作者chaogold (新扇不扇不擅訕新)
看板IMO_Taiwan
標題Re: [問題] 一個印度朋友給我的組合題
時間Sun Aug 29 22:27:04 2004
※ 引述《darkseer (公假中)》之銘言：
: ※ 引述《chaogold (新扇不扇不擅訕新)》之銘言：
: : 每一次操作的正n邊形是同一個?
: : 鏡射出來的正n邊形是一直在的嗎?
: 我的表達實在不好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.
: 原題中的(a)就是我問的
: (b)(c)簡單的多(好奇怪的配置XD)
歐歐我懂意思了，
你表達的很清楚是我剛好不太了解 ~XD
十分有趣的問題
讓我想到另一個印度人問過的問題
我PO在這一篇後面好了
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