Design Principles of Early Stone Pagodas in Ancient Korean Architecture
Design Principles of Early Stone Pagodas in Ancient Korean Architecture
Key Terms
China
Korea
Japan
Architecture
Buddhism
Buddhist Architecture
Stupas
Pagodas
Palaces
Pavalion
Pillars
Ancient
Art
History
Religion
Zhoubi Suanshu (周髀算經) [The Arithmetical Classic of the Gnomon and the Circular Paths of Heaven]
Zhou bi suan jing (The Arithmetic Classic of the Gnomon and the Circular Paths of Heaven), which is sometimes written as Chou Pei Suan Ching
Jiuzhang Suanshu (九章算術) [The Nine Chapters on the Mathematical Art]
‘Jiuzhang Suanshu’ and ‘Zhoubi Suanjing’
Chiu chang suan shi (The Nine Chapters on the Mathematical Art), which is sometimes written as Jiu zhang suan shu
Tianyuan difang (Heaven is round and Earth is square)
Xiangtianfadi Guijufangyuan
Guijufangyuan Futuwanqian
Guijufangyuan Fuzhijusuo
Guijufangyuan Duxianggouwu
Jinchenggongque Taiziyuanfang
Guijufangyuan Tiandezhongzhou
Yingzao Fashi 營造法式 (Treatise on Architectural Methods, 1103 CE)
Source: “Design Principles of Early Stone Pagodas in Ancient Korean Architecture: Case Studies on the Stone Pagodas at Chŏngnimsa and Kamŭnsa Buddhist Temples”
Source: “Design Principles of Early Stone Pagodas in Ancient Korean Architecture: Case Studies on the Stone Pagodas at Chŏngnimsa and Kamŭnsa Buddhist Temples”
Source: “Design Principles of Early Stone Pagodas in Ancient Korean Architecture: Case Studies on the Stone Pagodas at Chŏngnimsa and Kamŭnsa Buddhist Temples”
Source: “Design Principles of Early Stone Pagodas in Ancient Korean Architecture: Case Studies on the Stone Pagodas at Chŏngnimsa and Kamŭnsa Buddhist Temples”
Source: “Design Principles of Early Stone Pagodas in Ancient Korean Architecture: Case Studies on the Stone Pagodas at Chŏngnimsa and Kamŭnsa Buddhist Temples”
Source: “Design Principles of Early Stone Pagodas in Ancient Korean Architecture: Case Studies on the Stone Pagodas at Chŏngnimsa and Kamŭnsa Buddhist Temples”
Source: “Design Principles of Early Stone Pagodas in Ancient Korean Architecture: Case Studies on the Stone Pagodas at Chŏngnimsa and Kamŭnsa Buddhist Temples”
Source: “Design Principles of Early Stone Pagodas in Ancient Korean Architecture: Case Studies on the Stone Pagodas at Chŏngnimsa and Kamŭnsa Buddhist Temples”
Source: “Design Principles of Early Stone Pagodas in Ancient Korean Architecture: Case Studies on the Stone Pagodas at Chŏngnimsa and Kamŭnsa Buddhist Temples”
Source: “Design Principles of Early Stone Pagodas in Ancient Korean Architecture: Case Studies on the Stone Pagodas at Chŏngnimsa and Kamŭnsa Buddhist Temples”
Source: “Design Principles of Early Stone Pagodas in Ancient Korean Architecture: Case Studies on the Stone Pagodas at Chŏngnimsa and Kamŭnsa Buddhist Temples”
Source: “Design Principles of Early Stone Pagodas in Ancient Korean Architecture: Case Studies on the Stone Pagodas at Chŏngnimsa and Kamŭnsa Buddhist Temples”
Source: “Design Principles of Early Stone Pagodas in Ancient Korean Architecture: Case Studies on the Stone Pagodas at Chŏngnimsa and Kamŭnsa Buddhist Temples”
Source: “Design Principles of Early Stone Pagodas in Ancient Korean Architecture: Case Studies on the Stone Pagodas at Chŏngnimsa and Kamŭnsa Buddhist Temples”
Source: “Design Principles of Early Stone Pagodas in Ancient Korean Architecture: Case Studies on the Stone Pagodas at Chŏngnimsa and Kamŭnsa Buddhist Temples”
Source: “Design Principles of Early Stone Pagodas in Ancient Korean Architecture: Case Studies on the Stone Pagodas at Chŏngnimsa and Kamŭnsa Buddhist Temples”
Source: “Design Principles of Early Stone Pagodas in Ancient Korean Architecture: Case Studies on the Stone Pagodas at Chŏngnimsa and Kamŭnsa Buddhist Temples”
Source: “Design Principles of Early Stone Pagodas in Ancient Korean Architecture: Case Studies on the Stone Pagodas at Chŏngnimsa and Kamŭnsa Buddhist Temples”
Source: Reconsidering a proportional system of timber-frame structures through ancient mathematics books: a case study on the Muryangsujŏn Hall at Pusŏksa Buddhist Monastery.
Source: Reconsidering a proportional system of timber-frame structures through ancient mathematics books: a case study on the Muryangsujŏn Hall at Pusŏksa Buddhist Monastery.
Source: Reconsidering a proportional system of timber-frame structures through ancient mathematics books: a case study on the Muryangsujŏn Hall at Pusŏksa Buddhist Monastery.
Source: Reconsidering a proportional system of timber-frame structures through ancient mathematics books: a case study on the Muryangsujŏn Hall at Pusŏksa Buddhist Monastery.
Source: Reconsidering a proportional system of timber-frame structures through ancient mathematics books: a case study on the Muryangsujŏn Hall at Pusŏksa Buddhist Monastery.
Source: Reconsidering a proportional system of timber-frame structures through ancient mathematics books: a case study on the Muryangsujŏn Hall at Pusŏksa Buddhist Monastery.
Source: Reconsidering a proportional system of timber-frame structures through ancient mathematics books: a case study on the Muryangsujŏn Hall at Pusŏksa Buddhist Monastery.
Source: Reconsidering a proportional system of timber-frame structures through ancient mathematics books: a case study on the Muryangsujŏn Hall at Pusŏksa Buddhist Monastery.
Source: Reconsidering a proportional system of timber-frame structures through ancient mathematics books: a case study on the Muryangsujŏn Hall at Pusŏksa Buddhist Monastery.
Source: Reconsidering a proportional system of timber-frame structures through ancient mathematics books: a case study on the Muryangsujŏn Hall at Pusŏksa Buddhist Monastery.
Source: Reconsidering a proportional system of timber-frame structures through ancient mathematics books: a case study on the Muryangsujŏn Hall at Pusŏksa Buddhist Monastery.
Source: Reconsidering a proportional system of timber-frame structures through ancient mathematics books: a case study on the Muryangsujŏn Hall at Pusŏksa Buddhist Monastery.
Source: Reconsidering a proportional system of timber-frame structures through ancient mathematics books: a case study on the Muryangsujŏn Hall at Pusŏksa Buddhist Monastery.
Source: Reconsidering a proportional system of timber-frame structures through ancient mathematics books: a case study on the Muryangsujŏn Hall at Pusŏksa Buddhist Monastery.
