The Architecture and Sacred Temple Geometry of Japanese Buddhist Temples

The Architecture and Sacred Temple Geometry of Japanese Buddhist Temples

Key Terms

  • Japanese Architecture
  • Japanese Temple Architecture
  • Japanese Traditional Mathematics
  • Wasan
  • Japanese Buddhist Temples
  • Pagodas
  • Stupa
  • Chorten
  • Wayō, Daibutsuyō, Zenshūyō, Setchūyō
  • Sangaku
  • Fukagawa Hidetoshi  
  • Tony Rothman 
  • Don Pedoe
  • J. Rigby
  • Pagoda, ta, mandala, Sumeru, Yicihui pillar, Yongningsi, Songyuesi
  • Diagram of a Gorinto 
  • Hokyointo Pagoda
  • Tahoto Pagoda
  • Sotobo
  • Square
  • Circle
  • Regular Polyhedra
  • Cube, Sphere, Pyramid, SemiSphere, Chintamani
  • Earth, Water, Fire, Air, Universe
  • Plato and Aristotle
  • Shingon, Kukai, 5 Stories, Circle
  • Tendai, Saicho, 3 stories, Square
  • Diamond World, Matrix World
  • Adrian Snodgrass
  • Tracy Miller
  • Gojunoto

The Architecture of Japanese Buddhist Temples

 December 19, 2021   

Natalie Solari


Overview:

This exhibition takes a closer look at the main buildings of five Japanese Temple Complexes. Temples are the places of worship in Japanese Buddhism, and are also used to display sacred Buddhist objects. It is believed that Buddhist images could have been brought to Japan as early as 522 (Beguin). Japanese Buddhism has made an abundant impact on Japanese culture and continues to influence society today. The architectural elements of Buddhist temples are meant to embody themes and teachings of Buddhism. 

Most Buddhist temples in Japan are designed around four main architectural styles: Wayō, Daibutsuyō, Zenshūyō, and Setchūyō. Temples designed in the wayō style take a minimalistic approach to architecture. Natural timber and generally plain materials are used. Wayō architecture was made during the Heian period, between 794 CE and 1185 CE. Typically these structures feature thin columns and a low ceiling. A beam is run through the columns to reinforce the top parts of  columns. The wayō style emphasizes more Japanese-style architecture than the features of Chinese-style architecture. Inside the structures inner space divisions are fluid, many feature screens and thin. A true connection is meant to be felt between the interior and exterior of the building. 

In the late 12th and early 13th century CE, a more monumental style emerged. The daibutsuyō style was based on Song Dynasty architecture. Daibutsuyō style architecture is characterized by thick woodwork and penetrating tie beams. The ends of the penetrating tie beams are decorated with moldings also known as ‘kurigata’. The thick woodwork of the structure is typically left exposed to show its elements. This style takes a grander approach than the wayō style. Daibutsuyō style architecture utilizes horizontal elements.

Zenshūyō is another style that emerged in the late 12th or early 13th century CE. Zenshūyō style temples are based on contemporary Chinese architecture derived from the Song Dynasty. The style is named after the Zen sect of Buddhism that was introduced to Japan. These temples typically incorporate earthen floors, decorative curved pent roofs, pointed windows, and paneled doors. Slim columns and low ceilings are used to create calming spaces for meditating. The complexes have a generally linear layout. Kōzan-ji’s butsuden is the oldest extant building in the Zenshūyō style in Japan. 

The last style of temple architecture incorporates a fusion of elements from the three other styles. This style was called setchūyō, and was used during the Muromachi period. By the end of the Muromachi period, Japanese Buddhist architecture and construction methods had been perfected and building types were conventionalized. 

Although the temples are designed around a few different styles, there are some key features that distinguish these Japanese Buddhist temples. Characteristics of most Japanese Temples include post and lintel support, a gentle curved roof, and thin walls. The use of a single central pillar or column. embodies the Axis Mundi of Buddhism. Having the cardinal directions reflected through the structure is important. The most prominent examples of the iconic form are represented in Pagodas and Indian Stupas. Many of these temples are incorporated into complexes with several other structures that include a main hall, a pagoda, and other facilities for prayer and meditation. Many of these temple complexes are surrounded by a large wall and gates. Entering the complex is supposed to feel like a journey through meditation. These spaces are intended to evoke feelings of peace. 

Title: Phoenix Hall at Byodoin (998 CE)
Category: Japanese Buddhist Architecture
Architectural style: Wayō
Location: Uji, Japan
Author Name: Jean-Pierre Dalbéra
Medium: image/jpeg 
Date of Creation: 15 May 2018
Dimensions: 2,400 × 1,600 pixels
Image Link: https://commons.wikimedia.org/wiki/File:Le_temple_Byodo-in_(Uji,_Japon)_(42809689812).jpg

Description:
The Phoenix Hall is the main hall at Byodo-in temple. Phoenix Hall was established in 1053 CE, in the late Heian period. The hall houses the Shrine of  the Buddha Amida. Phoenix Hall is an example of Wayo architecture as well as shinden-zukuri, the style of Japanese nobility’s residences. Phoenix Hall incorporates unique architecture which consists of the main corridor, left and right wing corridors, and a tall corridor. The shape of the building resembles the body and spreading wings of the Phoenix. Its main corridor faces south to bring in sunlight and opens on to the pond of a beautiful garden. A Pure Land style garden is centered around the Ajino-ike Pond, that reflects the architecture of the structure. A true connection is felt between the interior and exterior of the hall. 

The central corridor is topped by a hip-and-gable roof and also features a pent roof enclosure. Hip-and-gable roofs are characterized by a rounded hip roof that cascades down on all sides, and a triangular gable at each end. Two phoenix statues are positioned on top of the roof. The stairs leading to the main entrance are made of marble, but the structure of the hall is made of wood. The doors and walls are decorated by richly colored paintings, and the ceiling and pillars are also covered with colorful patterns. The brightly colored exterior clashes with the minimalistic Wayō style, but the gentle lines of the exterior and openness of the interior hold on to its values. 

Title: Great Buddha Hall, Todai-ji temple complex

Category: Japanese Buddhist Architecture

Architectural style: Daibutsuyō

Location: Nara, Japan

Author Name: Felix Filnkössl

Medium: image/jpeg 

Date of Creation: 18 August 2010

Dimensions: 4,000 × 2,248 pixels

Image Link: https://commons.wikimedia.org/wiki/File:Todai-ji.jpg

Description:

The Great Buddha Hall at Todai-ji temple complex displays the grand features of the daibutsuyō architectural style. The Great Buddha hall houses the world’s largest bronze Buddha Vairocana statue. This Buddhist temple complex was once one of the powerful Seven Great Temples. Two towering guardians sit on top of the massive entryway of the temple, protecting the great Buddha. The great architects of Todaiji temple complex developed the Yakushiji axial plan with paired pagodas into one of greater complexity (Ikeuchi 2007). The hall was erected in the early 8th century CE, and later reconstructed in 1709. The Great Buddha hall was built at a very large scale, displaying the power and prestige of the imperial house of Japan. Columns are arrayed throughout the rectangular base to represent universal order. Many horizontal braces are run through vertical posts called Nuki to make the structure solid.

As a daibutsuyō style hall, structural elements are left exposed without the covering of a ceiling as decoration. The vast structure is made entirely of wood, commonly seen in Japanese architecture. Building structures out of wood was seen as a way to celebrate life. A gently sloping roof was used to help blend in the large structure to its natural surroundings. The roof tiles were carefully crafted to channel water to prevent erosion.

Title: Kondô, Fudôin Hiroshima

Category: Japanese Buddhist Architecture

Architectural style: Zenshūyō

Location: Hiroshima, Japan

Author Name: Fraxinus2

Medium: image/jpeg 

Date of Creation: 11 October 2012

Dimensions: 1,771 × 1,240 pixels

Image Link: https://commons.wikimedia.org/wiki/File:Fud%C3%B4in_3.jpg

Description:

Kondô Hall is the main hall of Fudôin Temple. This hall was built in the Zenshūyō architectural style. Kondô at Fudôin is an Important Cultural Property, as one of the few remaining historic structures in Hiroshima. After careful studies of historic documents and writing found on the ceilings, it is believed that Kondô Hall was originally built in Yamaguchi in 1540 at the site of Koshakuji Temple. The Kondô Hall was later relocated to its current location in Hiroshima when Ekei expanded the temple. The structure miraculously survived the atomic bomb drop in 1945 on the city. Kondô Hall is the only National Treasure in Hiroshima City. The structure features massive beams, the longest being over 7 meters (Davies). Kondô Hall has a irimoya, a unique combination of gable and hip roof with a mokoshi (an extra roof). The grand roof casts shadows on the ground below, adding to the sacred atmosphere. Oversized eaves give the interior a characteristic dimness, which contributes to the temple’s sacred atmosphere. Paintings of angels and dragons fill the ceilings. This structure appears less conspicuous and more meditative than the other styles of architecture. This structure houses the statue of Yakushi Nyorai, also known as the Medicine Buddha. The statue was carved by the pioneer sculptor Jocho, who was a famous Japanese sculptor in the early 11th century.

