0A> </s> ▁In ▁mathematics ▁and , ▁in ▁particular , ▁differential ▁geometry ▁a ▁circular ▁surface ▁is ▁the ▁image ▁of ▁a ▁map ▁ ƒ   :   I   ×   S 1   →   R 3 , ▁where ▁I   ⊂   R ▁is ▁an ▁open ▁interval ▁and ▁S 1 ▁is ▁the ▁unit ▁circle , ▁defined ▁by ▁ ▁where ▁ γ , ▁u , ▁v ▁: ▁I ▁→ ▁R 3 ▁and ▁r   :   I   →   R > 0 , ▁when ▁ ▁Moreover , ▁it ▁is ▁usually ▁assumed ▁that ▁u   ·   u ▁=   v   ·   v ▁=   1 ▁and ▁u ▁· ▁v ▁= ▁ 0 , ▁where ▁dot ▁denotes ▁the ▁canonical ▁scalar ▁product ▁on ▁R 3 , ▁i . e . ▁u ▁and ▁v ▁are ▁unit ▁length ▁and ▁mut ually ▁per pend icular . ▁The ▁map ▁ γ   :   I   →   R 3 ▁is ▁called ▁the ▁base ▁curve ▁for ▁the ▁circular ▁surface ▁and ▁the ▁two ▁maps ▁u ,   v   :   I   →   R 3 ▁are ▁called ▁the ▁direction ▁frame ▁for ▁the ▁circular ▁surface . ▁For ▁a ▁fixed ▁t 0   ∈   I ▁the ▁image