정사각형 칠교판으로 만들 수 없는 볼록다각형에 대한 고찰

Abstract

Objectives It is known that at most 20 convex polygons can be formed using all seven pieces of the puzzle, but this limit is imposed by the omission of the premise that the puzzle is a square divided into seven pieces. This study analyzes a convex polygon that is conjectured to be impossible to create using the puzzle and then uses the puzzle to prove that it cannot actually be constructed as the convex polygon.
 Methods The proof is based on the assumption that the given convex polygon cannot be formed using sev-en-piece puzzles. It proceeds in two different ways, depending on how the pieces are arranged within the square shape.
 Results We accomplished this in two ways: either by placing in the pieces having the largest area or by initially arranging the pieces on an angle and the diagonal of a square. Consequently, we have proved that the convex poly-gon cannot be formed by seven-piece puzzles.
 Conclusions The actual number of convex polygons that can be formed by seven-piece puzzles was 19, not 20. This study is significant because it provides a corollary for the number of convex polygons that can be constructed using all the pieces of the puzzle.