MathDB
Miklos Schweitzer 1964_4

Source:

September 20, 2008
geometrygeometric transformationreflectionadvanced fieldsadvanced fields unsolved

Problem Statement

Let A1,A2,...,An A_1,A_2,...,A_n be the vertices of a closed convex n n-gon K K numbered consecutively. Show that at least n\minus{}3 vertices Ai A_i have the property that the reflection of Ai A_i with respect to the midpoint of A_{i\minus{}1}A_{i\plus{}1} is contained in K K. (Indices are meant mod  n . \textrm{mod} \;n\ .)
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