MathLabs

第1题

确定所有 finite sets S S 的在least three 点s 中plane which satisfy following condition: F或any two distinct 点s A A 且 B B 中 S S , perpendicular bisect或的直线 segment AB AB 是an ax是的symmetry 的 S S .
第 6/6 步：Verify converse
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通俗地说

Regular polygons have 所有chord-bisect或reflecti上symmetries.

S={vertices of a regular r-gon},r≥3S=\{\text{vertices of a regular }r\text{-gon}\},\quad r\ge3
详细分析

F或顶点 的any regular polygon, perpendicular bisect或的每个chord 是a reflecti上ax是的polygon, hence 的its vertex set. 所以 exactly vertex sets 的regular polygons satisfy condition.