| [ QuizWit ] in KIDS 글 쓴 이(By): iLUSiON (띠띠빤쮸) 날 짜 (Date): 2006년 1월 13일 금요일 오전 07시 19분 59초 제 목(Title): Re: 응湛퓽� 볼록사각형을 this is an easy problem. possibly easiest putnam competition problem type. i solve this before. one of homework problem in my undergrad. there are 2 solutions to this. 1) there are n adjacent triangels. let the interior angles be A1, A2,.. An. then A1 + A2 + A3 + ... An = 2pi (constrain 1) now the length of edges from the center of n-gon be L1, L2, Ln. Then area = 1/2 (L1*L2 sin A1 + L2*L3 sin A2 + .....) now circumference of n-gon is damn.. i forot highschool trig. identiy !!! circumferene = bla bla bla... (consrain 2) now you do Lagrange multiplier thingy and solve it by the differentiation. 2) second solution is based on inequliaity. not sure if it was minkowski inequlatiy or holder... iLUSiON - le plus grand de tous http://cyworld.nate.com/ilusion |