Title: Temple of Golden Pavilion Kinkaku-ji
Category: Japanese Buddhist Architecture
Architectural style: Setchūyō
Location: Kyoto, Japan
Author Name: Ondraness
Medium: image/jpeg 
Date of Creation: 9 September 2019
Dimensions: 5,312 × 2,988 pixels
Image Link: https://commons.wikimedia.org/wiki/File:Golden_pavilion,_Kinkakuji.jpg

Description:
Kinkaku-ji is located on the Rokuon-ji temple complex. This Japanese Buddhist temple exhibits the Setchūyō architectural style used to design Japanese Buddhist temples. Setchūyō emerged in Japan during the Muromachi period, characterized by the fusion of elements from preceding styles. Buddhist temples in Japan follow a general structure of columns and lintels that support a large and gently curved roof. Kinkaku-ji is known for its gold leaf exteriors of the upper two floors. In Pure Land Buddhism gold represents spiritual purity which is reflected through the structure. 

Each level of the temple incorporates a different style of architecture. Shiden style is displayed on the first floor, an open space decorated with natural wood pillars and white plaster. This floor emphasises the surrounding landscape and garden design. The second floor of the temple embodies the style used in samurai residences. Paintings of birds, clouds, and instruments cover the ceilings and walls. The third and final floor is built in the style of a Chinese Zen Hall, with lavish decoration. The sacred relics of the Buddha are kept in this sacred space. A large thatched pyramid roof covers the structure. The temple is topped with a bronze phoenix ornament.

Title: Kakurin-ji Temple Main hall

Category: Japanese Buddhist Architecture

Architectural style: Setchūyō

Location: Kakogawa, Japan

Author Name: 663highland

Medium: image/jpeg 

Date of Creation:  7 December 2008

Dimensions: 4,592 × 3,056 pixels

Image Link:https://commons.wikimedia.org/wiki/File:Kakogawa_Kakurinji12n4592.jpg

Description:

Kakurin-ji Temple is the 20th temple of the Shikoku Ohenro Pilgrimage. Kakurin-ji is incredibly difficult to reach due to its location at the top of a steep mountain. Sitting at 550 meters elevation, the temple is the 5th highest structure on the pilgrimage route. The Main Hall at Kakurin-ji Temple embodies the Setchūyō architectural style used to design Japanese Buddhist temples. The Main Hall, which was named a National Treasure of Japan, was built in 1397. The Main Hall was designed with the East Asian hip-and-gable roof, the structure stands tall off the ground and appears to float. The roof is a bold feature of the structure. With the location high on a mountain and the unique architecture a sacred Buddhist space is created. A beautiful three-storey pagoda sits to the right of the Main Hall. 


Bibliography:

Images:

Daibutsuden (Great Buddha Hall), Todai-ji temple complex

(4,000 × 2,248 pixels, file size: 5.91 MB, MIME type: image/jpeg)

Image Author: Felix Filnkössl

Date: 18 August 2010

Fudôin Hiroshima Kondô

‎(1,771 × 1,240 pixels, file size: 521 KB, MIME type: image/jpeg)

Image Author: Fraxinus2

Date: 11 October 2012

Kakurinji Buddhist temple in Kakogawa

(4,592 × 3,056 pixels, file size: 10.49 MB, MIME type: image/jpeg)

Image Author: 663highland

Date: 7 December 2008

Temple of Golden Pavilion Kinkaku-ji, Kyoto

(5,312 × 2,988 pixels, file size: 4.89 MB, MIME type: image/jpeg)

Image Author : Ondraness

Date: 9 September 2019

Temple Byōdō-in (Uji, Japan)

(2,400 × 1,600 pixels, file size: 3.53 MB, MIME type: image/jpeg)

Image Source: Le temple Byodo-in (Uji, Japon)

Image Author: Jean-Pierre Dalbéra

Date: 15 May 2018

Texts:

TRACING THE ORIGIN OF JAPANESE PAGODAS ALONG THE SILK ROAD

Source: TRACING THE ORIGIN OF JAPANESE PAGODAS ALONG THE SILK ROAD

Source: TRACING THE ORIGIN OF JAPANESE PAGODAS ALONG THE SILK ROAD

Source: TRACING THE ORIGIN OF JAPANESE PAGODAS ALONG THE SILK ROAD

Source: TRACING THE ORIGIN OF JAPANESE PAGODAS ALONG THE SILK ROAD

Source: TRACING THE ORIGIN OF JAPANESE PAGODAS ALONG THE SILK ROAD

Source: TRACING THE ORIGIN OF JAPANESE PAGODAS ALONG THE SILK ROAD

Sangaku–Japanese Mathematics and Art in the 18th,19th and 20th Centuries

Source: Sangaku–Japanese Mathematics and Art in the 18th,19th and 20th Centuries

Source: Sangaku–Japanese Mathematics and Art in the 18th,19th and 20th Centuries

Source: Sangaku–Japanese Mathematics and Art in the 18th,19th and 20th Centuries

Source: Sangaku–Japanese Mathematics and Art in the 18th,19th and 20th Centuries

Source: Sangaku–Japanese Mathematics and Art in the 18th,19th and 20th Centuries

Source: Sangaku–Japanese Mathematics and Art in the 18th,19th and 20th Centuries

Source: Sangaku–Japanese Mathematics and Art in the 18th,19th and 20th Centuries

Source: Sangaku–Japanese Mathematics and Art in the 18th,19th and 20th Centuries

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Key Sources of Research

Japanese Temple Geometry Problems and Inversion

Japanese Temple Geometry Problems Sangaku 

Paperback 

by  Fukagawa  (Author)

Don Pedoe

Language ‏ : ‎ English
ISBN-10 ‏ : ‎ 0919611214
ISBN-13 ‏ : ‎ 978-0919611214

The Architecture of Japanese Buddhist Temples

Natalie Solari

Sacred Mathematics: Japanese Temple Geometry 

Hardcover – July 21, 2008 

by  Fukagawa Hidetoshi  (Author), Tony Rothman  (Author), Freeman Dyson  (Foreword)

Authors Fukagawa Hidetoshi, Tony Rothman
Contributor Freeman Dyson
Edition illustrated
Publisher Princeton University Press, 2021
ISBN 1400829712, 9781400829712
Length 392 pages

Sangaku Proofs: A Japanese Mathematician at Work

(Cornell East Asia Series, 175) Paperback – January 31, 2015

Patterns and layering
Japanese Spatial Culture, Nature and Architecture

Sangaku: Reflections on the Phenomenon

https://www.cut-the-knot.org/pythagoras/Sangaku.shtml

“Japanese Temple Geometry.”

Rothman, Tony, and Hidetoshi Fukagawa.

 Scientific American 278, no. 5 (1998): 84–91. http://www.jstor.org/stable/26057787.

“Design Principles of Early Stone Pagodas in Ancient Korean Architecture: Case Studies on the Stone Pagodas at Chongnimsa and Kamunsa Buddhist Temples.” 

Cha, Juhwan, and Young Jae Kim.

Religions 10, no. 3 (2019): 1-18, https://doi.org/10.3390/rel10030208.

https://www.mdpi.com/2077-1444/10/3/208

Sangaku – Japanese Temple Mathematics

Rosalie Hosking
Department of Mathematics and Statistics

Click to access 20120720_JapaneseTempleMaths_RosalieHosking.pdf

Design Principles of Early Stone Pagodas in Ancient Korean Architecture

 July 17, 2019 

The art of sangaku

Batchelor, M.

Nature Phys 4, 669 (2008). https://doi.org/10.1038/nphys1069

SANGAKU: SACRED MATHEMATICS IN JAPAN

A thesis submitted in partial satisfaction of the requirements for the degree of
MASTER OF ARTS in MATHEMATICS

by Katsuhito Sugano

September 2017

TRACING THE ORIGIN OF JAPANESE PAGODAS ALONG THE SILK ROAD

Koji Miyazaki
Professor Emeritus, Kyoto University, Japan

Archi-Cultural Translations through the Silk Road 2nd International Conference, Mukogawa Women’s Univ., Nishinomiya, Japan, July 14-16, 2012 Proceedings

MATH 400: SANGAKU, JAPANESE TEMPLE GEOMETRY

RYAN FAMELI

Japanese Buddhist Architecture

https://www.buddhist-art.com/blog/japanese-buddhist-architecture/

Japanese Buddhist Architecture

japanese building

Japanese Buddhist Architecture mainly includes the architecture of Buddhist temples which was influenced by the architectural styles from China. Earlier, the attempts were to make the Buddhist architecture as original as it was looked in China but gradually the buildings were localized due to the problems posed by local weather and Japanese tastes.

