황금비율의 특성으로 본 불국사 석가탑의 외접방형

Abstract

The Sakyamuni Pagoda(or "Seokgatap" in Korean) of the Bulguksa temple is a geometrical art piece. Three kinds of golden ratios(golden sections, golden rectangles and golden diagonals) were also found there before. Minimum bounding rectangles(after, "MBR") might be needed in some pre-fixed ratios to make a drawing for the building. This study is to contribute for finding the macro structure of the pagoda from the view point of golden ratios of MBRs. The application of golden ratios in MBRs could be tested by some characters found at the pagoda before. They are the height-width ratios in “φn” as basic form, and two derived forms aφn and (√5)n. The study found that the pagoda is consisted of the three kinds of MBRs in the ratios, namely, the Body-wheel MBR(φ2), the Upper-cover MBR((√5)-4) and the Base MBR(φ0/2) by testing their characters. It also found that the height of the Body-wheel MBR and the Base MBR are golden sectioned by testing their characters. A set of golden diagonals which make a ratio structure for the three MBRs are found. And now we can use two kinds of ratio models for the height and width of the pagoda. The first is the “Three Kinds Golden Ratio MBRs Model” which has three height variables and two width variables. The second is the “Three Kinds Golden Ratio MBRs_Extended Model” which has nine height variables and two width variables. The two models were tested with the real values measured on the eastern side 3D drawing of the pagoda by Photoshop cs2. As only some limited errors were found there, and we can safely conclude that the pagoda was designed and constructed on the principle of golden ratio, not only from the view point of micro structure, but also from the view point of macro structure.