Source: Reconsidering a proportional system of timber-frame structures through ancient mathematics books: a case study on the Muryangsujŏn Hall at Pusŏksa Buddhist Monastery.
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Design Principles of Early Stone Pagodas in Ancient Korean Architecture
“Design Principles of Early Stone Pagodas in Ancient Korean Architecture: Case Studies on the Stone Pagodas at Chŏngnimsa and Kamŭnsa Buddhist Temples”
Ritual architecture, or lizhi jianzhu 禮制建築, is a unique category in traditional Chinese architecture. Compared to other traditional Chinese architectural types-for instance, Buddhist architecture 佛教建築, palace architecture 宮殿建築, or mausoleum architecture 陵墓建築-ritual architecture is not as clearly defined and contains a much broader range of buildings with a variety of functions.1 Ritual architecture originally refered to structures built to fulfill the Confucian ideals. However, since Confucianism as a religious practice is not as specifically defined as Buddhism or Daoism, structures for worship, ritual sacrifice, or memorial function that cannot be fitted into Buddhism or Daoism are all grouped under the category of ritual architecture, including such diverse building types as the memorial archways for chaste women, shrines dedicated to gods of the five sacred peaks, Confucian temples, and the Altars of Heaven. The complicated nature of ritual architecture originates from the diversity of local beliefs in traditional Chinese society, which cannot be simplified as merely “Confucian.” Tracy Miller’s book The Divine Nature of Power: Chinese Ritual Architecture at the Sacred Site of Jinci takes up the challenge and makes a fine contribution to our understanding of the complexity of both ritual practices in ancient China and the physical environment that was created by and for such diverse and often contradictory practices. The main argument of the book is that the original source of divinity at the site of modern day Jinci is neither the founder of the Jin state, Shu Yu of the Zhou Dynasty, nor his mother, Yi Jiang, as is widely assumed,2 but the life-giving water as represented by the local water goddess-the Spirit of the Jin Springs (pp. 10, 178). Such a conclusion is supported by recent archaeological discoveries (p. 177), a closer examination of historical documents (p. 178), and the extant buildings, sculptures, and paintings in and the general layout of the Jinci complex (pp. 12-13, 179-184). What led to the confusion and opposition about the identity of the main deity worshiped at Jinci are the competing local patronages, whose wills were materialized in various documents and folklores as well as art and architectural forms (pp. 13-14, 181-183). Such a thesis and reasoning procedure are clearly delineated in the introduction and conclusion of the book. Like other ritual architecture throughout China, Jinci is a collection of shrines and temples dedicated to a variety of deities. The most important ones and at the same time the most relevant to the thesis of the book are the Sage Mother Hall 聖母殿 and the Shu Yu of Tang Shrine Complex 唐叔虞祠, on which most of the chapters of this book focus. Chapter 2 discusses the ambiguous meaning of the name “Jinci 晉祠” and its potential for different interpretations on the identity of main deities. The author argues that the term “Jinci” allows the site to be interpreted as either dedicated to the rulers of Jin State or the Spirit of the Jin Springs. It also provides a general introduction of the present physical layout of the complex in the beginning section. Chapters 3 and 4 focus on the changing significance of Shu Yu across time and the impact that had on the shrine complex built for him. Chapter 3 also discusses the significance of the Taiyuan city, where Jinci is located, as a seat of local power, and suggests that this might be the reason why it was misunderstood as the place where the Jin State was originally founded. In chapter 4, based on historical documents from official dynastic histories to stele inscriptions, the author tries to delineate a picture of both an idealized Shu Yu shrine and the evolvement of the cult of Shu Yu as a state founder. Chapters 5 and 6 turn to the worship of the Spirit of the Jin Springs. Chapter 5 focuses on the textual study of the importance of the spring water to the local agrarian community and the purpose for building a temple at the site of the Jin Springs-to provide shelter for human encounters with the nature spirits that reside there. Chapter 6 offers the most in-depth stylistic analysis of the art and architecture of the Sage Mother Hall in this book, including a…
佛寺設計：空間•結構•場所 The Design of Chinese Monasteries: Space, Structure, and Place Online Symposium on Buddhist Architecture
Reconsidering a proportional system of timber-frame structures through ancient mathematics books: a case study on the Muryangsujŏn Hall at Pusŏksa Buddhist Monastery.
Ten-story Stone Pagoda from Gyeongcheonsa Temple Site
Exhibition Name Ten-story Stone Pagoda of Gyeongcheonsa Temple Nationality/Period Goryeo Dynasty Provenance Gyeonggi-do Materials Stone Category religion – Buddhism – adoration – pagoda Dimensions H. 1,350.0cm Designation National Treasure 86 Accession Number Bongwan 6753 Location Path to History
Pagodas were first erected in East Asia after the arrival of Buddhism. Chinese Buddhists usually built brick pagodas, while those in Japan and Korea erected wooden and stone pagodas, respectively. Most Korean stone pagodas were made from granite, but this massive ten-story pagoda is the first one known to be made from marble. It once stood on the grounds of Gyeongcheonsa Temple, located at the foot of Mt. Buso in Gwangdeok-myeon, Gaepung-gun, Gyeonggi-do Province. This pagoda is also extraordinary in terms of its form, which is much more complex than most other pagodas. Its shape is very unusual, with a three-tier base, a complex polygonal shape for the lower part (from the first to the third tier), and a square upper part. The base and the main body are elaborately decorated with carvings of Buddhas, bodhisattvas, and floral designs, and there is an inscription engraved on the body of the first story, stating that the pagoda was built in 1348 (4th year of Goryeo King Chungmok). The eaves of the roof stones reflect the influence of Goryeo wooden architecture, which would later also influence the Ten-story Stone Pagoda at the Wongaksa Temple Site (National Treasure No.2), built during the Joseon Dynasty. This pagoda was taken from its original site and smuggled to Japan in 1907 by Tanaka Mitsuaki, the Japanese Minister of Imperial Household Affairs. It was eventually recovered with the help of two Western journalists, Ernest T. Bethell from England and Homer Hulbert from America, who launched an international press campaign denouncing the theft. The pagoda was reconstructed at Gyeongbokgung Palace in 1960, where it remained until 1995, when it was dismantled to repair serious damage from weathering and acid rain. The exhaustive conservation treatment project took ten years, and in 2005 the restored pagoda was reconstructed at its current location, prominently displayed on the “Path to History” inside the National Museum of Korea.
Pagodas of Bulguksa Temple
Feb 17, 2014
Bulguksa Temple’s two most famous features are the Dabotap Pagoda, the Pagoda of Many Treasures or of Multiple Jewels, and the Seokgatap Pagoda, the Sakyamuni Buddha Pagoda. They stand within the central courtyard in front of the historic main hall, dedicated to the Sakyamuni, one of the Buddha’s titles. When the Royal Asiatic Society brings visitors on its annual Gyeongju Tour, these are the most impressive monuments that we see.
