Banshan
Banshan was a phase of the Chinese Neolithic Yangshao culture, c. 2600 to 2300 BC. The Banshan site is in Gansu. In 1923 and 1924, Swedish scholar J. G. Anderson discovered the sites of Banshan, Machang and Xindian at Lajia on the north bank of the Yellow River
Lower Xiajiadian culture
The Lower Xiajiadian culture is an archaeological culture in Northeast China, found in southeastern Inner Mongolia, northern Hebei and western Liaoning, China. Subsistence was based on millet farming supplemented with animal hunting. Archaeological sites have yielded the remains of pigs, dogs and cattle; the culture built permanent settlements and achieved high population densities. The population levels reached by the Lower Xiajiadian culture in the Chifeng region would not be matched until the Liao Dynasty; the culture was preceded through the transitional Xiaoheyan culture. The type site is represented by the lower layer at Xiajiadian, Inner Mongolia. Stone and pottery artefacts were discovered at Lower Xiajiadian sites, while gold, lacquer, jade and bronze artefacts are found; the most found copper and bronze artefacts are earrings. People of the Lower Xiajiadian practiced oracle bone divination; the culture prepared its oracle bones by polishing the bones before heating them. Inscriptions are not found on examples of oracle bones of the Lower Xiajiadian.
People had good access to local sources of stone basalt, which were used in construction and tool-making. Lower Xiajiadian houses were round, made from mud and stone, were built with stone walls. Lower Xiajiadian settlements were protected by cliffs or steep slopes. Stone walls were sometimes erected around the non-sloped perimeter of its settlement. Walls were not thick. Walls with watchtowers and were built by sandwiching a rammed earth core with two sides of stone walls. Upper Xiajiadian culture Xinglonggou Yueshi culture Shelach, Leadership Strategies, Economic Activity, Interregional Interaction: Social Complexity in Northeast China, ISBN 0-306-46090-4
Longshan culture
The Longshan culture sometimes referred to as the Black Pottery Culture, was a late Neolithic culture in the middle and lower Yellow River valley areas of northern China from about 3000 to 1900 BC. The first archaeological find of this culture took place at the Chengziya Archaeological Site in 1928, with the first excavations in 1930 and 1931; the culture is named after the nearby modern town of Longshan in Shandong. The culture was noted for its polished black pottery; the population expanded during the 3rd millennium BC, with many settlements having rammed earth walls. It decreased in most areas around 2000 BC until the central area evolved into the Bronze Age Erlitou culture. A distinctive feature of the Longshan culture was the high level of skill in pottery making, including the use of pottery wheels, producing thin-walled and polished black pottery; this pottery was widespread in North China, found in the Yangtze River valley and as far as the southeastern coast. Until the 1950s, such black pottery was considered the principal diagnostic, all of these sites were assigned to the Longshan culture.
In the first edition of his influential survey The Archaeology of Ancient China, published in 1963, Kwang-chih Chang described the whole area as a "Longshanoid horizon", suggesting a uniform culture attributed to expansion from a core area in the Central Plain. More recent discoveries have uncovered much more regional diversity than thought, so that many local cultures included within Chang's Longshanoid horizon are now viewed as distinct cultures, the term "Longshan culture" is restricted to the middle and lower Yellow River valley. For example, the contemporaneous culture of the lower Yangtze area is now described as the Liangzhu culture. At the same time, researchers recognized the diversity within the Yellow River valley by distinguishing regional variants in Henan and Shaanxi from the Shandong or "classic" Longshan. In the fourth edition of his book, Chang moved from a model centered on the Central Plain to a model of distinctive regional cultures whose development was stimulated by interaction between regions, a situation he called the "Chinese interaction sphere".