Historical development of Japanese Buddhist Architectures

The development of Japanese Buddhist Architectures can be broadly divided into the following periods

Asuka and Nara Periods 

The Buddhism and the Buddhist architecture were literally imported from China via Korea in the 6th century. As the Buddhism was introduced in Japan, the Buddhist temples were started to build in the country but due to the hostile behavior of supporter of the local kami, the buildings were no longer stand by itself and there are no written records of the architectural styles of that period.

But later the Buddhism got its support from the Prince Shotoku. He ordered the construction of Buddhist templeShitennoji in Osaka (593) and Horyu-ji near his palace in Ikaruga (603). During this period, the temple layout was strictly prescribed and followed. This act helped to maintain the architectural style uniform. In this period the main gate was constructed facing south and the most sacred area surrounded by a semi-enclosed roofed corridor accessible through a middle gate. The temple complex also contains the main hall with Buddha statue, and pagoda which houses sacred objects. The other structures include a lecture hall, a belfry, a sutra repository, priests and monks quarters and bathhouse.

Nara Period observed quite different architectural development. The temple structures, such as pagodas and main halls, had increased significantly in size. The placement of the pagoda moved to a more peripheral location and the roof bracketing system increased in complexity as roofs grew larger and heavier.

In the 8th century, Kami worship and Buddhism was reconciled and thus shrine-temples were founded to support both groups. This coexistence of Buddhism and Kami worship continued until the Kami and Buddhas Separation Order of 1868.

Heian period 

In this period, Buddhism was more localized with addition Japanese elements, local beliefs. With this localization Fujiwara no Michinaga and retired Emperor Shirakawa erected new temples and hence developed Jodo-Kyo architectureand the new Wayo architectural style.

In the early period, Rokushu architectonic traditions were also observed. This style of architecture was developed only in the plains but in mountainous areas, it was an original style. The architectural style was characterized by the simplicity which uses local resources like natural timber.

The architecture includes a main hall which is generally divided into two parts; an outer area for novices and an inner area for initiates. The roof is a hip and gable which covers both the areas. The floor is little raised which is made up of wood.

Kamakura and Muromachi periods 

In Kamakura period, Daibutsu style and the Zen style of architectural designemerged. The first style represents the antithesis of the simple and traditional Wayo style while the Zen style characterized as earthen floors, subtly curved pent roofs, cusped windows, and paneled doors.

In Muromachi periods, the above-mentioned style of architecture was often combined to form the new style of architecture, Eclectic style of architecture.

Other notable periods in the history of the development of Japanese Buddhist architecture were Azuchi-Momoyama and Eddo periods, and Meiji period. In these periods the Buddhist architectures were also developed accordingly focusing on the local beliefs and use of local resources.

General features of Japanese Buddhist Architectures

Actually, the architectural styles of Japanese Buddhist buildings were imported from China and various other Asian countries. With time, these architectural styles were localized in order to suit the Japanese tastes, and the local resources and weather.

Japanese architects have used a locally available material, mainly wood in various forms. It is hard to see the buildings that use stones except for certain specific uses as in temple podia and pagoda foundations.

Almost all the buildings share the common general structure: columns and lintels to support a large and gently curved roof. The walls are also paper thin, which is often movable. We can notice that the arches and barrel roofs are completely absent. It is recorded that gable and eave curves are gentler that in China and columnar entasis limited.

The most impressive component of the Japanese Buddhist architecture is the roof. The roof has the slightly curved eaves that extend far beyond the walls, covering verandas. These oversize eaves give the interior a characteristic dimness, which contributes to the temple’s atmosphere. The building normally consists of a single room at the center called Moya.

As it is already mentioned that the inner walls are paper thin and often movable, the room size can be modified as per required. Hence, the large, single space offered by the main hall can, therefore, be altered according to the need.

Sometimes the architecture is shared by both sacred and profane building structures. Therefore, these architectural features made it easy to convert a lay building into the Buddhist temple. The popular Horyu-Ji Buddhist temple in Nara Prefecture is the excellent example. This building was once used to be the mansion for the noblewoman.

The blossoming of Japanese mathematics. 

Lu, P.

Nature 454, 1050 (2008). https://doi.org/10.1038/4541050a

https://www.nature.com/articles/4541050a

The blossoming of Japanese mathematics

27 August 2008

At the beginning of the seventeenth century, Tokugawa Ieyasu completed the unification of Japan. His shogunate ruled for more than 250 years and oversaw a period of peace, but with restricted foreign contact. Poetry, music and literature flourished during this time of relative isolation. A unique form of Japanese culture of the period was sangaku — a combination of mathematics and art on votive tablets. Illustrated wooden shingles up to several metres across bearing geometry problems were hung from Shinto shrines and Buddhist temples for public display. Many historical sangaku answers appeared on tablets without proof, perhaps to demonstrate the mathematical prowess of the presenter. And their sacred context remains unclear: the tablets might have been educational or may have signalled gratitude for divine assistance in solving a mathematical problem. Of the thousands of tablets created, only a fraction survive, and they have received scant coverage in histories of Japanese mathematics.

Now Fukagawa Hidetoshi, a mathematics teacher, and writer Tony Rothman present a collection of sangaku problems in their book, Sacred Mathematics. The puzzles range from simple algebra within the grasp of any intermediate-school student, to challenging problems that require graduate-school mathematics to solve. Copious illustrations and many detailed solutions show the scope, complexity and beauty of what was tackled in Japan during the Tokugawa shogunate.

Credit: A. SHINBUN

The book offers a feast for recreational geometers looking for fun new problems, presented and solved in clever ways. Yet the authors give little insight into how these problems were solved at the time, or whether unique Japanese methods were involved. The sangaku figures are mostly redrawn with modern notation, and solutions offered in the compact form of present-day Western mathematics. Illustrating traditional Japanese and modern Western methods side by side would have been instructive. The book thus achieves only limited success in showcasing sangaku as exemplars of a uniquely Japanese style of mathematics, because that style is never elucidated.

Fukagawa and Rothman illuminate the mathematics more than the history and context of the tablets. Citations to mathematical theorems abound, yet references supporting their historical claims are absent. More seriously, the historical commentary reflects a romantic bias that a unique Japanese culture flowered because of its complete isolation. The book states, for instance, that “a unique brand of homegrown mathematics flourished, one that was completely uninfluenced by developments in the western mathematics”. This generalization is historically unsupported, and obstructs an accurate consideration of the interplay of factors that drove the development of Japanese mathematics.

Along similar lines, the authors also dismiss the millennium that preceded the seventeenth century as “a dark age” paralleling that in Europe, during which relatively little was accomplished in mathematics. By ignoring the medieval Islamic world, they fall into the same trap as Eurocentric mathematical historians who focus exclusively on ancient Greece and modern Europe. This omission undermines their discussion of the Chinese foundation of Japanese mathematics. World-leading achievements in mathematics, science and technology — even astronomers from Persia — reached China during the medieval period by the Silk Road and other routes. The book describes in great detail how Seki Takakazu, “Japan’s most celebrated mathematician”, calculated π to 11 digits in the eighteenth century. But it does not mention Jamshid Mas’ud al-Kashi, who determined π correctly to 16 digits some three centuries earlier while residing in Samarkand (in what is now Uzbekistan), one of the most important cities along the Silk Road.

The complex events that followed Japan’s opening to the West after the shogunate’s end in the 1860s are given similarly short shrift. The response of Japanese mathematics to this influx of ideas is dispatched with the glib statement that “resistance was futile”. By quoting a science-fiction character from Star Trek that annihilates everything in its path by assimilation, Fukagawa and Rothman trivialize Japan’s complicated process of reintegration with the international community, and miss the opportunity to shed light on how its early mathematics contributed to Japan’s present-day leadership in science and technology.

