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44-601: The architecture of the Asian Centre building, in which the Asian Library is located, is based on a traditional pagoda , and the building was designed by Donald Matsuba at the cost of $ 1.6 million Canadian dollars. The building was intended to be a centennial gift funded by the Government of Japan , serving as a symbol of Asian-Canadian and Canada–Japan relations . The Asian studies idea was created by Geoffrey Brian Hainsworth and

88-630: A Petrie polygon projection plane of the tesseract . The list (sequence A006245 in the OEIS ) defines the number of solutions as eight, by the eight orientations of this one dissection. These squares and rhombs are used in the Ammann–Beenker tilings . A skew octagon is a skew polygon with eight vertices and edges but not existing on the same plane. The interior of such an octagon is not generally defined. A skew zig-zag octagon has vertices alternating between two parallel planes. A regular skew octagon

132-398: A power of two : The regular octagon can be constructed with meccano bars. Twelve bars of size 4, three bars of size 5 and two bars of size 6 are required. Each side of a regular octagon subtends half a right angle at the centre of the circle which connects its vertices. Its area can thus be computed as the sum of eight isosceles triangles, leading to the result: for an octagon of side

176-510: A spire crowning the top. Its walls are 2.5 m thick, with a ground floor diameter of 10.6 m. Another early brick pagoda is the Sui dynasty Guoqing Pagoda built in 597. The earliest large-scale stone pagoda is a Four Gates Pagoda at Licheng , Shandong, built in 611 during the Sui dynasty . Like the Songyue Pagoda, it also features a spire at its top, and is built in the pavilion style. One of

220-411: A stupa , by way of Portuguese. The origin of the pagoda can be traced to the stupa (3rd century BCE). The stupa, a dome shaped monument, was used as a commemorative monument to house sacred relics and writings. In East Asia, the architecture of Chinese towers and Chinese pavilions blended into pagoda architecture, eventually also spreading to Southeast Asia. Their construction was popularized by

264-542: A . The coordinates for the vertices of a regular octagon centered at the origin and with side length 2 are: Coxeter states that every zonogon (a 2 m -gon whose opposite sides are parallel and of equal length) can be dissected into m ( m -1)/2 parallelograms. In particular this is true for regular polygons with evenly many sides, in which case the parallelograms are all rhombi. For the regular octagon , m =4, and it can be divided into 6 rhombs, with one example shown below. This decomposition can be seen as 6 of 24 faces in

308-455: A Buddhist vihara. The architectural structure of the stupa has spread across Asia, taking on many diverse forms specific to each region. Many Philippine bell towers are highly influenced by pagodas through Chinese workers hired by the Spaniards . One proposed etymology is from a South Chinese pronunciation of the term for an eight-cornered tower, Chinese: 八角塔 , and reinforced by the name of

352-566: A central pagoda might not have been either desirable or possible. In the Song dynasty (960–1279), the Chan (Zen) sect developed a new 'seven part structure' for temples. The seven parts—the Buddha hall, dharma hall, monks' quarters, depository, gate, pure land hall and toilet facilities—completely exclude pagodas, and can be seen to represent the final triumph of the traditional Chinese palace/courtyard system over

396-489: A famous pagoda encountered by many early European visitors to China, the "Pázhōu tǎ" (Chinese: 琶洲塔 ), standing just south of Guangzhou at Whampoa Anchorage . Another proposed etymology is Persian butkada , from but , "idol" and kada , "temple, dwelling." Yet another etymology is from the Sinhala word dāgaba , derived from Sanskrit dhātugarbha or Pali dhātugabbha : "relic womb/chamber" or "reliquary shrine", i.e.

440-492: A few of his colleagues. 49°16′00″N 123°15′32″W  /  49.2668°N 123.2588°W  / 49.2668; -123.2588 This article relating to library science or information science is a stub . You can help Misplaced Pages by expanding it . Pagoda A pagoda is a tiered tower with multiple eaves common to Thailand , Cambodia , Nepal , China , Japan , Korea , Myanmar , Vietnam , and other parts of Asia. Most pagodas were built to have

484-402: A list inscribed on it of the recently successful examination candidates, in hopes that it would reverse the trend and win the county supernatural favor. Pagodas come in many different sizes, with taller ones often attracting lightning strikes , inspiring a tradition that the finial decoration of the top of the structure can seize demons. Today many pagodas have been fitted with wires making