Pagodas evolved from the ancient Hindu and Buddhist stupa funerary-monuments of northern India as the new faith spread along the Silk Road into China almost two millennia ago, becoming wooden and brick towers. In Korea, this architectural tradition evolved into solid granite pagodas, usually about three to seven meters tall, with hollow spaces in one of their lower stories to contain holy relics such as sarira crystals or sutra scriptures.
More than 1,000 of these remain extant today, especially common in the southern regions of Korea. However, the Dabotap Pagoda and the SeokgatapPagoda tower over all the others as being the most excellent specimens for their complex ingenious architecture, profound philosophical depth and aesthetic charm. They are considered to be an inseparable and opposite-but-complimentary eum-yang pair, a yin-yang pair, standing together in view of the Buddha, offering all those who look upon them a lesson in monumental stone.
According to this view, the Dabotap Pagoda represents the eum characteristics of being female, dark, cold, of energy moving downward and inward, and of the transformation of heavenly principles into the myriad physical forms we enjoy on this earth. In contrast, the Seokgatap Pagoda represents the yang characteristics of being male, bright, hot, of energy moving upward and outward and of the spiritual aspirations of humankind.
Another classical way of looking at their polarities is to interpret the SeokgatapPagoda as the historical Buddha himself when he was teaching the Lotus Sutra, and the Dabotap Pagoda as his disciples listening to him. This is symbolized by the Dabo, or the Prabhutaratna Buddha-icon, which is said to manifest itself whenever and wherever the sutra is taught. The disciples are enlightened by the Buddha’s teachings and become beings who shine like precious jewels.
The Dabotap Pagoda or Many Treasures Pagoda is considered one of the most remarkable traditional structures in East Asia. Koreans are very proud of it and they depict it on their 10-won coin. Some 10.4 meters tall, this highly decorative pagoda’s fame comes from its extremely complex and delicate philosophically-based design. At the base are four sets of steps, which lead to four lion guards, symbolizing wisdom in Buddhism. Above the lions are a number of well-fitted granite blocks. The pillars stand on an elevated platform approached by four staircases, each with ten steps signifying the Ten Perfections or Virtues, the paramitas, of Buddhist thought.
This pagoda has had an unfortunate modern history. It was disassembled by the Japanese for repair in 1924 when Korea was under colonial rule. As this grand-scale project was underway, the lack of thorough protection resulted in its inner sarira caskets and three of the original stone lions being stolen, and they have never been recovered.
The Seokgatap Pagoda, or Sakyamuni Buddha Pagoda, stands 8.2 meters tall and is the finest example of a typical Korean Buddhist pagoda, being the cumulative apogee of all the earlier tradition and the prototype for many subsequent constructions. It is also called the Muyeongtap Pagoda, or Pagoda Without a Reflection, denoting the sad legend of the Baekje stonemason, Asadal, who built these pagodas. An old myth says that his wife, Asanyeo, traveled from afar to be with him because she missed him so much, but he was not allowed to see her until the work was finished due to ritual-taboo restrictions. She waited by a pond across the valley, waiting for the top of this pagoda to appear above the temple walls in the reflection on the water, but when no such reflection came after many months, she threw herself into the pond in despair. Unfortunately, the Seokgatap Pagoda has been under repair since early 2013, so you cannot see it these days, just as poor Asanyeo was not able to witness its beauty.
It is universally admired for its perfect proportions and its simple, graceful style. It has three main stories, like many of the pagodas from the Silla era, “three” being a sacred number in Buddhism and in many other spiritual traditions. In Buddhism, “three” symbolizes various triads, such as the Three Jewels of the Buddha himself, his Dharma teachings and the Sangha community of monks, or the corresponding division of Buddhist scriptures into sutras, sastras and vinaya, or the Cheon-Ji-In Trinity, the Heaven, Earth and Humanity Trinity, at the foundation of all Northeast Asian religious culture.
The Seokgatap Pagoda was first dismantled for repair in 1977. At that time, a collection of precious treasures was found inside, including a set of reliquary for sarira crystals and a paper scroll of the “True Words of Pure and Clean Light Scripture.” Scholars determined that this sutra was printed between 706 and 751, thus being the world’s oldest extant xylographic publication.
These Buddhist pagodas are a symbolic expression of doctrine. The ideological underpinnings of the Dabotap Pagoda and the Seokgatap Pagoda are said to be based on the centrally-important Lotus and Flower-Garland Sutras, scriptures emphasizing that sentient beings undergoing suffering in their lives on earth need to cultivate themselves both spiritually and physically to attain enlightened liberation. Their prominent location in the very center of Bulguksa Temple shows that 8th-century Koreans valued these Buddhist teachings very highly.
By David A. Mason A Professor of Korean Cultural Tourism at Nam-Seoul University
Discover Korea with the RAS [The Royal Asiatic Society Korea Branch, founded in 1900, is an association of people, Koreans and non-Koreans alike, who wish to deepen their knowledge of Korean life, culture and history, and share that knowledge with others in English. http://www.raskb.com/ ]
The cultural heritage authorities of South Korea today officially unveiled the country’s oldest stone Buddhist pagoda following a record restoration effort that stretched over almost two decades—the longest is the country’s history. The Iksan Mireuksaji Stone Pagoda (익산 미륵사지 석탑) at the ancient Mireuksa temple complex in southern North Jeolla Province is the oldest extant stone pagoda in South Korea, constructed during the influential Baekje kingdom (18 BCE–660 CE).
Standing 14.5 meters high, 12.5 meters wide, and weighing some 1,830 tons, the restored pagoda, designated as National Treasure No.11 and standing in the west of the Mireuksa temple complex, now has only six tiers, but historians believe it originally had nine, matching Mireuksa’s 27.67-meter, nine-level eastern pagoda, which was completely reconstructed in 1993 in accordance with historical records. The pagoda is believed to have lost its upper levels sometime in the 16th century during the Kingdom of Great Joseon (1392–1897), which favored Confucianism over Buddhism.
The National Research Institute of Cultural Heritage, which has led the lengthy project, noted that a full report would soon be published detailing the restoration process, which cost an estimated US$20.3 million, including the dismantling and reconstruction of the Buddhist monument.
“We made special efforts to secure the ingenuity and the structural stability of the stone tower of Mireuk Temple,” an institute official was quoted as saying. “We plan to publish a report outlining the result and the process of the restoration work by the end of this year.” (Yonhap News Agency)
Established during the Baekje kingdom and located in the modern city of Iksan, Mireuksa temple was founded late in the reign of King Mu (r. 600–641). The restored pagoda is one of only two Baekje pagodas that have survived to the present day. It was designated a national treasure in 1962 and was added to UNESCO’s World Heritage list in July 2015 as part of the Baekje Historic Areas World Heritage Site.
Mireuksa was the largest temple in the ancient kingdom of Baekje, which is notable for being instrumental in introducing and propagating Buddhism on the Korean Peninsula, and is now considered an example of the most advanced architectural skills of the Baekje, Goguryeo, and Silla kingdoms, which co-existed on the peninsula. The temple is also renowned for its ancient four-meter stone flagpole supports, which date to the Later Silla (660–935).