Review Sacred Mathematics
Japanese Temple Geometry

by Fukagawa Hidetoshi and Tony Rothman

https://www.cut-the-knot.org/books/Reviews/SacredMathematics.shtml

Sangaku–Japanese Mathematics and Art in the 18th,19th and 20th Centuries

Hidetoshi Fukagawa

Kani-city, Gifu,509-0235,Japan E-mail:RXW05750@nifty.ne.jp

Kazunori Horibe
Aichi Prefectural Kasugai-Higashi Senior High School Tajimi-city,Gifu,507-0824.Japan E-mail:kazunori@horibe.jp

Proceedings of Bridges 2014: Mathematics, Music, Art, Architecture, Culture

“Sangaku in Multiple Geometries: Examining Japanese Temple Geometry Beyond Euclid”

Hartmann, Nathan,

(2022). Honors College Theses. 118.

https://digitalcommons.murraystate.edu/honorstheses/118

The New Temple Geometry Problems in Hirotaka’s Ebisui Files

Miroslaw Majewski (馬裕褀) mirek.majewski@yahoo.com

Jen-Chung Chuan (全任重) jcchuan@math.nthu.edu.tw

Nishizawa Hitoshi (西澤 一) nisizawa@toyota-ct.ac.jp

Art & Spirit in Mathematics: The Lessons of Japanese Temple Geometry (part I)

Article by Newcomb Greenleaf

Art & Spirit in Mathematics: The Lessons of Japanese Temple Geometry (part II)

Article by Newcomb Greenleaf

Japanese Temple Geometry

January 2004
Authors:
Jill L Vincent
University of Melbourne
Claire Vincent

https://www.researchgate.net/publication/234610115_Japanese_Temple_Geometry

Sangaku

https://en.wikipedia.org/wiki/Sangaku

Japan and Temple Geometry

Click to access s8646.pdf

JAPANESE TEMPLE GEOMETRY

https://www.obscurehistories.org/japanese-temple-geometry

Solving Sangaku With Traditional Techniques

January 2017
Authors:
Rosalie Hosking
Yokkaichi University

https://www.researchgate.net/publication/313160226_Solving_Sangaku_With_Traditional_Techniques

Chapter 1. Early Edo Period

https://www.ndl.go.jp/math/e/s1/1.html

Traditional Japanese mathematics problems of the 18th and 19th centuries

深川 英俊, J. Rigby
Published 2002

https://www.semanticscholar.org/paper/Traditional-Japanese-mathematics-problems-of-the-深川-Rigby/898c6d52a4009d043b50d1b38684e73ce7d7909b

Mathematical Treasures of Japan in the Edo Period

Author(s): 

Frank J. Swetz (Pennsylvania State University)

https://maa.org/book/export/html/1438298

SYMMETRY IN TRADITIONAL JAPANESE MAtHEMATICS

Hidetoshi Fukagawa

Symmetry: Culture and Science Vol. 8, No. I, 24-54, 1997

Click to access fukagawa.pdf

A REVIEW OF THE HISTORY OF JAPANESE MATHEMATICS

Tsukane OGAWA

Revue d’histoire des math ́ematiques, 7 (2001), p. 137–155

Click to access RHM_2001__7_1_137_0.pdf

https://eudml.org/doc/252078


Traditional Japanese mathematics: wasan 和算

2/2/2012

http://naruhodo.weebly.com/blog/traditional-japanese-mathematics-wasan

Traditional Japanese mathematics problems of the 18th and 19th centuries; Japanese temple geometry problems San Gaku. 

Kimberling, C.

The Mathematical Intelligencer 28, 61–63 (2006). https://doi.org/10.1007/BF02987007

Rothman helps reveal intricacies of ancient math phenomenon

By Chad Boutin on June 15, 2006, 5 p.m.

https://www.princeton.edu/news/2006/06/15/rothman-helps-reveal-intricacies-ancient-math-phenomenon

Japan’s “Wasan” Mathematical Tradition: Surprising Discoveries in an Age of Seclusion

Apr 30, 2024
Abe Haruki

https://www.nippon.com/en/japan-topics/c12801/

The Symbolism of Stupa

Adrian Snodgrass

The Symbolism of the Stupa. 


Snodgrass, Adrian. 

Revised Edition ed., Ithaca: Cornell University Press, 2018. muse.jhu.edu/book/59279.

Of Palaces and Pagodas: Palatial Symbolism in the Buddhist Architecture of Early Medieval China

Tracy Miller

Front. Hist. China 2015, 10(2): 222–263 DOI 10.3868/s020-004-015-0014-1

https://www.semanticscholar.org/paper/Of-Palaces-and-Pagodas%3A-Palatial-Symbolism-in-the-Miller/3337db8b0e561613dd38bbc56e883e4dba24ffc3

SPACE IN JAPANESE ZEN BUDDHIST ARCHITECTURE

DIMENSI (Journal of Architecture and Built Environment) 29(1)
January 2004 29(1)

Authors:
Antariksa Sudikno
Brawijaya University

https://www.researchgate.net/publication/43329661_SPACE_IN_JAPANESE_ZEN_BUDDHIST_ARCHITECTURE

Japanese Buddhist architecture

https://en.wikipedia.org/wiki/Japanese_Buddhist_architecture

Buddhist Stupas and Their Symbols in Vajrayana Buddhism in Bhutan

Dorji Phuntsho

  • MA in Buddhist Studies, Philosophy, and Comparative Religions, Tsebar Lower Secondary School
    Pemagatshel, Bhutan

(IJESIR) International Journal of Science and Innovative Research
e-ISSN: 2724-3338
2021, 02(07)
https://www.ijesir.org Paper id: 0100061IJESIR

The Stupa Buddhism in Symbolic Form

Jay G. Williams

Mandalas: The Matrix and Diamond World in Shingon Buddhism

One Hundred and Eight Rosary Beads in Landscape and Architecture Design

January 2024
DOI:10.2139/ssrn.4683951
Authors:
Amelia Carolina Sparavigna
Politecnico di Torino

Stupa, Pagoda and Chorten –
Origin and Meaning of Buddhist Architecture

Wah Sang Wong
Associate Professor
The University of Hong Kong
Hong Kong

Perfecting the Mountain:On the Morphology of Towering Temples in East Asia

Tracy Miller

Department of History of Art, Vanderbilt University, USA)

Journal of Chinese Architecture History 10 (2014): 419-449

The power of the five elements

Early Buddhist Architecture In Context The Great Stapa At Amaravata Ca 300 Bce 300 Ce 

MA — The Japanese Concept of Space and Time

Kiyoshi Matsumoto

Apr 24, 2020

A Masterpiece of Zen Temple Architecture

https://www.gov-online.go.jp/eng/publicity/book/hlj/html/202102/202102_13_en.html

STUDY ON THE PHILOSOPHY AND ARCHITECTURE OF ZEN BUDDHISM IN JAPAN

On syncretism religion and monastery arrangement plan

Antariksa

Lecturer, Dept. of Architecture, Faculty of Engineering, Brawijaya University

e-mail: antariksa@brawijaya.ac.id / antariksa_42@mailcity.com

naturalizing buddhist cosmology in the temple architecture of china: the case of the yicihui pillar

Tracy Miller, Vanderbilt University

Performing Center in a Vertical Rise: Multilevel Pagodas in China’s Middle Period

Wei-cheng Lin

https://quod.lib.umich.edu/a/ars/13441566.0046.005/–performing-center-in-a-vertical-rise-multilevel-pagodas?rgn=main;view=fulltext

Dynamic performance of a multi-story traditional timber pagoda

Yajie Wu

, Xiaobin Song

, Xianglin Gu

, Lie Luo

Department of Structural Engineering, Tongji University, Shanghai 200092, China

Received 18 October 2017, Revised 27 December 2017, Accepted 1 January 2018, Available online 11 January 2018, Version of Record 11 January 2018.

What is the Importance of the Pagoda in Chinese Culture

https://chinese-temple.com/blogs/chinese-temple-blogs/what-is-the-importance-of-the-pagoda-in-chinese-culture

Morphological Study on Multi-storied Brick Pagodas of the Tang Dynasty: An Analysis Method Based on Historical Patterns and Mathematical Models. 

Wang, S., Chen, X., Xu, Y., Wang, K., Lai, J., & Shi, L. (2020).

International Journal of Architectural Heritage15(11), 1655–1670. https://doi.org/10.1080/15583058.2020.1712497

Investigation into the Architectural Design of a Traditional Japanese Wooden Pagoda.

Zhang, Yijie & Tang, He-Sheng & Xue, Songtao & Xun, Yang. (2015).

Journal of Asian Architecture and Building Engineering. 14. 241-246. 10.3130/jaabe.14.241.

The Background of Stone Pagoda Construction in Ancient Japan.

Satō, Asei. (2021).

Religions. 12. 1001. 10.3390/rel12111001.

https://www.mdpi.com/journal/religions/special_issues/Buddhist_Architecture

https://www.mdpi.com/2077-1444/12/11/1001

Ancient Chinese Pagodas – Hardcover

Zhang Yuhuan; Luo Zewen
9787030001054: Ancient Chinese Pagodas
Hardcover
ISBN 10: 7030001052

ISBN 13: 9787030001054
Publisher: Science Press, 1988

Five Story Pagoda (Gojyu-no-to)

https://nstmyoshinji.org/historical-places/five-story-pagoda/

Chinese Arts – Architecture
Monasteries and Pagodas 寺院與佛塔

http://www.chinaknowledge.de/Art/Pagodas/pagodas.html

The wooden Pagodas of China

C.

