Photos of Interactive Mathematics Miscellany and Puzzles

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Let BED,HIF, DLJ,FGA, ACB,JKH be six equilateral triangles and BED=HIF, DLJ=FGA, ACB=JKH and AF+BD=AB. Then show that GCELKI be a new regular hexagon and area(GCELKI)=3*\sqrt(3)/2(FA^2+AB^2+BD^2)