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528-790: A notable exception being the eighteenth-century orientalist pagoda designed by Sir William Chambers at Kew Gardens in London. The pagodas in Himalayas are derived from Newari architecture , very different from Chinese and Japanese styles. During the Southern and Northern dynasties , pagodas were mostly built of wood, as were other ancient Chinese structures. Wooden pagodas are resistant to earthquakes, and no Japanese pagoda has been destroyed by an earthquake, but they are prone to fire, natural rot, and insect infestation. Examples of wooden pagodas: The literature of subsequent eras also provides evidence of

572-613: A number of octagonal churches in Norway . The central space in the Aachen Cathedral , the Carolingian Palatine Chapel , has a regular octagonal floorplan. Uses of octagons in churches also include lesser design elements, such as the octagonal apse of Nidaros Cathedral . Architects such as John Andrews have used octagonal floor layouts in buildings for functionally separating office areas from building services, such as in

616-414: A reference octagon has its eight vertices at the midpoints of the sides of the reference octagon. If squares are constructed all internally or all externally on the sides of the midpoint octagon, then the midpoints of the segments connecting the centers of opposite squares themselves form the vertices of a square. A regular octagon is a closed figure with sides of the same length and internal angles of

660-404: A regular octagon of side length a is given by In terms of the circumradius R , the area is In terms of the apothem r (see also inscribed figure ), the area is These last two coefficients bracket the value of pi , the area of the unit circle . The area can also be expressed as where S is the span of the octagon, or the second-shortest diagonal; and a is the length of one of

704-408: A religious function, most often Buddhist , but sometimes Taoist , and were often located in or near viharas . The pagoda traces its origins to the stupa , while its design was developed in ancient India . Chinese pagodas ( Chinese : 塔 ; pinyin : Tǎ ) are a traditional part of Chinese architecture . In addition to religious use, since ancient times Chinese pagodas have been praised for

748-447: A side a , the span S is The span, then, is equal to the silver ratio times the side, a. The area is then as above: Expressed in terms of the span, the area is Another simple formula for the area is More often the span S is known, and the length of the sides, a , is to be determined, as when cutting a square piece of material into a regular octagon. From the above, The two end lengths e on each side (the leg lengths of

792-484: A truncated square. The sum of all the internal angles of any octagon is 1080°. As with all polygons, the external angles total 360°. If squares are constructed all internally or all externally on the sides of an octagon, then the midpoints of the segments connecting the centers of opposite squares form a quadrilateral that is both equidiagonal and orthodiagonal (that is, whose diagonals are equal in length and at right angles to each other). The midpoint octagon of

836-491: Is r16 and no symmetry is labeled a1 . The most common high symmetry octagons are p8 , an isogonal octagon constructed by four mirrors can alternate long and short edges, and d8 , an isotoxal octagon constructed with equal edge lengths, but vertices alternating two different internal angles. These two forms are duals of each other and have half the symmetry order of the regular octagon. Each subgroup symmetry allows one or more degrees of freedom for irregular forms. Only

880-667: Is vertex-transitive with equal edge lengths. In three dimensions it is a zig-zag skew octagon and can be seen in the vertices and side edges of a square antiprism with the same D 4d , [2 ,8] symmetry, order 16. The regular skew octagon is the Petrie polygon for these higher-dimensional regular and uniform polytopes , shown in these skew orthogonal projections of in A 7 , B 4 , and D 5 Coxeter planes . The regular octagon has Dih 8 symmetry, order 16. There are three dihedral subgroups: Dih 4 , Dih 2 , and Dih 1 , and four cyclic subgroups : Z 8 , Z 4 , Z 2 , and Z 1 ,

924-606: Is Beijing's Yonghe Temple , which was the residence of Yongzheng Emperor before he ascended the throne. It was donated for use as a lamasery after his death in 1735. Examples of Han dynasty era tower architecture predating Buddhist influence and the full-fledged Chinese pagoda can be seen in the four pictures below. Michael Loewe writes that during the Han dynasty (202 BC – 220 AD) period, multi-storied towers were erected for religious purposes, as astronomical observatories , as watchtowers , or as ornate buildings that were believed to attract

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968-404: Is an eight-sided polygon or 8-gon. A regular octagon has Schläfli symbol {8} and can also be constructed as a quasiregular truncated square , t{4}, which alternates two types of edges. A truncated octagon, t{8} is a hexadecagon , {16}. A 3D analog of the octagon can be the rhombicuboctahedron with the triangular faces on it like the replaced edges, if one considers the octagon to be