The wooden Pagodas of China

Buddhist architectureChinaconservationHistoryPagodarestorationstructurestimbertraditionalUNESCOworld heritage

October 2, 2013

Although timber is rarely used as a construction material in modern-day China, history tells us that it was used extensively in the past. The Chinese used timber as roofing and flooring material and incorporated timber beams and columns in their structures. The structural system mainly relied on the timber framework as the walls were non-load bearing. This form of construction did not restrict the location of openings in the structure and hence there was more freedom to decide where the windows could be placed, without worrying too much about the safety and stability of the structure. It was deemed essential to paint the framework to prevent the onset of rot in the timber. With time, the painting of the pagodas became an integral part of the Chinese architectural style.  Colours are very symbolic in Chinese architecture and are used to mark the importance and function of the structure. The colour yellow is associated with nobility and was used in royal structures. Red and green are considered colours of life.

The origin of the pagodas in China dates back to the period of the advent of Buddhism from India. The pagodas were meant to be religious monuments which preserved holy objects ranging from relics and keepsakes to sacred documents. The Chinese architects integrated the Indian style of constructing stone stupas into the traditional architectural style and came up with a suitable design. The pagodas were tall and symmetric. They were built using different materials- stone, bricks, wood, iron, glazed tiles and occasionally, even gold! They were multi-storeyed with the number of floors always being an odd number. The minimum number of floors was 3 and most of them went up to 9, or even more. At the apex, pagodas were topped with a steeple – a symbol of the power of heaven. There are some speculations as to why the pagodas always had many storeys, which I have mentioned below.

Among the religious buildings in China, I am most enchanted by their pagodas, particularly the Yingxian Pagoda which also goes by the name of Sakyamuni. This used to be the tallest wooden pagoda in the world until 2007, when the construction of the Tianning pagoda (Changzou temple) was completed. The Sakyamuni Pagoda is about 67.31m in height, while the one at Changzou is more than two times taller (153.79m).

Map of Chinese pagodas

Housed in the Fogong Temple, the Sakyamuni pagoda was constructed in 1056 A.D. during the reign of the Liao Dynasty. The pagoda is erected on a stone platform measuring 4 metres in height. The pagoda itself is built entirely out of wood obtained from the Xingan larch trees that were found in abundance in Northern China. When you look at the Sakyamuni pagoda from outside, it appears to be a 5 storeyed structure; although in reality it is 9 storeys high. This is because the four mezzanine layers are concealed within the five outer storeys. The ground floor is topped by two tiers of eaves.

A model of the Sakyamuni pagoda at the Hong Kong Heritage Museum
A model of the Sakyamuni pagoda at the Hong Kong Heritage Museum

The plan of the building is octagonal in shape and consists of two concentric rings of columns. The columns are not vertical, but inclined to the apex of the pagoda. The angle of inclination depends on the position of the columns in the pagoda, and hence on the load carried.

Concentric rings of columns (source: Lam et al.)
Concentric rings of columns (source: Lam et al.)
vertical section of pagoda
Vertical section of the pagoda (source: Lam et al.)

A series of tie beams connects the columns in each ring. An individual beam is connected to a column by means of a slot which forms the connection (tenon and mortise joint). The connections are comprised of only tenon and mortise joints and dou gong brackets. A dou gong bracket is composed of three components – a wooden block called ‘dou’, a lever arm called ‘ang’ and a short arm called ‘gong’.

DOUGONG

In the Yingxian pagoda, the dugong brackets are arranged in layers so that they can transfer the loads from the roof to the subsequent storeys. There are 54 different types of dou gong brackets used in the pagoda. The dou gong system is arranged akin to a basket of flowers. The layered dou gong bracket system symbolizes a hierarchical system and is therefore used only in buildings of importance. The number of layers of these brackets is proportional to the degree of importance of the building. In the Yingxian pagoda, they are set under the overhanging eaves of the building and between the top of each column and cross beam.

The connections between the wooden members were originally supposed to be tight fitted joints. But as it is widely known, timber undergoes shrinkage with time and dries out. Due to this the connections became loose but are still kept together by gravity loads. In the event of an earthquake, the connections are able to move and dissipate energy and hence contribute to the high seismic resistance of the Yingxian pagoda. Additional stability is derived from the relatively short columns. Records reveal that during a high intensity earthquake lasting seven days during the reign of  the Yuan Dynasty, the pagoda stood firm. Even when the Yingxian County area was affected by the severe earthquakes in Xingtai and Tangshan of Hebei Province and in Helinger of Inner Mongolia, the wooden pagoda did not suffer any major damage. In 1996, this structure was listed as a UNESCO World Heritage Site.

Although this wooden pagoda has been able to withstand several earthquakes, severe winds, lightning strikes, high amounts of precipitation and wars in the past 958 years, it is highly unlikely that it is going to last for another millennium. Column heads and ridge beams are twisted and broken. Some of the interior columns have developed cracks. The tower of the pagoda leans slightly to the north-east. There is an obvious tilt in the first and second floors and the scientific community has issued warnings about the inability of the structure to withstand a violent storm or an earthquake. In 2001, the State Administration of Cultural Heritage (SAHC) called for ideas from both local and global experts.

Finally, the following repair intervention options were proposed:

Options to restore the Pagoda and the problems they pose
Options to restore the Pagoda and the problems they pose

However, more than a decade on, the structure is still in disrepair and its condition is deteriorating by the day. In March 2012, the local government of  the county of Yingxian commissioned a project to reduce moisture-induced problems by replacing rotten tiles and fixing the cracks in the building. To a certain extent, this protects the building from problems like erosion due to rain and snow loads and leakage through the dilapidated roof.

The authorities in China say that once the pagoda makes it to UNESCO’s list of protected World Heritage relics, swift measures will be taken towards restoration as there will be enough funds to carry out the necessary measures. In a situation which involves the preservation and restoration of a structure with such a glorious heritage and something so vital to the Chinese identity, it should be of prime importance that the repair interventions be carried out as soon as possible. But with financial and bureaucratic issues, one has to wait and watch what becomes of the Yingxian Pagoda and just hope for the best.

References and further reading:

“STRUCTURAL PERFORMANCE OF DOU-GONG BRACKETS OF YINGXIAN WOOD PAGODA UNDER VERTICAL LOADING” – Enchun Zhu, Zhiyong Chen, Jinglong Pan, Frank Lam

“EXAMPLE OF TRADITIONAL TALL TIMBER BUILDINGS IN CHINA – THE YINGXIAN PAGODA” – Frank Lam, Minjuan He, Chichao Yao

http://www.china.org.cn/china/Off_the_Wire/2013-06/11/content_29096992.htm

http://whc.unesco.org/en/tentativelists/5803/

10 incredibly beautiful pagodas from around the world

https://www.wanderlustmagazine.com/inspiration/10-incredible-pagodas-from-around-the-world/

Top Five Most Beautiful Pagodas in Japan

https://www.jrpass.com/blog/top-five-most-beautiful-pagodas-in-japan

5 Beautiful Pagodas in Japan

https://blog.japanwondertravel.com/pagodas-in-japan-35558

A Gallery of Ancient Japanese Pagodas

https://www.worldhistory.org/collection/125/a-gallery-of-ancient-japanese-pagodas/11/#gallery_wrapper

https://www.chcp.org/Pagoda

THE PAGODA: AN ANCIENT SHRINE
In films and photographs of China and Japan, you’ve seen the striking multi-storied structures known as pagodas. While these familiar towers are the foremost representations of Asian architecture, you may be unaware that they serve as Buddhist monuments, marking the burial site of a Buddhist relic or the tomb of a monk.The pagoda, or ta in Chinese, made its first appearance in China about 68 A.D. when Buddhism arrived from India. As the religion spread during the sixth century, from China to Japan and Korea, the pagoda became a defining form in religious architecture.A towering structure of superimposed stories with overhanging roofs, the pagoda generally is built up from a square, circular, or polygon-shaped foundation. Its origin stems from merging the ancient Indian stupa (the “heap” of brick and stone stacked on the surface of a tomb) with the traditional Chinese multi-storied tower, whch was constructed of timber and topped with a spire.Over the centuries, the design details of the pagoda have evolved and its use has been adapted in Western cultures (often for commercial structures), but its basic shape and its function as a memorial have remained constant in Asia.

The Top 10 Classic Chinese Pagodas

https://www.chinahighlights.com/travelguide/architecture/pagoda.htm

Top 10 Classic Chinese Pagodas

Pagodas constitute a special branch of Chinese architecture. They originally served religious purposes, but gradually became more civilian in nature.

Different from the more typical low-rise buildings, pagodas were first popularized in ancient China. They provided people with spectacular views and often featured in Chinese poems.

Below we describe briefly the top 10 time-honored classic pagodas in China, for your reference.

1. Wooden Pagoda of Ying County

In China, this is known as the Yingxian wooden pagoda. It is the oldest and tallest all-wooden pagoda in the world. It was built in 1056 and served as a Buddhist temple.