In the 1980s, Yan Wenming proposed the term "Longshan era" to encompass cultures of the late Neolithic across the area, though he assigned the Central Plain a leading role. The most important crop was foxtail millet, but traces of broomcorn millet and wheat have been found. Rice grains have been found in Shandong and southern Henan, a small rice field has been found on the Liaodong peninsula. Specialized tools for digging and grinding grain have been recovered; the most common source of meat was the pig. Sheep and goats were domesticated in the Loess Plateau area in the 4th millennium BC, found in western Henan by 2800 BC, spread across the middle and lower Yellow River area. Dogs were eaten in Shandong, though cattle were less important. Small-scale production of silk by raising and domesticating the silkworm in early sericulture was known. Remains have been found in Shaanxi and southern Henan of scapulae of cattle, pigs and deer that were heated as a form of divination. Evidence of human sacrifice becomes more common in Shaanxi and the Central Plain in the late Longshan period.
Excavations in the 1950s in Shanxian, western Henan, identified a Miaodigou II phase transitional between the preceding Yangshao culture and the Henan Longshan. A minority of archaeologists have suggested that this phase, contemporaneous with the late Dawenkou culture in Shandong, should instead be assigned to the Yangshao culture, but most describe it as the early phase of the Henan Longshan; some scholars argue that the late Dawenkou culture should be considered the early phase of the Shandong Longshan culture. Miaodigou II sites are found in central and western Henan, southern Shanxi and the Wei River valley in Shaanxi; the tools and pottery found at these sites were improved from those of the preceding Yangshao culture. Agriculture was intensified, the consumption of domesticated animals increased. Similarities in ceramic styles of central Henan Miaodigou II with the late Dawenkou culture to the east and the late Qujialing culture to the south suggest trade contacts between the regions. There were expansions from middle and late Dawenkou sites toward central Henan and northern Anhui which coincides the era of maximum marine transgression.
The late period of the Longshan culture in the middle Yellow River area is contemporaneous with the classic Shandong Longshan culture. Several regional variants of the late middle Yellow River Longshan have been identified, including Wangwan III in western Henan, Hougang II in northern Henan and southern Hebei, Taosi in the Fen River basin in southern Shanxi, several clusters on the middle reaches of the Jing River and Wei River collectively known as Kexingzhuang II or the Shaanxi Longshan; as the Neolithic population in China reached its peak, hierarchies of settlements developed. In physically circumscribed locations, such as the basin of the Fen River in southern Shanxi, the Yellow River in western Henan and the coastal Rizhao plain of southeast Shandong, a few large centers developed. In more open areas, such as the rest of Shandong, the Central Plain and the Wei River basin in Shaanxi, local centers were more numerous and evenly spaced. Walls of rammed earth have been found in 20 towns in Shandong, 9 i
Gnomon
A gnomon is the part of a sundial that casts a shadow. The term is used for a variety of purposes in other fields. A painted stick dating from 2300 BC was excavated at the astronomical site of Taosi is the oldest gnomon known in China; the gnomon was used in ancient China from the second century BC onward in order determine the changes in seasons and geographical latitude. The ancient Chinese used shadow measurements for creating calendars that are mentioned in several ancient texts. According to the collection of Zhou Chinese poetic anthologies Classic of Poetry, one of the distant ancestors of King Wen of the Zhou dynasty used to measure gnomon shadow lengths to determine the orientation around the 14th century BC; the ancient Greek philosopher Anaximander is credited with introducing this Babylonian instrument to the Ancient Greeks. The ancient Greek mathematician and astronomer Oenopides used the phrase drawn gnomon-wise to describe a line drawn perpendicular to another; the term was used for an L-shaped instrument like a steel square used to draw right angles.
This shape may explain its use to describe a shape formed by cutting a smaller square from a larger one. Euclid extended the term to the plane figure formed by removing a similar parallelogram from a corner of a larger parallelogram. Indeed, the gnomon is the increment between two successive figurate numbers, including square and triangular numbers; the ancient Greek mathematician and engineer Hero of Alexandria defined a gnomon as that which, when added to an entity, makes a new entity similar to the starting entity. In this sense Theon of Smyrna used it to describe a number which added to a polygonal number produces the next one of the same type; the most common use in this sense is an odd integer when seen as a figurate number between square numbers. Perforated gnomons projecting a pinhole image of the Sun were described in the Chinese Zhoubi Suanjing writings; the location of the bright circle can be measured to tell the time of year. In Arab and European cultures its invention was much attributed to Egyptian astronomer and mathematician Ibn Yunus around 1000 AD.