An initial makeshift attempt to restore the stone pagoda was undertaken with concrete in 1915, during the Japanese occupation of Korea, after which the monument stood untouched until the National Research Institute of Cultural Heritage initiated the current restoration effort.
An inscribed gold plate was discovered during the restoration process, detailing the pagoda’s origin. From wikipedia.org
In 1999, the institute concluded that the pagoda was in serious need of repair, and the restoration project began in earnest in 2001, becoming Korea’s longest restoration initiative for a single cultural heritage item—the restoration team spent 10 of those years carefully dismantling the pagoda. According to reports, about 185 tons of concrete was removed and new locally sourced granite blocks were commissioned and added to the tower, making up about 35 per cent of the restored structure, which is now composed of 1,627 stone blocks.
In 2009, during the painstaking process to dismantle the pagoda, an engraved gold sheet was discovered shedding new light on the history of the pagoda. The inscription indicates that the monument was commissioned in 639 CE by the second wife of King Mu of Baekje (r. 600–641).
As of 2018, South Korea has 13 listed World Heritage sites,** many of which stand in testament to the country’s long and influential Buddhist heritage, including Seokguram Grotto and Bulguksa Temple in North Gyeongsang Province, the Baekje Historic Areas in South Chungcheong and North Jeolla, the Gyeongju Historic Areas in North Gyeongsang, and the mountain fortress city of Namhansanseong in Gyeonggi.
The tower before restoration. From wikipedia.org
According to data from the 2015 national census, the majority of South Korea’s population—56.1 per cent—holds no religious affiliation. Christians make up the largest religious segment of the population at 27.6 per cent, while Buddhists account for 15.5 per cent.
Kim Bongryol PhD, Professor of Architecture, Korea National University of Arts
A Buddhist Temple Is a Complex of Buildings
Buddhism was introduced to China from India and Central Asia, and it was already prevalent in China by the fourth century when the religion was first introduced to the Korean peninsula. At that time, the peninsula was divided into three separate kingdoms: Goguryeo 高句麗 (37 BCE–668 CE), Baekje 百濟 (18 BCE–660 CE), and Silla 新羅 (57 BCE–935 CE). Buddhism was welcomed by the royal houses of the Three Kingdoms, which pursued Buddhism competitively. The royal houses took the principal initiative for its spread, and Buddhism flourished in uniquely Korean forms, which came to characterize the architecture of Buddhist temples.
Following the introduction of Buddhism, the royal houses of the Three Kingdoms constructed huge temples in the heart of their capital cities. Goguryeo built Jeongneungsa 定陵寺 in Pyeongyang 平壤 to manage the royal tombs. Baekje constructed Mireuksa 彌勒寺 in Iksan 益山, a new city to which the capital of Baekje later moved. Silla constructed Hwangnyongsa 皇龍寺 in the heart of Gyeongju 慶州. The early seventh-century Mireuksa was built on a huge site on which three temples were placed in juxtaposition according to the Buddhist doctrine stating that Maitreya (Mireuk in Korean), the Future Buddha, would come to the world to save all living beings through three sermons. It is said that Mireuksa covered a land area of 165,000 square meters and was home to as many as three thousand monks. Hwangnyongsa was founded in 570 CE and covered an area of 80,000 square meters. A nine-story wooden pagoda was built at its center. This wooden pagoda rose 80 meters and had stairs inside that led to the top floor. It served as an observatory to view the city. Construction of temples by the royal houses drove the development of technology and improved the quality of Korean architecture overall, not to mention advancing Buddhist architecture.
According to Mahayana Buddhism, which is the mainstream of Korean Buddhism, the whole universe consists of three thousand worlds, which means near infinity, and one Buddha presides over each of these three thousand worlds. Buddhism has expanded from the belief in the one and only Buddha Shakyamuni to the belief in three thousand Buddhas. In particular, Mahayana doctrine emphasizes the “Path of the bodhisattva,” a key teaching of Mahayana ethics, which says “Seek enlightenment above, transform sentient beings below.” Countless bodhisattvas such as Avalokiteshvara, Manjushri, and Samantabhadra became popular and were venerated as second only to Buddha Shakyamuni. Also, in Central Asia and China, indigenous deities were added to the Buddhist pantheon, and these native gods became objects of worship in Korea as well. As a result, Central Asian Luminous Kings, the Daoist gods of the Big Dipper’s seven stars, and the Korean Mountain Spirit, not to mention many other Buddhist deities, all became objects of worship in Korea.
Buddhist temples in Korea necessarily included image halls for multiple Buddhas, bodhisattvas, and other deities. According to the principle of “One World, One Buddha,” or the existence of one Buddha at a time, a single building should enshrine only one object of worship, requiring that a temple have various buildings for worship. During the Joseon 朝鮮 period (1392–1910), when Confucianism was espoused by the ruling class and the elite literati-bureaucrats severely suppressed Buddhism, the Buddhist community in an effort to ensure its own survival unified all beliefs in different Buddhas and bodhisattvas. The distinctions between Buddhist sects were removed, and buildings for a number of Buddhas, bodhisattvas, and other deities were built on the premises of one single temple.
Located in the southern part of the Korean peninsula, Tongdosa 通度寺 has sixteen buildings in total for worship: five separate buildings for five Buddhas including Shakyamuni, Amitabha, Bhaishajyaguru, Vairochana, and Maitreya; four buildings for bodhisattvas and arhats including Avalokiteshvara, Kshitigarbha, and the Arhats; and six building for other deities including Chilseong 七星 (the Daoist Gods of the Seven Stars of the Big Dipper), Dokseong 獨聖 (Hermit Sage), Sansin 山神 (Mountain Spirit), the Four Heavenly Kings, and more.
Korean Buddhism prohibited the marriage of monks and established an obligation to live an austere, celibate life. Although a Buddhist sect that permits the marriage of monks came into being in the twentieth century, celibate monks still dominate the Buddhist community in Korea and are considered morally superior among laypeople. Temples, therefore, are monasteries where monks who renounced the world reside, study, and meditate.
The basic rule at a temple is “one room, one monk.” For this reason, a temple needs as many rooms as the number of monks residing there in addition to facilities like a kitchen, dining hall, bathing area, and toilets. A number of buildings for common use are also required, including a lecture hall to study and discuss sutras, a prayer hall for all monks to chant together, and a hall to practice Seon 禪 (Ch. Chan, Jp. Zen) or meditation. It has been general practice in traditional Korean architecture to assign one function to each building. As the residences for monks, dining hall, lecture hall, prayer hall, and meditation hall were each separately constructed as independent buildings, the area for monks alone could include some ten buildings. Korean Buddhist architecture was bigger and more dignified than secular architecture. In fact, monasteries were in no way inferior to royal palaces in leading contemporaneous architecture. Numerous Buddhist temples were built during the Joseon period even in the face of the heavy political and economic suppression of Buddhism. The tradition of large scale, ornamented buildings, which was established in the early stage when Buddhism was first introduced to Korea, still continues today.
