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 3/6 步：证明 hull 是regular
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通俗地说

The same reflecti上argument equalizes 角s.

∠AiAi+1Ai+2=∠Ai+1Ai+2Ai+3\angle A_iA_{i+1}A_{i+2}=\angle A_{i+1}A_{i+2}A_{i+3}
详细分析

应用ing perpendicular-bisect或symmetry 到 Ai A_i 且 Ai+3 A_{i+3} shows corresponding adjacent 角s 是equal. 故 所有hull 角s 是equal as well as 所有side 长度s, so hull 是a regular r r 译文：-gon.