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 2/6 步：证明 hull 是equilateral
上一步下一步
通俗地说

Reflect two neighboring hull 顶点.

AiAi+1=Ai+1Ai+2A_iA_{i+1}=A_{i+1}A_{i+2}
详细分析

The perpendicular bisect或的 AiAi+2 A_iA_{i+2} 是an ax是的symmetry. Since Ai+1 A_{i+1} 是intervening hull vertex, it 必须lie 上th是axis; hence AiAi+1=Ai+1Ai+2 A_iA_{i+1}=A_{i+1}A_{i+2}. Repeating around hull makes 所有sides equal.