Italian astronomer and cosmographer Paolo Toscanelli is associated with the 1475 placement of a bronze plate with a round hole in the dome of the Cathedral of Santa Maria del Fiore in Florence to project an image of the Sun on the cathedral's floor. With markings on the floor it tells the exact time of each midday as well as the date of the summer solstice. Italian mathematician, engineer and geographer Leonardo Ximenes reconstructed the gnomon according to his new measurements in 1756. In the Northern Hemisphere, the shadow-casting edge of a sundial gnomon is oriented so that it points due northward and is parallel to the rotational axis of Earth; that is, it is inclined to the northern horizon at an angle that equals the latitude of the sundial's location. At present, such a gnomon should thus point precisely at Polaris, as this is within 1° of the north celestial pole. On some sundials, the gnomon is vertical; these were used in former times for observing the altitude of the Sun when on the meridian.
The style is the part of the gnomon. This can change as the Sun moves. For example, the upper west edge of the gnomon might be the style in the morning and the upper east edge might be the style in the afternoon. A three-dimensional gnomon is used in CAD and computer graphics as an aid to positioning objects in the virtual world. By convention, the x-axis direction is the y-axis green and the z-axis blue. NASA astronauts used a gnomon as a photographic tool to indicate local vertical and to display a color chart when they were working on the Moon's surface; the 1985 novel Masters of Atlantis by Charles Portis is a satirical chronicle of a fictional secret society called Gnomonism. In the book The Tower at the End of the World by Brad Strickland, a giant tower and thin stairs turn out to be the gnomon of a giant sundial; the island the tower is found on is called "Gnomon Island". The Gnomon of Saint-Sulpice inside the church of Saint Sulpice in Paris, built to assist in determining the date of Easter, was fictionalized as a "Rose Line" in the novel The Da Vinci Code.
The 2017 novel Gnomon by Nick Haraway is a novel set in a high-tech surveillance state. MarsDial Gazalé, Midhat J. Gnomons, from Pharaohs to Fractals, Princeton University Press, Princeton, 1999. ISBN 0-691-00514-1. Heath, Thomas Little, A History of Greek Mathematics, Dover publications, ISBN 9780486240732. Laërtius, The Lives and Opinions of Eminent Philosophers, trans. C. D. Yonge. London: Henry G. Bohn, 1853. Mayall, R. Newton. 1994, ISBN 0-486-41146-X Waugh, Albert E. Sundials: Their Theory and Construction, Dover Publications, Inc. 1973, ISBN 0-486-22947-5. The dictionary definition of gnomon at Wiktionary Media related to Gnomons at Wikimedia Commons
King Wen of Zhou
King Wen of Zhou was count of Zhou during the late Shang dynasty in ancient China. Although it was his son Wu who conquered the Shang following the Battle of Muye, Count Wen was posthumously honored as the founder of the Zhou dynasty and titled King. A large number of the hymns of the Classic of Poetry are praises to the legacy of King Wen; some consider him the first epic hero of Chinese history. Born Ji Chang, Wen was the son of Tairen and Ji Jili, the count of a small state along the Wei River in present-day Shaanxi. Jili was betrayed and executed by the Shang king Wen Ding in the late 12th century BC, leaving the young Chang as the count of Zhou. Wen married Taisi and fathered ten sons and one daughter by her, plus at least another eight sons with concubines. At one point, King Zhou of Shang, fearing Wen's growing power, imprisoned him in Youli after he was slandered by the Marquis of Chong, his eldest son, Bo Yikao, went to King Zhou to plead for his freedom, but was executed in a rage by lingchi and made into meat cakes which were fed to his father in Youli.
