| [ QuizWit ] in KIDS 글 쓴 이(By): guest (OTiS) 날 짜 (Date): 1998년02월19일(목) 19시57분03초 ROK 제 목(Title): manhole ! obviously this is trivial convex geometry problem... any convex object that behaves the following property. 1: Let L be the diameter of the convex object the diameter of the convex body is defined as the largest length of its projection. 2. Let M be the smallest length of its projection. if L-M >= 0 then the object will passs thru the hole. (works only for convex body..otherwise the problem is complicated.) Hence we must have L-M < 0 I think i mixed up the equality sign. Hence "Circle" in 2dimension and "Spehre" in n -dimension is the only objects. END OF THE PROOF. wow... i didn't know the proof might be this simple... it is nice isn't it.. ? |