A temple is a unified premises consisting of a prayer section for laypeople and a monastic section for resident monks. According to Mahayana tradition, the prayer section requires a number of buildings for various objects of worship (Buddhas, bodhisattvas, and other deities), and under the tradition of ascetic living, the monastic quarters need multiple buildings, some for eating and sleeping and others for practicing the faith. This is the reason Korean Buddhist temples consist of so many independent buildings. Accordingly, although it is important to make each building impressive, the relationship between buildings within a temple complex has even great significance. Architectural concerns such as the integration and separation of the prayer and monastic sections, the hierarchical distinctions between buildings dedicated to Buddhas and those for subordinate deities, and the association between the interior spaces within buildings and outside spaces between buildings are truly complex issues that are governed by the religious and sectarian tradition of each temple.
Buildings and Structural Elements
Contrary to the European tradition in which materials and building techniques clearly differed between religious and secular structures, Korean Buddhist architecture is not significantly different from that of administrative buildings or common residences. Ancient temples in Egypt and medieval churches in Europe are exquisite, imposing stone edifices, which contrast with ordinary residences made of wood. Korean Buddhist structures, on the other hand, were wooden buildings just like ordinary houses. Construction techniques that were developed for Buddhist architecture were also applied to secular buildings and the technological gap between the two remained narrow. Accordingly, in the Korean architectural tradition, the plan and construction of Buddhist architecture represent characteristics of Korean architecture in general.
The main parts of a building are the stone base, the timber column-and-beam skeleton, and the heavy pitched roof with overhanging eaves. Once a site is selected, the ground is rammed hard and the stone foundation is laid. This platform functions as the support for a row of columns and keeps the wooden structure from rotting due to infiltration of ground moisture into the wooden structure. The corners of the foundation are reinforced with stones, bricks, or tiles. Such stone bases with elaborate facings were generally used for Buddhist structures.
The wooden structure of Korean buildings is composed of framing with vertical columns and horizontal beams. The heavy weight of the roof is transmitted to the beams which in turn distribute the load to the columns and the ground. The columns are connected by lintels which together frame the walls. Spaces within the framework are filled with clay or wood to form a wall or are fitted with windows or doors to provide light and access. For windows and doors of Buddhist structures, a wooden frame decorated with carved floral patterns is covered with translucent Korean paper. Such windows and doors function as barriers that allows air to pass while reducing the effects of cold and heat from outside.
Brackets—supporting elements that are both functional and decorative—are placed on top of the column heads below the eaves. On the brackets are small columns that form a frame for the roof. Rafters of about ten centimeters in diameter are densely laid on the roof-frame to make a sloping roof. The roof is finished by laying tiles on its inclined surfaces. The roof tiles are a type of fired earthenware that make the entire building structurally stable by compressing the frame with their heavy weight while also protecting the building from rain and snow. Korean roof tiles come in convex and concave pairs. Concave tiles are shaped like a quarter cylinder and convex tiles are semicircular in profile. Concave tiles are laid first while convex tiles are placed across the joints between the concave tiles, affording perfect waterproofing for the roof. Specially manufactured roof tile ends are used along the edge of the eaves. Concave and convex roof tile ends are all attached with angled sides so that rainwater can be channeled away from the building. The angled sides of the roof tile ends are decorated. On Buddhist structures, decorative designs that symbolize Buddhism, such as the lotus and phoenix, were stamped on the angled sides. On the peak of the roof, large ornamental tiles called chimi 鴟尾 in Korean crowned the ends of the main roof ridge. This special type of roof tile resembles the tail of an imaginary fish or wings of a bird.
Korean wooden structures were extremely vulnerable to fire. Most were destroyed during war or by accidental fires. Although some buildings have been rebuilt, it is difficult to restore them to their original state. Once they catch fire, major structural components such as columns and beams burn quickly and the whole building collapses. Only the foundation and its stone or clay facing remain along with the roof tiles. Much of the original structure of many European buildings ruined in wars or by fire remain standing for extraordinarily long periods of time because they were made of stone, but the remains of ruined Korean structures are flattened, as can be witnessed at many historic sites. Most artifacts excavated from such ruins are roof tiles, which are fire-resistant. Roof tile ends decorated with exquisitely impressed designs have been discovered in large numbers and displayed in museums.
Unlike wooden buildings in Europe, Korean wooden buildings have long extended eaves in delicately curved lines, which are very impressive. These cantilevered eaves project out from the beams that support the rafters. A special system called gongpo 栱包 (wooden bracket system used to support the heavy tiled roofs at the ends of the eaves) was devised to make the eaves extend in a beautifully curved line. Placed between the heads of the columns and the roof frame, the gongpo disperses the weight to the beams and columns by transmitting the vertical load from the rafters. Elaborate multi-cluster wooden brackets on the heads of the columns create a single structure themselves, which is the most characteristic of all exterior components of Korean structures. Gongpo are also important ornamental components often bearing carved lotus and cloud designs.
At the center of the interior space, Buddhist images are enshrined on top of a wooden altar. This altar is also called the sumidan 須彌壇 as it symbolizes Mount Sumeru, which is regarded as the center of the Buddhist universe. On the ceiling directly above the sumidan hangs a separate house-shaped canopy called a datjip 닫집 in Korean, which serves as a roof for the Buddhist statues enshrined on the altar. The interior of the datjip is filled with sculptures in the shape of a dragon, phoenix, and clouds to represent Buddhist heaven. Buddhist architecture does not divide the interior of a building into compartments but treats it as a single space.
The walls and ceiling are adorned with painted images of Buddha, heavenly beings, and various symbolic motifs such as lotuses. This was meant by the Koreans to create a splendid and magnificent Buddhist paradise. The five basic colors used in Korean architecture are red, yellow, blue, black, and white. The coloring technique is systematic and follows a specific set of rules. In addition to serving as interior and exterior decoration, applied paint protects the wooden building against rotting.
Relationship between Image Halls and Pagodas
Cave temples and stupas are archetypes of early Buddhist architecture. Caves were natural places for monks who had entered the Buddhist priesthood to practice austerity, and stupas were places for lay devotees to pray. Originally, the stupa, which means “burial mound for enlightened beings” in Sanskrit, was a mound that enshrined relics of the Buddha Shakyamuni and was worshiped as the symbol of the Buddha. China received the tradition of the stupa in the form of the high-storied building from India through Central Asia. Chinese pagodas were mainly built with bricks, but in Korea stone was the preferred material for constructing pagodas. Although both wooden and brick pagodas were also constructed in Korea, most Korean pagodas were built from stone and represent an architectural type distinguishable from the Chinese brick pagodas and Japanese counterparts made of wood.
Cave temples were developed on the Deccan Plateau in India. The earliest examples were created by cutting into sandstone rock to create spaces for Buddhist monks to stay. As visits to monks by lay devotees increased over time, caves for worship were also created, promoting the development of cave temple complexes. In regions where Buddhism spread, constructing a cave temple was regarded as the greatest way of accumulating merit. It soon created an international boom for hollowing out cave temples. This architectural form developed in Ajanta and Nashik in India, spread through Bamiyan and Kizil in Central Asia, and traveled to China, where the cave temples of Dunhuang 敦煌 and Yungang 雲崗 were built. Korea, too, aspired to construct cave temples after Buddhism was first introduced to the peninsula. However, the major rock type which covers the land surface of Korea is granite, which is too hard to cut into. In India and China, cave temples were comparatively easy to construct because the bedrock was much softer limestone, sandstone, and mudstone. Seokguram Grotto 石窟庵, the representative example of Korean cave temples, constructed in the eighth century, is in fact a stone chamber artificially built with stone and covered with a dome.
