作者chaogold (新扇不扇不擅讪新)
看板IMO_Taiwan
标题Re: [问题] 一个印度朋友给我的组合题
时间Sun Aug 29 22:27:04 2004
※ 引述《darkseer (公假中)》之铭言：
: ※ 引述《chaogold (新扇不扇不擅讪新)》之铭言：
: : 每一次操作的正n边形是同一个?
: : 镜射出来的正n边形是一直在的吗?
: 我的表达实在不好XD
: 直接po原文好了
: Let P be an n-gon , lying on a plane. We name its edges 1,2,3,..........n.
: If S = s_1, s_2,.............. be a finite or infinite sequence such that for each i s_i is in {1,2........n}.
: We move P in accordance with the sequence S such that we first reflect P through s_1
: ( the number s_i corresponds to the s_i th edge of the polygon P ) and then through s_2
: and so on. Show the following holds :
: a) Show that there exists a infinite sequence S such that if we move P according to S then
: then we can cover the whole plane.
: b) Prove that the sequence S is'nt periodic.
: c) Assume that P is a regular pentagon with the radius of its circumcircle as 1 and let D be
: another circle with radius 1.00001 lying in the plane arbitrary. Does there exist a sequence
: S such that we move P accordingly then P reside in D completely.
: 原题中的(a)就是我问的
: (b)(c)简单的多(好奇怪的配置XD)
欧欧我懂意思了，
你表达的很清楚是我刚好不太了解 ~XD
十分有趣的问题
让我想到另一个印度人问过的问题
我PO在这一篇後面好了
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