It’s a 9-storey pagoda 67.3 meters tall, and 30.3 meters in diameter at the bottom, with an octagonal floor plan. It is constructed with wood, without any nails.

54 different kinds of dougong (斗拱,a unique Chinese structure of interlocking beams and crossbeams) were applied in the building, providing architects with some interesting research.

2. Giant Wild Goose Pagoda

The  Giant Wild Goose Pagoda, also known as the  Big Wild Goose Pagoda, in the Da Ci’en Temple (mercy and kindness temple) complex in Xi’an, is one of the most famous Buddhist pagodas in China, but built with brick.

Dating from 652 AD during the Tang dynasty, it was first built for storing sutras and housing translators of Buddhist classics.

Due to age-induced decay, it has undergone several refurbishments. Today, the pagoda still maintains its original shape after reconstruction during the Ming dynasty. It has 7-storeys and is 64 meters tall.

3. The Iron Pagoda of Yougou Temple, Kaifeng

The Iron Pagoda in Kaifeng, Henan Province was built in 1049 during the Song dynasty. It is also a Buddhist pagoda, with Song-dynasty style; brick-made with glazed tiles.

The “iron” pagoda was not made of iron but brick. Its name became popular during the Yuan dynasty (1271-1368), because its color and sturdiness makes it look like iron.

With 13-storeys, it’s an octagonal-based structure at a height of 55.9 meters. The Iron Pagoda with its densely stacked multiple storeys looks taller than the Yingxian Wooden Pagoda (at 67.3 meters).

4. Three Pagodas of Chongsheng Monastery

Located 1.5 km northwest of Dali old town, the  Three Pagodas of  Chongsheng Monastery are three independent pagodas which form a symmetric triangle. They are also known as the Dali White Pagodas, since they are all covered with white mud.

The middle one, also known as the Qianxun Pagoda (千寻塔), is the oldest and tallest, built about 1,150 years ago. The other two were built only about 100 years ago.

The Three Pagodas are renowned in Dali for their antiquity, size and well-preserved state.

5. Leifeng Pagoda

Leifeng Pagoda is at the north of West Lake, Hangzhou. Most Chinese people know about it because of the Legend of White Snake, a famous Chinese folk tale.

The original pagoda was built in 975 AD. It’s an octagonal, five-storey structure built of brick and wood. During the Ming dynasty (1368-1644), the pagoda was attacked and its wooden structure was burned.

After that, the remaining brick skeleton fell into decay, since people believed its brick could repel illness and competed to steal the bricks. The pagoda eventually collapsed in 1924 due to lack of maintenance.

It was reconstructed in 2001, with a steel and copper structure, but restoring its previous architectural style.

It is one of the top 10 beautiful places of West Lake.

6. Liuhe/Six Harmonies Pagoda

Liuhe Pagoda, literally the Six Harmonies pagoda, was built in 970 during the Song dynasty (960-1127). Located along the Qiantang River, it was originally built to dispel the annual tidal bores of the Qiantang River.

The pagoda stands 59.9 meters tall. Seen from the outside it’s a 13-storey octagonal wooden structure; while from the inside it’s a 7-storey masonry structure. It is one of the best-preserved masonry-timber structure pagodas in China. What’s more, there’s an ancient Chinese pagoda model exhibition hall next to the pagoda.

7. Tiger Hill Pagoda

Located in Suzhou, the  Tiger Hill Pagoda is one of the landmarks of Suzhou. The 7-storey pagoda is 48 meters tall, built with brick but in the timber-style of earlier eras. It’s a representative 10th-century brick pagoda in the Yangtze River basin.

The original pagoda was first built in 601; the existing one began construction in 959 and finished in 961. During the Ming dynasty (1368-1644), the pagoda began to lean towards the northwest, due to its foundations. Now it’s known as the “leaning tower of China“.

8. Songyue Pagoda

The Songyue Pagoda is located at Songyue Monastery in Henan Province. It was built in 523 and has a rare dodecagonal shape. It is regarded as the earliest brick-structure pagoda in China still extant.

The pagoda was built with brick at a height of 40 meters, with an adhesive mixture of sticky rice juice and yellow mud.

9. Feihong/Flying Rainbow Pagoda

Feihong Pagoda at Guangsheng Temple in Shanxi Province is the largest and best-preserved glazed Chinese pagoda. Feihong literally means flying rainbow, a name arising from the pagoda’s colorful decoration.

Feihong is 47.6 meters tall, with 13-storeys. It is a masonry structure built using brick in octagonal pavilion style. Its eaves diminish inwardly at each tier. Around the pagoda’s surface are exquisite sculptures and glazed ornaments.

10. Miaoying Temple White Stupa Pagoda

Located in Xicheng District, Beijing, the White Stupa Pagoda is a rare Tibetan Stupa. It was designed and built in 1271 by a Nepalese architect Anigo, during the reign of Genghis Khan (1206-1227).

Standing at a height of 59.9 meters, it is the oldest and tallest Tibetan-style pagoda in China. It is composed of three parts: a 9-meter high Sumeru pedestal-style platform, an inverted bowl-shaped body and a steeple. Lots of diverse collections of Buddhist statuary were found in 1978 during the repairs.

The generate method of Multi-storey Chinese Pagodas

Tang Zhong Senior Engineer
Zhang Yijie Doctorand
Tongji University, Shanghai, China, tangzzzk@online.sh.cn

Japanese pagoda

https://en.wikipedia.org/wiki/Japanese_pagoda

https://en.wikipedia.org/wiki/Pagoda

Structures of Pagodas

http://www.china.org.cn/english/features/43490.htm

Structures of Pagodas
Different structures have been used in the building of pagodas, depending on the building materials. The structure and method of construction of a wooden pagoda are similar to those of a palace, temple, multistoreyed building or pavilion made of wood, i.e., the traditional beam or bracket system. It is usually composed of a frame, rafters, sheathing, eaves and roof. A pagoda made of bricks and stones, like other brick and stone buildings, is constructed by methods such as piling up bricks or stone blocks and making archways. Metal pagodas are made by moulding and casting metals. Though the building materials and methods of construction differ, the basic structure does not change drastically. A pagoda is composed of the following major parts:

Underground Palace

Most ancient buildings in China were built on solid ground. Usually nothing was built underground. The pagoda, however, was unique in having an underground palace, called the dragon palace or the dragon cave. This special structure is not found in other buildings, such as palaces, temples or multistoreyed buildings. It was added to a Buddhist pagoda to preserve Buddhist relics. According to a survey, Buddhist relics were not buried underground in India, but kept inside the pagodas. When the pagoda was introduced to China, it was combined with China’s traditional burial system. Whenever a pagoda was built, an underground palace was constructed first to preserve the relics and other objects to be buried with the dead. This underground palace was similar to the underground palaces of the mausoleums of emperors and kings in ancient China, but it was usually much smaller and contained fewer funerary objects. The most important thing in an underground palace of a pagoda is a stone container with layer upon layer of cases made of stone, gold, silver, jade and other materials. The innermost case contains the Buddhist relics. The funerary objects in the palace may include copies of Buddhist scriptures and statues of Buddha. Underground palaces were usually built of brick and stone in square, hexagonal, octagonal or round shapes. Occasionally such a structure was built inside the pagoda or semiunderground.

In olden times some superstitious people believed that certain pagodas had been built on “sea holes” to prevent sea water from surging out. If the pagoda fell, the place would be submerged by the sea. The myth came from ignorance of the structure of underground palaces. Sometimes when an underground palace became damaged over the years, underground water would seep into it, and people would mistake it for a “sea hole.” Since Liberation in 1949 thorough investigations have been made of the underground palaces in many important pagodas in Beijing, Hebei, Jiangsu, Hubei and other parts of the country.

For a general understanding of underground pagoda palaces in China let’s look at the underground palace of the sarira pagoda at Jingzhi Temple in Dingzhou, Hebei Province. The name of this particular underground palace was the sarira cabinet, which was inscribed on the wall of the palace, located in the middle of the pagoda’s foundation. A stone shaped like a roof, 60 centimeters deep in the ground, was placed on top of a square hole leading down to the underground palace. The palace room is not an exact square, its east wall being 2.2 meters, west wall 2.1 meters, north wall 2.17 meters and south wall 2.2 meters wide. An arched door is on the south wall. The walls, 2.34 meters high, are joined to the ceiling interlocking brackets. All four walls have murals depicting heavenly kings, Indra, Brahma, boys and maidservants. On the north wall characters read “True Relics of Sakyamuni”, and on both sides are paintings of his ten great disciples. The most incredible thing is that the colors of the columns, brackets, beams and murals are as fresh and bright as if new. Such completely fresh mural paintings of the Song Dynasty cannot be found in buildings aboveground.