1012-761: Is the Liaodi Pagoda. In April 2007 a new wooden pagoda Tianning Temple of Changzhou was opened to the public, the tallest in China, standing 154 m (505 ft). Chinese iconography is noticeable in Chinese and other East Asian pagoda architectures. Also prominent is Buddhist iconography such as the image of the Shakyamuni and Gautama Buddha in the abhaya mudra . In an article on Buddhist elements in Han dynasty art, Wu Hung suggests that in these temples, Buddhist symbolism

1056-528: The Northern Wei and Sui dynasties (386–618) experiments began with the construction of brick and stone pagodas. Even at the end of the Sui, however, wood was still the most common material. For example, Emperor Wen of the Sui dynasty (reigned 581–604) once issued a decree for all counties and prefectures to build pagodas to a set of standard designs, however since they were all built of wood none have survived. Only

1100-566: The Songyue Pagoda has survived, a circular-based pagoda built out of brick in 523 AD. The earliest extant brick pagoda is the 40-metre-tall Songyue Pagoda in Dengfeng Country, Henan . This curved, circle-based pagoda was built in 523 during the Northern Wei dynasty , and has survived for 15 centuries. Much like the later pagodas found during the following Tang dynasty, this temple featured tiers of eaves encircling its frame, as well as

1144-733: The g8 subgroup has no degrees of freedom but can be seen as directed edges . The octagonal shape is used as a design element in architecture. The Dome of the Rock has a characteristic octagonal plan. The Tower of the Winds in Athens is another example of an octagonal structure. The octagonal plan has also been in church architecture such as St. George's Cathedral, Addis Ababa , Basilica of San Vitale (in Ravenna, Italia), Castel del Monte (Apulia, Italia), Florence Baptistery , Zum Friedefürsten Church (Germany) and

1188-401: The circumradius as The regular octagon, in terms of the side length a , has three different types of diagonals : The formula for each of them follows from the basic principles of geometry. Here are the formulas for their length: A regular octagon at a given circumcircle may be constructed as follows: A regular octagon can be constructed using a straightedge and a compass , as 8 = 2 ,

1232-632: The domination of wooden pagoda construction. The famous Tang dynasty poet, Du Mu , once wrote: 480 Buddhist temples of the Southern Dynasties, uncountable towers and pagodas stand in the misty rain. The oldest standing fully wooden pagoda in China today is the Pagoda of Fugong Temple in Ying County, Shanxi , built in the 11th century during the Song/ Liao dynasty (see Song architecture ). During

1276-529: The earliest brick and stone pagodas was a three-storey construction built in the (first) Jin dynasty (266–420) , by Wang Jun of Xiangyang . However, it is now destroyed. Brick and stone went on to dominate Tang , Song , Liao and Jin dynasty pagoda construction. An example is the Giant Wild Goose Pagoda (652 AD), built during the early Tang dynasty. The Porcelain Pagoda of Nanjing has been one of

1320-511: The efforts of Buddhist missionaries , pilgrims, rulers, and ordinary devotees to honor Buddhist relics. Japan has a total of 22 five-storied timber pagodas constructed before 1850. The earliest styles of Chinese pagodas were square-base and circular-base, with octagonal -base towers emerging in the 5th–10th centuries. The highest Chinese pagoda from the pre-modern age is the Liaodi Pagoda of Kaiyuan Monastery, Dingxian, Hebei , completed in

1364-591: The favor of spirits, deities, and immortals . Pagodas built during the Sui and Tang dynasty usually had a square base, with a few exceptions such as the Daqin Pagoda: Pagodas of the Five Dynasties, Northern and Southern Song, Liao, Jin, and Yuan dynasties incorporated many new styles, with a greater emphasis on hexagonal and octagonal bases for pagodas: Pagodas in the Ming and Qing dynasties generally inherited

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1408-517: The finial into a lightning rod . Wooden pagodas possess certain characteristics thought to resist earthquake damage. These include the friction damping and sliding effect of the complex wooden dougong joints, the structural isolation of floors, the effects of wide eaves analogous to a balancing toy, and the Shinbashira phenomenon that the center column is bolted to the rest of the superstructure. Pagodas traditionally have an odd number of levels,