Although many cave temples were built, most temples were free-standing complexes with proper monks’ quarters. Also, at the initial stage, worship of Buddhist images was not yet introduced, and the stupa was the sole object of devotion. Around the second century BCE, Buddhist statues in the form of human figures appeared in the Gandhara and Mathura regions of India, and such statues became established as objects of worship. It was only natural that Buddhist statues in realistic human form eventually replaced the abstract symbol of the stupa as the central object of worship. This led to the need for the construction of a new building to enshrine Buddhist statues. Because Buddhist sculptures are covered in very expensive gilding, the image hall came to be called the “golden hall.”
The image hall itself became an object of worship because of the Buddhist statues enshrined within. The pagoda standing outside the image hall continued to be an object for a different, more abstract worship. Accordingly, ancient temples comprised an image hall and pagoda together, and the architectural form of the Buddhist temple complex was determined entirely by the relationship between the image hall and the pagoda.
Each of the ancient kingdoms of Korea had its own architectural layout for temples. For example, the architectural type of Goguryeo was “one pagoda, three image halls,” with one pagoda surrounded by image halls on three sides. Baekje adopted the “one pagoda and one image hall” model in which a pagoda, image hall, and lecture hall were placed along a shared axis. In Silla, the “twin pagodas” type, in which two pagodas were located in front of the image hall, was preferred.
Around the tenth century, the Seon School (Kr. Seonjong 禪宗), or Meditation School, was introduced to the Korean peninsula. It was received with enthusiasm by the Korean Buddhist community and was established as the major sect of Korean Buddhism going forward. The Seon School rejected existing icons and freed itself from the existing architectural patterns. Stupa worship, or the “cult of relics,” began to weaken, and this naturally made the pagoda lose importance. Buddhist pagodas became smaller in size and were pushed to the periphery of temple compounds away from the center. Temples without pagodas that have only an image hall quickly became the mainstream model.
Diversity in Architectural Forms
Religious architecture in Europe focuses upon the building itself. That is, architecture is a shrine or a church. Buddhist architecture in Korea, on the other hand, is a set of buildings, where a building functions like a single room. For example, the Pantheon in Rome is a religious building and also a piece of religious architecture that enshrines gods. A Buddhist temple in Korea has as few as five and as many as sixty buildings and all these together are considered one architectural whole. The relationship between the buildings and their orientation to the natural topography are essential architectural characteristics. In other words, Korean architecture can be defined as a relationship between buildings and topography rather than as a building itself. This relationship can be considered as an architectural layout or plan. It has taken on diverse forms for a number of reasons, such as when the temple was founded, where the temple is situated, and the sect and religious lineage to which the temple belongs.
Temples founded in ancient times followed strict standards because they were built mostly in capital cities with state support. The “one pagoda, three image halls,” “one pagoda and one image hall,” and “twin pagodas” layouts mentioned earlier are representative architectural plans of ancient temples. These three types all share a common feature in that the perimeter was surrounded by long cloisters forming a border with neighboring sites, which was entirely appropriate for an urban setting. Cloisters composed of a line of buildings make sense due to the flat topographical conditions of a city, enabling temples to be built in standard form.
After the medieval period—particularly during the Joseon period when Buddhism was suppressed—Buddhist temples in the cities were demolished by force and disappeared. Only those deep in the mountains survived. Generous contributions from powerful elites were no longer provided and temples faced financial hardship. Accordingly, inefficient structures like long cloisters disappeared and instead freer architectural arrangements better suited to the irregular, mountainous topography developed. Although the buildings of new temples were generally smaller than those of the past, their number increased to accommodate the beliefs of various schools of Buddhism. The architecture of syncretic Buddhism was more suitable for sloping terrain. Breaking away from geometric layouts, a more organic plan came into being and became the established tradition of Buddhist architecture of Korea.
By the early ninth century, five important sects of Buddhism had been established in Korea. Afterward, Seon Buddhism was introduced in the late ninth and tenth centuries and nine core schools of Seon Buddhism emerged. During the Goryeo 高麗 period (918–1392), when Buddhism was the state religion, the religion reached its apex and some twenty sects flourished. In the thirteenth century, Lamaism, a form of Esoteric Buddhism, was introduced to Korea from Yuan 元 (1279–1368) China. Each of these sects had its own scriptures and teachings, its own main Buddha, and its own view of the universe. It was only natural that the architectural models, which symbolize spiritual principles, should differ among the various types of Buddhism.
For example, temples associated with the Pure Land School, which emphasized a belief in a Buddhist paradise (or Buddha land 佛國土), created an architectural form centered on the external space surrounded by buildings. The inner courtyard of the temple itself was regarded as a representation of the Western Paradise. Temples associated with the Dharma-Character School (Kr. Beopsang jong, Ch. Faxiang zong 法相宗), which promoted Buddhist precepts in religious practice, adopted a strict arrangement of gate-pagoda-stone lantern-image hall-Buddhist statues on a shared axis. Seon temples, on the other hand, were free from such specific constraints. Some were of unprecedented architectural layout with two pagodas placed both in front and behind the image hall. Some followed no architectural pattern at all.
Temples of the Doctrinal School (Kr. Gyojong 敎宗) took a different stance. While temples associated with the Doctrinal School regarded image and lecture halls as important locations for worship and for studying sutras, respectively, Seon emphasized mediation rooms and monks’ living quarters as spaces for religious practice and therefore constructed monastery buildings with spaces for such activities. As advocates for the Doctrinal School and Esoteric Buddhism tend to decorate temples magnificently, they emphasized color and decorative designs. Seon Buddhism, in contrast, regarded all decoration as nothing but emptiness, and emphasized extremely minimal ornament.
The Korean peninsula is small in size with a land area of only 220,000 square kilometers. Its topography is folded into many mountains and valleys, both large and small, making communications between regions difficult and thereby allowing folk cultures peculiar to each region to develop. In particular, the traditions of the Three Kingdoms that coexisted in the early centuries of the development of Buddhism persisted as cultural differences in later history. For example, many buildings in the region of the former Baekje kingdom, which has vast plains, sprawl horizontally, while many of those in the mountainous region of the former Silla kingdom are very vertical.
This discussion has shown that the diversity found in Korean Buddhist architecture developed through the ages, influenced by topography, religious schools, and regional traditions. Although relatively few Buddhist temples remain today, each extant example has unique architectural characteristics resulting from this complex matrix of factors.