A great number of cultural relics were also excavated from this underground palace, including gold and silver ware, porcelain, glassware and wood carvings. Since this pagoda was reconstructed during the Song Dynasty and many funerary objects from deteriorated sites of the Sui and Tang dynasties were also buried in the palace, a few gilded bronze cases of the Sui Dynasty and two stone coffins containing relics of the Tang Dynasty were also unearthed. The large stone case in the middle of the underground palace had been in the basement of the Sui Dynasty pagoda and was replaced after the pagoda was reconstructed. The inscriptions on the stone case indicated its contents and date of burial. Inside were three carved gold coffins, four silver pagodas and a lot of gold and silver ware, porcelain, glazed objects, pearls and other relics.

The underground pagoda palaces resulted from combining the Indian system of burying Buddhist relics in pagodas with the traditional Chinese system of tomb burial.

In cleaning out and repairing old pagodas, many underground palaces and Buddhist and cultural relics buried in them were discovered. Objects found in the Iron Pagoda at Ganlu Temple in Zhenjiang and Huqiu Pagoda in Suzhou, Jiangsu Province, Qianshengxiang Pagoda at Yellow Crane Tower in Wuchang, Hubei Province, the Twin Pagodas at Qingshou Temple in Beijing, Wanjin Pagoda in Nong’an, Jilin Province, and Qianxun Pagoda at Chongsheng Temple in Dali, Yunnan Province, have all provided valuable data for the study of underground pagoda palaces.

Base

The base, on top of the underground palace, supports the whole superstructure. In early times most pagodas had relatively low bases. For instance, the two oldest pagodas in China the pagoda at Songyue Temple of the Northern Wei Dynasty and the Four-Door Pagoda in Licheng of the Sui Dynasty both have very simple, low bases made of brick and stone. Some bases are only ten or twenty centimeters high. They soon become indistinct and even unrecognizable from the ground after being damaged over the years. The base of Xuanzang Pagoda at Xingjiao Temple in Xi’an has become so undistinguishable that the pagoda seems to have been built right on the ground. During the Tang Dynasty, in order to make pagodas such as the Big and Small Wild Goose Pagodas in Xi’an look magnificent, huge bases were built under them. Large bases were also added to pavilion-style pagodas during the Tang Dynasty, for example, the Pagoda of Monk Fanzhou in Anyi of Shanxi Province and the Dragon and Tiger Pagoda at Shentong Temple in Licheng near Jinan.

After the Tang Dynasty the pagodas’ substructure developed into two parts by adding a pedestal to the original base. The effect was a loftier and more majestic pagoda. The lower part of the substructure–the platform –is usually low and without much decoration. The pedestal, in contrast, became the most prominent part of the pagoda with gorgeous decorations. In the process of development the pedestal construction of the multi-eaved pagodas of the Liao and Kin dynasties was most out-standing.

This part of the substructure of pagodas from the Liao and Kin dynasties was called the Sumeru pedestal. According to Buddhist literature, Sumeru is the largest mountain in the world and the home of Buddha and bodhisattvas. To call the pedestal of a pagoda by the name of Sumeru meant that it was a most stable foundation. The supports of palaces, temples, statues of Buddha and other objects were also called Sumeru pedestals. At Tianning Temple in Beijing the pedestal of the pagoda is an octagonal structure on a platform of medium height. The pedestal is divided into two levels. On the first level there are six niches on each side with lion heads carved inside. Carved columns separate the niches. On the lower part of the second level there are five small niches, each with a statue of Buddha inside. On the columns between the niches are images of heavenly guardians in relief sculpture. The brackets on the upper part of the pedestal are decorated with finely carved brick banisters. The banisters are joined to the first storey of the pagoda by a lotus-petal capital. The whole Sumeru pedestal is about one fifth the height of the pagoda.

Later, huge and gorgeous pedestals became very common for other types of pagodas. For a Lamaist pagoda the pedestal, as a major part of the entire structure, often makes one third of its total height. The pedestals of pagodas on vajrasanas, the bulk of the structure, are much bigger than the small pagodas on top of them. Pagodas across streets also have pedestals higher than the pagodas they support. Adopting large pedestals in pagoda construction is closely connected with the traditional Chinese architecture, which always sets great store by the role of base platforms. A large base platform not only provides the building above with a solid and firm foundation but also makes it look majestic and powerful.

Body

The body, or main part, of a pagoda varies depending on the style of architecture. The classification of pagodas was based on the style of the body of the pagoda. Since we have already discussed the outer forms and structures of the pagoda, we are going to concentrate on the inner structure of the pagoda body.

A pagoda may be solid or hollow. Solid pagodas are filled with bricks, stones or rammed earth. Occasionally, a wooden framework is installed inside a solid pagoda to strengthen the bearing capacity of outreaching parts of the pagoda. On the whole, however, the inner structure of a solid pagoda is relatively simple. The following section will focus on hollow pagodas.

1. Wooden pagodas. Wooden pagodas of many storeys were popular during the later years of the Han Dynasty and the Wei, Jin and Northern and Southern dynasties. Most of them have four sides. From historical accounts and existing examples in Japan we have learned that wooden pagodas of this type were composed of the following parts–columns around each level of the pagoda, three rooms on each of the four sides on each level, beams and brackets on the capital of the columns to join with the upper storey, and verandas with banisters around each storey. Eaves stretch out above each of the storeys. As in other multistoreyed buildings, there are stairs for people to climb up and down. 

The wooden pagoda in Yingxian County, Shanxi Province, is the best preserved of its kind in China today. It has five levels of eaves on the exterior and five levels of balconies, but there are also five mezzanines in between the main storeys, making it a ten-storey building. The pagoda is octagonal with three rooms and four columns on each side of each exterior storeyed, and the landing are quite spacious. The balconies have protecting banisters so that people can walk around the pagoda freely and enjoy the view. In the middle of the pagoda a huge statue of Buddha was installed. In order to strengthen the structure, double-layer walls were built with post trusses and struts in between to prop up the framework. Spiral stairs lead to each level. Since the pagoda is such a huge and complex structure, the components vary greatly in size and form. For instance, there are more than sixty different kinds of brackets. However, the method of construction was the same as for other wooden buildings.

2. Pagodas with brick exteriors and wooden interiors. The brick walls form the body of the pagoda like a hollow tube, so it is also called a tube-style structure. This structure was used in the construction of both multistoreyed and multi-eaved pagodas during early periods. According to the design for the height of each storey and the positions of doors and windows, holes were left when the brick walls were built for placing the floor slabs and putting up door and window frames. Sometimes pillars were erected at the corners to support the floor above. In most cases spiral stairs were built along the walls.

The number of storeys in a pagoda of this type usually corresponded to the positions of doors and windows and levels of eaves on the outside, and people could ascend them to enjoy the view around. The Big Wild Goose Pagoda in Xi’an, Gongchen Pagoda at Lin’an near Hangzhou and the Twin Pagodas at Luohanyuan Temple in Suzhou are examples of this category. The actual number of storeys in a multi-eaved pagoda, however, usually did not correspond to the positions of doors, windows and eaves, because the eaves were built so close to each other above ground level that there was not enough space for a complete storey in the interior. The pagoda at Songyue Temple, the Small Wild Goose Pagoda and Qianxun Pagoda at Dali’s Chongsheng Temple are typical of this category.

3. Pagodas with a central wooden pillar. Most early wooden pagodas had a central pillar as the mainstay of the structure. A huge pillar, erected right in the middle of the pagoda, propped up the frame from the ground to the top. Descriptions of this construction have been found in historical accounts. A five-storeyed pagoda at Falong Temple in Japan is an existing example of this type. The central pillar helps stabilize the structure. The only extant example of this type in China is the wooden pagoda at Tianning Temple in Zhengding. Since the pagoda is a mixture of wood and brick, the pillar was erected in the upper half of the pagoda, not on the bottom floor, but the central-pillar structure is quite obvious. It is a valuable example in the study of this type of pagoda.

4. Pagodas made of both wood and brick. This type of pagoda was a transition from wooden pagodas to pagodas made of bricks and stones. The body of the pagoda was made of bricks; the eaves, verandas and banisters were made of timber. Wooden columns, beams and eaves were joined to the brick walls for interior framework. This structure was popular during the Song Dynasty. The square pagoda at Songjiang in Shanghai, the Pagoda of Six Harmonies in Hangzhou, Ruiguang Pagoda and Beisi Pagoda in Suzhou are typical of this type.