1452-402: The last implying no symmetry. On the regular octagon, there are eleven distinct symmetries. John Conway labels full symmetry as r16 . The dihedral symmetries are divided depending on whether they pass through vertices ( d for diagonal) or edges ( p for perpendiculars) Cyclic symmetries in the middle column are labeled as g for their central gyration orders. Full symmetry of the regular form

1496-518: The most famous brick and stone pagoda in China throughout history. The Zhou dynasty started making the ancient pagodas about 3,500 years ago. Pagodas, in keeping with the tradition of the White Horse Temple , were generally placed in the center of temples until the Sui and Tang dynasties. During the Tang, the importance of the main hall was elevated and the pagoda was moved beside the hall, or out of

1540-509: The original central-pagoda tradition established 1000 years earlier by the White Horse Temple in 67. Although they were built outside of the main temple itself, large pagodas in the tradition of the past were still built. This includes the two Ming dynasty pagodas of Famen Temple and the Chongwen Pagoda in Jingyang of Shaanxi . A prominent, later example of converting a palace to a temple

1584-551: The same size. It has eight lines of reflective symmetry and rotational symmetry of order 8. A regular octagon is represented by the Schläfli symbol {8}. The internal angle at each vertex of a regular octagon is 135 ° ( 3 π 4 {\displaystyle \scriptstyle {\frac {3\pi }{4}}} radians ). The central angle is 45° ( π 4 {\displaystyle \scriptstyle {\frac {\pi }{4}}} radians). The area of

1628-403: The sides, or bases. This is easily proven if one takes an octagon, draws a square around the outside (making sure that four of the eight sides overlap with the four sides of the square) and then takes the corner triangles (these are 45–45–90 triangles ) and places them with right angles pointed inward, forming a square. The edges of this square are each the length of the base. Given the length of

1672-418: The spectacular views they offer, and many classical poems attest to the joy of scaling pagodas. The oldest and tallest pagodas were built of wood, but most that survived were built of brick or stone. Some pagodas are solid with no interior. Hollow pagodas have no higher floors or rooms, but the interior often contains an altar or a smaller pagoda, as well as a series of staircases for the visitor to climb to see

1716-496: The styles of previous eras, although there were some minor variations: Tiered towers with multiple eaves: Stupas called "pagodas": Places called "pagoda" but which are not tiered structures with multiple eaves: Structures that evoke pagoda architecture: Structures not generally thought of as pagodas, but which have some pagoda-like characteristics: Octagon In geometry , an octagon (from Ancient Greek ὀκτάγωνον ( oktágōnon )  'eight angles')

1760-405: The temple compound altogether. In the early Tang, Daoxuan wrote a Standard Design for Buddhist Temple Construction in which the main hall replaced the pagoda as the center of the temple. The design of temples was also influenced by the use of traditional Chinese residences as shrines, after they were philanthropically donated by the wealthy or the pious. In such pre-configured spaces, building

1804-430: The triangles (green in the image) truncated from the square), as well as being e = a / 2 , {\displaystyle e=a/{\sqrt {2}},} may be calculated as The circumradius of the regular octagon in terms of the side length a is and the inradius is (that is one-half the silver ratio times the side, a , or one-half the span, S ) The inradius can be calculated from

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1848-468: The view from an opening on one side of each tier. Most have between three and 13 tiers (almost always an odd number) and the classic gradual tiered eaves. In some countries, the term may refer to other religious structures. In Vietnam and Cambodia, due to French translation, the English term pagoda is a more generic term referring to a place of worship , although pagoda is not an accurate word to describe

1892-484: The year 1055 AD under Emperor Renzong of Song and standing at a total height of 84 m (275 ft). Although it no longer stands, the tallest pre-modern pagoda in Chinese history was the 100-metre-tall wooden pagoda (330 ft) of Chang'an , built by Emperor Yang of Sui , and possibly the short-lived 6th century Yongning Pagoda ( 永宁宝塔 ) of Luoyang at roughly 137 metres. The tallest pre-modern pagoda still standing

1936-474: Was fused with native Chinese traditions into a unique system of symbolism. Some believed reverence at pagodas could bring luck to students taking the Chinese civil service examinations . When a pagoda of Yihuang County in Fuzhou collapsed in 1210, local inhabitants believed the disaster correlated with the recent failure of many exam candidates in the prefectural examinations The pagoda was rebuilt in 1223 and had

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