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The Seokguram Grotto in Korea and the Gougu Rule: Rebuttal of the √2 and √3 Hypothesis and a New Interpretation of the Underlying Method

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Abstract

Miyoji Yoneda’s controversial 1940 paper analyzing the compositional method of the Seokguram grotto triggered a series of debates among historians and critics about Yoneda’s approach. Surprisingly, much of the discussions after Yoneda focused on visually plausible diagrams full of rhetoric. However, their arguments have been weak and unconvincing without reliable demonstration. This paper begins by discussing mathematical knowledge at the time of the Grotto’s construction. Next, it outlines and proves that the Gougu rule provides the fundamental method for organizing the grotto layout. This paper sheds light on long-standing debates centered on the design method of the grotto and clarifies the underlying design principle.

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References

  • Bemis, Albert Farwell. 1936. The Evolving House, Vol. 3. Rational Design, Cambridge: Technology Press

  • Bureau of Cultural Property Management. 1967. A Report on Seokguram Renovation Work.

  • Cullen, Christopher. 1996. Astronomy and mathematics in ancient China: the Zhou bi suan jing. Cambridge: Cambridge University Press.

  • Dauben, Joseph W. 1998. Ancient Chinese mathematics: the Jiu Zhang Suan Shu vs Euclid's Elements. Aspects of proof and the linguistic limits of knowledge. International Journal of Engineering Science 36: 1339-1359.

  • Euclid. 1956. The thirteen books of the elements. Translated with introduction and commentary by Sir Thomas L. Heath. New York: Dover Publications.

  • Ghyka, Matila 1977. The Geometry of Art and Life, New York: Dover Publications

  • Hambidge, Jay. 1919. The Diagonal. Yale University Press; reprinted as The Elements of Dynamic Symmetry, New York: Dover Publication, 1967.

  • Hambidge, Jay. 1924. The Parthenon and Other Greek Temples: Their Dynamic Symmetry. Yale University Press.

  • Heath, Frederick. 1937. Modular Masonry. Master thesis, Seattle: University of Washington

  • Hwang, Su-young. 1974. Bulguksa and Seokguram. Seoul: King Sejong the Great Memorial Committee (In Korean).

  • Hwang, Su-young, and Jang-heon Ahn. 1989. Seokguram Cave Temple. Seoul: Yegyong (in Korean).

  • Kang, Woo-Bang. 1990. Perfection and Harmony: The principle of Korean Buddhist Sculpture. Youl Hwa Dang Publisher (In Korean).

  • Kangshen, Shen, John N. Crossley, and Anthony W-C Lun. 1999. The Nine Chapters on the Mathematical Art: Companion and Commentary. Oxford: The Oxford University

  • Kim, Pu-sik. 1145. Samguk sagi (translated into modern Korean by P.D. Yi). Seoul: Eul-Yoo, 1983 (in Korean).

  • Lay-Yong, Lam and Ang Tian-Se. 1986. Circle Measurements in Ancient China. Historia Mathematica 13: 325-340.

  • Manguel, Alberto. 2006. Done on paper: the dual nature of numbers and the page. In: The Life of Numbers, Antonio Duran, Georges Ifrah, Alberto Manguel, eds. A K Peters/CRC Press.

  • Mun, Myong-dae. 2000. Seokguram: The Cave Temple of Tohamsan. Seoul: KPI Publishing Co, (In Korean)

  • Nam, Cheonwoo. 1991. Seokbulsa, Seoul: Iljogak (In Korean).

  • Plato. 1965. Timaeus and Critias. London: Penguin Books

  • Salguero-Andujar, Francisco, Fulgencio Prat Hurtado, Inmaculada Rodriguez-Cunill and Joseph Cabeza-Lainez. 2021. Architectural Significance of the Seokguram Buddhist Grotto in Gyeongju (Korea). Buildings 12(1): 3

  • Schwartz, Randy. 2008. A Classic from China: The Nine Chapters. The Right Angle 16(2): 8-12

  • Seong, Nakju. 1999. Seokguram: ideology and aesthetics. Seoul: Gaemagowon (In Korean)

  • Shin. Hyung-jun. 2001. Criticism of the mathematical proportional Aesthetics of Seokguram through numerical verification. Master thesis, Seoul: Korea University (In Korean)

  • Shin, Young hoon and Kim Daebyuk. 1998. Seokbulsa·Bulkuksa, Seoul: Chosun Ilbo, (In Korean).

  • Siu, Man-Keung. 1993. Proof and Pedagogy in Ancient China: examples from Liu Hui's commentary on Jiu Zhang Suan Shu. Educational Studies in Mathematics 24: 345–357.

  • Straffin, Philip D. Jr. 1998. Liu Hui and the First Golden Age of Chinese Mathematics. Mathematics Magazine 71(3): 163-181.

  • Thom, Alexander, and Archibald Stevenson Thom. 1978. Megalithic Remains in Britain and Brittany. Oxford: Oxford University Press

  • van der Waerden, Bartel L. 1983. Geometry and Algebra in Ancient civilizations. Berlin: Springer-Verlag

  • Yoneda, Miyoji. 1976. Research into ancient Korean Architecture. Translated by Shin, Young hoon, Seoul: Hanguk munhwasa (in Korean).

  • Yoon, Jang Seob and Chae-Shin Yoon. 1998. Seokbusa. Seoul: Hakcheon (In Korean).

  • Yoon, Chae-Shin. 2020. The Stones of Seokguram Speak: Floor Plan and Wall Design of Seokbulsa Grotto. Journal of Architectural History 29(1): 21-37 (In Korean)

  • You, Hong-Jun. 1994. My Field Investigation for Cultural Heritage, Vol. 2. Seoul: Changbi publishers (In Korean)

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Acknowledgements

This work was supported by the INHA University Research Grant. All images are by the author.

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Correspondence to Jin-Ho Park.

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Park, JH. The Seokguram Grotto in Korea and the Gougu Rule: Rebuttal of the √2 and √3 Hypothesis and a New Interpretation of the Underlying Method. Nexus Netw J 24, 825–842 (2022). https://doi.org/10.1007/s00004-022-00617-9

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