5. Pagodas with a brick pillar as the mainstay. These were products of China’s traditional brick and stone architecture at its highest development. The main body of the pagoda is completely brick. The stairs, floors, verandas and eaves are all built of brick or stone as integral parts of a complex whole. In the middle of the pagoda a huge brick pillar props up the roof. Every floor level is connected to the central pillar and the walls to form an integrated whole. The floors are built by means of arch bonding and stacking bricks around the central pillar. There are two forms of stairs: One is built along the walls of the central pillar in a “z’ shape; the other winds through the hollow space in the central pillar. In the former case there is a landing around the pillar on every level. Examples of the first structure include the pagoda at Youguo Temple in Kaifeng, Henan Province, the pagoda at Lingyun Temple in Leshan, Sichuan Province, and the one at Famen Temple in Fufeng, Shaanxi Province. The second form is represented by Baodingshan Pagoda in Dazu, Sichuan Province, Liaodi Pagoda at Kaiyuan Temple in Dingzhou and the sarira pagoda in Jingxian County, Hebei Province. Most were built during the Song and Ming dynasties and reached advanced levels in brick and stone architecture.

6. Pagodas build on high platforms. The vajrasanastyle pagodas are pagodas with a huge platform as the main body. Brick or stone staircases were built inside the hollow platform for people to ascend the building. In the pedestal under the pagoda at Zhenjue Temple in Beijing there is a central pillar, and the room around it has a vault roof that serves as the exterior terrace on which small pagodas were erected. The pagodas at Beijing’s Biyun Temple and Hohhot’s Cideng Temple were both built in this style. Some other pagodas have staircases on the outside of the platforms, such as Qingjinhuayu Pagoda in Beijing’s Xihuang Temple and the pagoda at Yuanzhao Temple on Mount Wutai in Shanxi Province.

7. Other types of pagodas. The Lamaist pagoda, for instance, has a round, inverted-bowl-shaped body. During the Ming and Qing dynasties a recess called the yanguang gate was built on the front of the round structure. Sometimes a wooden framework was installed inside the inverted-bowl body to strengthen its stability. Sometimes the inverted-bowl style was combined with a multistoreyed pagoda, such as building a multistoreyed pagoda on top of an inverted-bowl structure, or with a tube-shaped pagoda, or others.

Steeple

Every pagoda is surmounted by a steeple, sometimes pointed and sometimes ball-shaped. They vary greatly in style and building materials. The most commonly used building materials for steeples are bricks, stones and metals.

The steeple, as the tallest part of the pagoda, is extremely important. In Chinese it is called cha, meaning land or territory representing “the country of Buddha.” Therefore, a Buddhist temple is also called cha in China. The lake to the north of Beihai Park in Beijing is called Shi Cha Hai, meaning the Lake of Ten Temples, because there used to be ten great Buddhist temples by the lake.

The steeple is also very important in the architectural structure, because it is the tip of the building. No matter whether the pagoda’s roof is square, hexagonal, octagonal or round, the rafters, sheathing and tile ridges all come to one point, where a component should be fixed to stabilize the roof structure and prevent rain from leaking into the building. The steeple performs these functions.

From the aesthetic point of view, the steeple, surmounting the whole structure of the pagoda, was the crowning image of the building. Therefore, great efforts were made to create a steeple that was exquisite, lofty and graceful.

Early stupas in India also had steeples, but they were not so tall and complex. For instance, a famous Indian stupa built around the first century has only a spire and three layers of umbrella-shaped decorations. After stupas were introduced to China, however, and combined with traditional architectural styles, the steeple of the pagoda, as the emblem of Buddhism, became more and more important and conspicuous. In Stories About Buddhist Temples in Luoyang the steeple of the pagoda at Yongning Temple was said to be as tall as “ten zhang” (33 meters), which may be an exaggeration, but it must have been quite tall. The decorative precious bottle on top of the steeple allegedly could hold 25 dan (2,500 liters) of grain. We can imagine how big it was. Below the precious golden bottle there were thirty tiers of gilded dew basins and many golden bells hanging around them. Since the steeple was very tall, four iron chains linked the steeple with the four comers of the pagoda roof to stabilize the structure. The iron chains were also ornamented with little golden bells.

Many pagoda steeples were built like small Lamaist dagobas. A typical example is the pagoda at Tianning Temple in Anyang, Henan Province. The five-storeyed pagoda is surmounted by a smaller Lamaist dagoba. In Miaoying Temple in Beijing the White Dagoba is composed of a small Lamaist dagoba on top of a larger dagoba. Some Buddhist scriptures say that Buddhist relics are placed in the tip of a pagoda steeple, but no such case has ever been discovered. Researchers believe this was a mistake and that the bottom of the steeple was intended.

The steeple of a pagoda is itself a small dagoba, composed of bottom, body and top with a pole in the middle. Sometimes there is a small cabinet at the bottom of the steeple to hold Buddhist relics, Buddhist sutras or gold, silver, jade and other valuable objects. Such hiding places were found in recent years when repairing old pagodas. At Qianxun Pagoda at Chongsheng Temple in Dali, Yunnan Province, Buddhist relics, scriptures and statues of Buddha were found in a hiding place at the bottom of the pagoda’s steeple, while nothing was found in the underground palace of the pagoda. Whether the underground palace had been robbed of its treasure or it was a mere symbolic form when the real relics and funerary objects had been hidden in the steeple remains an open question.

The base of the steeple was built on the roof of the pagoda, pressing on the rafters, sheathing, corner columns and tile ridges, with the steeple pole planted right in the middle. Steeple bases varied from one another; most were shaped like the Sumeru pedestal, or blooming lotus petals. Some were just plain square platforms. Many had carved patterns of lotus petals or honeysuckle leaves.

The most outstanding characteristic of the steeple was the discs around the pole of the steeple. They were called xianglun (wheel or disc) or golden basins or dew basins, as a symbol of honor or respect for the Buddha. Generally, the bigger the pagoda, the more and bigger the discs. In the early period there were no regulations as to the number of such discs on a particular pagoda. Some had as many as several dozen; others had three or five. Originally, the great wooden pagoda at Yongning Temple ha Luoyang, for instance, had thirty tiers of discs. The Four-Door Pagoda has five and Songyue Temple Pagoda has seven. In later times pagodas were built with one, three, five, seven, nine, eleven or thirteen discs. Most Lamaist dagobas have thirteen discs, which are therefore called “thirteen skies.” An umbrellalike canopy is usually built above the discs as part of the pagoda’s ornaments.

The top of the steeple is also the top of the pagoda. It was usually put above the canopy and consisted of a crescent moon and a precious bead. Sometimes the bead was put above or in the middle of a flame ornament. To avoid any indication of fire, the flame-shaped ornament was called “water smoke.”

The pole of the steeple was the central axle. All the components of a metal steeple were fastened to the pole, which supported the different parts of the steeple. Even small brick pagodas had a wooden or metal pole in the middle of the steeple. According to Buddhist literature, the pole was also called chazhu (steeple pillar) or jincha (golden steeple) or biaocha (symbolic steeple). It was usually made of wood or iron and placed on the roof of the pagoda.

These were the most representative steeple structures. Changes were made in different eras, areas and on different types of pagodas built of different materials. For instance, sometimes three, five, seven or nine metal balls were part of the spire of a pagoda, as in the Twin Pagodas of Chongxing Temple in Beizhen, Liaoning Province. Sometimes a huge canopy was put on top of the pagoda’s steeple, as in the Tianning Temple Pagoda in Beijing. The canopies had different shapes–round, square or octagonal. The spire of Haibao Pagoda in Yinchuan consisted of an onion-shaped ornament, possibly influenced by Islamic architecture. Guang Pagoda at Huaisheng Temple in Guangzhou is unique, since the steeple is a weather vane, completely different from an ordinary Buddhist pagoda.

In search of gojunoto, the five element Japanese pagoda

Symmetry Analysis of Oriental Polygonal Pagodas Using 3D Point Clouds for Cultural Heritage.

Chan TO, Xia L, Chen Y, Lang W, Chen T, Sun Y, Wang J, Li Q, Du R.

Sensors (Basel). 2021 Feb 9;21(4):1228. doi: 10.3390/s21041228. PMID: 33572401; PMCID: PMC7916231.

Seismic and Wind Performance of Five-Storied Pagoda of Timber Heritage Structure

https://www.scientific.net/AMR.133-134.79

Structural performance of Dou-Gong brackets of Yingxian Wood Pagoda under vertical load – An experimental study

Zhiyong Chen a b c, Enchun Zhu a b, Frank Lam d, Jinglong Pan a b
a
Key Lab of Structures Dynamic Behaviour and Control (Harbin Institute of Technology), Ministry of Education, Harbin 150090, China
b
School of Civil Engineering, Harbin Institute of Technology, Harbin 150090, China
c
Faculty of Forestry and Environmental Management, University of New Brunswick, Fredericton E3B 5A3, Canada
d
Department of Wood Science, University of British Columbia, Vancouver V6T 1Z4, Canada

Received 17 August 2013, Revised 12 June 2014, Accepted 9 September 2014, Available online 27 September 2014.

Engineering Structures
Volume 80, 1 December 2014, Pages 274-288

https://www.sciencedirect.com/science/article/abs/pii/S0141029614005501