* This essay is adapted from a text first published in English by Kim Bongryol in the exhibition catalogue The Smile of Buddha: 1600 Years of Buddhist Art in Korea (Brussels: Bozarbooks and Bai, 2008), 89–99. The publication of the current version has been coordinated by Lee Jae-jeong and Yang Sumi at the National Museum of Korea. It was edited by Keith Wilson and Sunwoo Hwang at the Smithsonian’s National Museum of Asian Art. The copyright belongs to Bozarbooks and Bai, Brussels.
Astronomy and mathematics in ancient China: The Zhou bi suan jing
by
Christopher Cullen, Cambridge University Press 1996.
Traditional Chinese Architecture: Twelve Essays
Fu Xinian Edited by Nancy S. Steinhardt Translated by Alexandra Harrer Series: Princeton-China Series Copyright Date: 2017 Published by: Princeton University Press https://doi.org/10.2307/j.ctt21668kt Pages: 448
Octagonal buildings in ancient Korea were mostly constructed in the likeness of Buddhist pagodas that emerged during the Goguryeo era. The ancient Chinese books of Jiuzhang Suanshu and Yingzao Fashi confirm that, in constructing Fogongsi’s Yingxian Wooden Pagoda, the ancients could not design a full-form regular octagonal plan in the pre-seventeenth century before the introduction of Western mathematics. Eight-cornered monuments in Japan and Korea faced the same challenge. Thus, this study examines the acceptance and limitations of adapting octagonal drawing methods in Korean architecture from Chinese and Western mathematics. It conducts comparative studies of architectural and mathematical history in pre-modern and modern times. It reveals that field carpenters applied Yingzao Fashi’s formula in constructing an octagon via a square’s diagonal ratio. Further, the Western method of constructing regular octagons was introduced to the Korean Peninsula in the eighteenth century but was not utilized at work sites. Ultimately, the concepts in mathematics texts had a certain influence on the formative beauty of wooden constructions.
Notes
1 In East Asia, there is a belief that the Sinhalese “dagoba” gradually became “pagoda,” though this derivation is subject to debate. Liang Sicheng contends that the term originates from the “ba jiao ta” 八角塔 (eight-cornered tower) because “ba jiao ta” might have been read as “pa go da” during the Tang Dynasty. The term “pagoda” became the accepted name for such monuments in European languages. In the southern region of China, in particular, the pronunciation of “ba jiao ta” was “pa-chiao-t’a” or “pa-go-ta” (Liang Citation1984). However, Liang was unaware that many eight-cornered towers or pagodas already existed in ritual shrines and have since been excavated in the Jilin Hwando 丸都 (Wandu, ch.) Mountain Fortresses, Gyeongju Najeong Well 蘿井, and Mingtang 明堂 (luminous hall) of Empress Wu from the Goguryeo and Silla period. Alternatively, the Dravidian term pagoda/pagavadi was derived from the Sanskrit bhagavadi (goddess, especially in reference to Kali) or the Persian butkada (temple) (Kim Citation2011, 116).
2 Under Japanese rule, Yoneda Miyoji analyzed the octagonal schematics of the Seokguram Grotto constructed in the eighth century and the ground plans of Goguryeo octagonal wooden pagodas from the fifth century. He also began examining Goguryeo’s octagonal building sites and noticed eight additional octagonal buildings for other purposes.
3 The mathematical books include Jiuzhang Suanshu Lizhu, annotated by Guo Shuchun, and Zhoubi Suanjing Lizhu, annotated by Chen Zhenyi and Wen Renjun.
4 The mathematical treatise comprises 13 books attributed to the ancient Greek mathematician Euclid.
5 Given Euclidean principles, it is impossible to draw a regular full-formed octagon with a non-scaled ruler and a compass.
6 In addition to the wooden construction, China also has a budo (small stone grave for housing the sarira or relics of a senior monk), a pagoda, and a building made of painted stone, judged to be of an early period. For example, regarding eight-sided votive pagodas in the northern Liang period (397–439) or the Dunhuang Grotto, there are eight-angled buildings with a polygonal plan within the Amitabha’s Paradise tableau (Amituo) in the north wall in Mogao Cave 107 and above a preaching scene of the Utmost-Superior-Dharani-of-the Buddha-Topknot’s tableau (Fuding Zunsheng Tuoluoni) centered on the south wall in Mogao Cave 217.
7 It is known that Matteo Ricci (1552–1610), along with Xu Guangqi (1562 ~ 1633) published the Jihe yuanben幾何原本 (Elements of Geometry 1607) by translating Euclid’s Elements, a mathematical treatise consisting of thirteenth books attributed to the ancient Greek mathematician Euclid.
8 The construction of the Foxiangge Pavilion, inspired by the Huanghelou 黃鶴樓 (Yellow Crane Tower) under Qianlong (r.1735–1796), is located at the center of the front hill of Wanshoushan 萬壽山 (Longevity Mountain). It was rebuilt by Cixi 慈禧太后 (1835–1908) in 1891 after it was destroyed by Anglo–French allied forces during the Second Opium War in 1860. It was reconstructed again by Cixi in 1903 after it was devastated a second time by European forces during the Boxer Rebellion in 1900 (Steinhardt Citation2019, 305–306). In 1987, a building survey of the Foxiangge Pavilion found that most of the wooden structures were seriously damaged, including missing decorative parts and roof tiles on the first floor. The brick joints also appeared to have wide cracks. In July 1988, large-scale repair work started after the Summer Palace Management Office 頤和園管理處reported a comprehensive repair plan approved by the Municipal Garden Bureau 市園林局, which was finished on September 13, 1989. (http://www.bjmacp.gov.cn/cn/spec/pastdiscovered/viewinfo.aspx?tabid=300907&iid=90&categoryid=100007, accessed on January 10, 2021)
9 A recent study arithmetically proves that the octagonal drawing method of the Yingzao Fashi applies the ratio of 5:12.07:13.07; thus, it is not considered a perfect regular octagon (Zhang, Yang, and Xiao Citation2018, 98). Even in the case of the Yingxian Wooden Pagoda, the calculations of the measured drawings show that it does not have an equilateral octagonal plan (Chen Citation1981, 72–80).
10 In addition to Yumedomo Hall, the Octagonal Hall at Eizan-ji Temple 栄山寺 八角堂 (763–764) has a length of 10.78 chi (3266 mm, 1 chi = 30.3 cm) on one side of each octagon and is defined as a building with an equilateral octagonal plan because all sides have the same length.
11 The archaeological remains at Toseongri and Sangori Villages (fifth century) have no cornerstones or internal rows in the foundation. These octagonal shapes are more inaccurate than other building sites because most cornerstones are lost; however, a few remain. Such anonymous sites were excluded from this study [Figure 13 and Figure 14].
12 Yoneda analyzed the octagonal building site in Cheongamri Village and identified two ways of making an octagonal plan. These methods were derived from the ceiling structure of Goguryeo burial mounds. The first method was to initiate a gradual reduction by rounding off the edges forming one half of a square. The second was to divide one side into three parts in a square, reducing it to eight angles. Thus, Yoneda considered the construction of an octagonal building on the temple site from a square-based octagon and, consequently, considered the main building at the Cheongamri site as based on a regular square-based octagonal plan. It is very reasonable to draw the octagon by making two points on one side of a square. However, considering the inscribed circle of the square, the length of the two sides of the isosceles triangle at each corner, excluding the diagonal, is too large to produce a regular octagon [Figure 12].
