Abstract
Ancient books on East Asian mathematics introduced to the Korean Peninsula enrich our understanding of the arithmetic notions that mold the creative thought processes of the ancients. They believed that all objects in the universe could be composed of circles and squares and all items could be expressed in terms of geometrical profiles. Through the combination of circles and squares, the ancient East Asians expressed the order of the world and unraveled it mathematically. These principles are evident in the construction principles of early Korean stone pagodas. In particular, the square root of 2 (√2) is a very important number in the delineation represented in the consolidation of inscribed and circumscribed circles with squares. Further, the square root of 2 is applied as a design principle in the construction of the stone pagodas at the temples Chŏngnimsa and Kamŭnsa. This article demonstrates that the ancients on the continuous impact of the Jiuzhang Suanshu and the Zhoubi Suanshu constructed the pagodas complying with design principles based on the arithmetic and geometric proportional systems of √2 times, which are intended to adjust compositional proportions and the gradual decrease in length to shape the tripartite partition of the foundation, the pagoda body, and the finial in stone pagodas.
Highlights
Following the introduction of Buddhism to the Korean Peninsula in 372 CE,1 the pagodas of the Koguryŏ, Paekche, and Silla Kingdoms followed a unique formative system such as square and octagonal shapes
[The Arithmetical Classic of the Gnomon and the Circular Paths of Heaven] and the Jiuzhang Suanshu, on mathematical reasoning from various angles, say that all things are composed of circles and squares, along with the contents of Tianyuan Difang (天圓地方) [Round Sky and Square Earth]
Through two ancient Chinese mathematical books, Zhoubi Suanjing and Jiuzhang Suanshu, we understand the proportional systems and the design principles of ancient Korean pagodas that retain a wide range of cultural traditions and the arithmetical thought and interpretation of the ancients
Summary
Following the introduction of Buddhism to the Korean Peninsula in 372 CE, the pagodas of the Koguryŏ, Paekche, and Silla Kingdoms followed a unique formative system such as square and octagonal shapes. The stone pagodas at the Mirŭksa (彌勒寺) and Chŏngnimsa (定林寺) Temples are considered to be the earliest Paekche-style pagodas, but experts still have not agreed on their construction dates Based on a proportional system, Im Yŏngbae’s study on “the design principles of pagoda architecture between Korea and Japan” postulated the seven-story Mirŭksa Pagoda; he pointed out that the width of the body stone of each side steadily decreases, corresponding to one-tenth of the main central bay as a standard unit for stonemasonry, comparable to the wooden pagoda at Horyuji Temple in Japan 1942)’s measurement survey found that the ch’ŏk unit employed to erect the pagoda at the Chŏngnimsa Temple was the Koryŏ cubit, which is about 35 cm long He concluded that the width of the square platform of the pagoda was 14 ch’ŏk (≒490 cm), and that. Yoneda proved that the pagoda was constructed according to the principle of equivalent division with 7 ch’ŏk (Yoneda 1976, pp. 107–22)
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