13 Assumedly, it has an octagonal plan on a platform; only the foundation remains are visible on the inner platform, while the rows of cornerstones are invisible. Further, the inner (outer) angle of the octagonal surface on the outermost rain gutter side is 135° (45°).
14 Chinese reports and recent research papers define octagonal buildings as square octagonal plans.
15 Although no column bases remain on the building site, the foundation remains, and the traces of platform siding have been maintained in relatively good condition.
16 In the actual measurement report, it was not described as an octagon since there are no cornerstones; only the approximate distance between the columns was described.
17 This temple site was named Heungnyunsa Temple when the Japanese surveyed the Silla era temples in Gyeongju in the 1910s. In 1976, however, tiles with the characters “xxx廟之寺” pressed into them were found there, and questions about the location of Heungnyunsa and Yeongmyosa were raised as soon as roof tiles with the name of Yeongmyosa engraved on them were found. Consequently, the name of the temple site was restored to Yeongmyosa Monastery 靈廟寺, not Heungnyunsa, which was built when Silla was under the reign of Queen Seondeok (r. 632–647). The Yeongmyosa Monastery site was investigated in test excavations in 1972 and 1977 and between 1978 and 1981, following the conclusion of the tests. Heungnyunsa 興輪寺 was the first Buddhist monastery ever established in Silla.
18 The first construction layout consisted of one pagoda and two halls arranged to the north and south of the pagoda respectively. In time, the temple fell into ruin and was then wholly reconstructed during the Unified Silla period (668–935 CE).
19 As per the Precision Measurement Survey Report on the Hwangudan, there are various dimensions between each column; however, an equilateral octagonal plan is considered by default.
20 Kim states that the method of dividing a regular quadrilateral in the octagonal drawing method is currently used by carpenters in the field. The same method is used when constructing a round purlin. In his writings, the term “regular octagon” is not used.
21 Regarding Korea, the Jiuzhang Suanshu and Zhoubi suanjing were recorded in Samguk Sagi 三國史記 (History of the Three Kingdoms) during the Unified Silla period in the middle of the seventh century. However, given the previous system, laws and ordinances, and astronomical systems, they may have been transmitted to the Baekje and Goguryeo dynasties in the fourth to fifth centuries. Moreover, in Japan, an arithmetic system similar to that in China was recorded in the Nihon Shoji in the sixth century.
22 They refer to the classical mathematical books from the Chinese Han Dynasty to the early Qing Dynasty as the official mathematical texts for imperial examinations in mathematics, as follows: Zhoubi suanjing (Zhou Shadow Mathematical Classic), Jiuzhang Suanshu 九章算術 (The Nine Chapters on the Mathematical Art), Haidao Suanjing 海島算經 (The Sea Island Mathematical Classic), Sunzi suanjing 孙子算經 (The Mathematical Classic of Sun Zi), Zhang Qiujian suanjing 張邱建算經 (The Mathematical Classic of Zhang Qiujian), Wucao suanjing 五曹算經 (Computational Canon of the Five Administrative Sections), Xiahou Yang suanjing 夏侯陽算經 (The Mathematical Classic of Yang Xiahou), Wujing suanshu 五經筭術 (Computational Prescriptions of the Five Classics), Jigu suanjing 緝古筭經 (Continuation of Ancient Mathematical Classic of Wang Xiaotong), and Zhui shu 綴述 (Method of Interpolation of Zu Chongzhi)
23 Xu likewise proved in Celiang yitong 測量異同 (Similarities and Differences in Measurement 1608) and Gougu yi 句股義 (Principle of Base and Altitude 1609) that Chinese gougu surveying bore theoretical, methodological, and instrumental similarities and differences with Western geometric-square surveying (Hashimoto and Jami Citation2001, 268).
24 Many studies have shown that the contents of the Jihe yuangben stem from lecture notes written by the French Jesuits Jean-François Gerbillon (1654–1707) and Joachim Bouvet (1656–1730). They do not refer to the fact that the first Chinese version of Euclid’s Elements bore the same Chinese title, the Jihe yuangben (1607). It was translated by Matteo Ricci (1552–1610) and Xu Guangqi 徐光啟 (1562–1633) (Ju et al. Citation2016, 111).
25 The Shuli jingyun describes the six-sided figure inscribed in a circle, the four-sided inscribed in a circle, the six-sided circumscribed in a circle, and the four-sided circumscribed in a circle.
26 There is evidence of proportional compasses provided by Fabrizio Mordente (1532–1608) and Thomas Hood (d. 1598) even earlier than Galileo, but these geometric instruments had functional operations inferior to the Galilean compass. (Pisano and Bussotti Citation2015, 213)
27 Fang met Adam Schall von Bell in 1659 in Beijing and satisfied his great desire of studying Western mathematics under the Polish Jesuit Johannes Nickolaus Smogulecki (1610–1656).
28 Korean scholars referred to the Xiyang xinfa lishu 西洋新法曆書 (Treatise on Calendrical Science 1645), later re-edited with the title, the Xinfa suanshu 新法算書 (New Methods in Mathematics 1666), and the Tianxue chuhan 天學初函 (First Collection of Writings on Heavenly Learning, 1626) (Jun Citation2006, 482–483).
29 Although Korean mathematics borrows from ancient China, it did not change with Chinese mathematics trend since the seventeenth century. Paradoxically, Korean mathematics developed, while Chinese mathematics declined during King Sejong’s regime (r. 1418–50).
30 According to the introductory (Qujingwei) section of the Yingzao Fashi by Li Jie (?–1110), the preliminary mathematical explanations end with an explicit quotation from Li Chunfeng’s commentary on the Jiuzhang suanjing “營造法式,取經圍: 九章算術及約斜長等密率修立下條. 諸徑圍斜長依下頂.”
31 Mathematical ideas in Korea mirror the basic ideas of ancient China, and it is necessary to refer to the systematic arithmetical ideas in the Lulizhi of Hanshu 漢書 to precisely ascertain them. Lulizhi 律歷志 (Treatise on Harmonics and Calendrics) says “The counting of numbers fits well with all things in the universe 萬物氣體之數, 天下之能事畢矣.” In this case, the basic propositions integrate the tune音律, the astronomical calendar 曆法, the art of divination 易數, and the weights and measures 度量衡. That is, the basic scales and mathematical systems of ancient architecture are indirectly included in this scope.
32 The Korean Mathematical History explains geometrical constructions in art crafts and architecture and the Yin-Yang and Five Element thought in the architectural plan, metrological system, and scale, revealing a close rapport with the logic of mathematics.
Application of and Changes in Construction Principles and Joint Methods in the Wooden Architecture of the Joseon Era: A Case Study on the Sungnyemun Gate in Seoul.
Reconsidering a proportional system of timber-frame structures through ancient mathematics books: a case study on the Muryangsujŏn Hall at Pusŏksa Buddhist Monastery.
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Viewpoints which Matter 