However, many officials - namely and notably San Yisheng and Hong Yao - respected Wen for his honorable governance and gave King Zhou so many gifts – including gold and women – that he released Wen, bestowed him his personal weapons and invested him with the special rank of Count of the West. In retribution, Wen offered a piece of his land in Western Luo to King Zhou, who in turn allowed Wen to make one last request, he requested that the Burning Pillar punishment be abolished, so it was. Subsequently, upon returning home Wen secretly began to plot to overthrow King Zhou. In his first year as Count of the West, he settled a land dispute between the states of Yu and Rui, earning greater recognition among the nobles, it is by this point that some nobles began calling him "king". The following year, Wen found Jiang Ziya fishing in the Pan River and hired him as a military counsellor, he repelled an invasion of the Quanrong barbarians and occupied a portion of their land. The following year, he campaigned against Mixu, a state whose chief had been harassing the smaller states of Ruan and Gong, thus annexing the three of them.
The following year, he attacked Li, a puppet of Shang, the year latter he attacked E, a rebel state opposed to Shang, conquering both. The following year he attacked Chong, home of Hu, Marquis of Chong, his arch-enemy, defeated it, gaining access to the Ford of Meng through which he could cross his army to attack Shang. By he had obtained about two thirds of the whole kingdom either as direct possessions or sworn allies; that same year he moved his capital city one hundred kilometers east from Mount Qi to Feng, placing the Shang under imminent threat. The following year, the Count of the West died before he could cross the Ford to accomplish his end. Four years from this, his second son, known as King Wu, followed his footsteps and crushed the Shang at Muye, founding the Zhou dynasty; the name "Wen" means "the Cultured" or "the Civilizing" and was made into an official royal name by King Wu in honor of his father. Many of the older odes from the Classic of Poetry are hymns in praise of King Wen.
King Wen is credited with having stacked the eight trigrams in their various permutations to create the sixty-four hexagrams of the I Ching. He is said to have written the judgments which are appended to each hexagram; the most used sequence of the 64 hexagrams is attributed to him and is referred to as the King Wen sequence. In 196 BC, Han Gaozu gave King Wen the title "Greatest of All Kings". Family tree of ancient Chinese emperors Ci Hai Bian Ji Wei Yuan Hui. Shanghai Ci Shu Chu Ban She, 1979 Wu, K. C; the Chinese Heritage. Crown Publishers, 1982. ISBN 0-517-54475-X
Huaxia
Huaxia is a historical concept representing the Chinese nation and civilization. It came forth out of a self-awareness of the Han Chinese people towards their ancestral tribes, collectively known as the Huaxia. According to the Zuo zhuan, xia signified the "grandness" in the ceremonial etiquette of China, while hua was used in reference to the "beauty" in the clothing that the Chinese people wore. Huaxia refers to a confederation of tribes—living along the Yellow River—who were the ancestors of what became the Han ethnic group in China. During the Warring States, the self-awareness of the Huaxia identity developed and took hold in ancient China. Huaxia defined a civilized society, distinct and stood in contrast to what was perceived as the barbaric peoples around them. Although still used in conjunction, the Chinese characters for hua and xia are used separately as autonyms; the official Chinese names of both the People's Republic of China and the Republic of China use the term Huaxia in combination with the term Zhongguo, that is, as Zhonghua.
The PRC's official Chinese name is Zhonghua Renmin Gongheguo, while that of the ROC is Zhonghua Minguo. Today, the term Zhongguo refers to the nation itself and Zhonghua to the civilization; the term Zhongguo is confined by its association to a state, whereas Zhonghua concerns culture. The term Huaren for a Chinese person is an abbreviation of Huaxia with ren. Huaren in general is used for people of Chinese ethnicity, distinct from Zhongguoren which refers to citizens of China. Although some may use Zhongguoren to refer to the Chinese ethnicity, such usage is not accepted by some in Taiwan. In overseas Chinese communities in countries such as Singapore and Malaysia, Huaren or Huaqiao is used as they are not citizens of China. Yan Huang Zisun the "Descendants of Yan and Huang" Zhongyuan, the central regions associated with Huaxia Zhonghua
The Nine Chapters on the Mathematical Art
The Nine Chapters on the Mathematical Art is a Chinese mathematics book, composed by several generations of scholars from the 10th–2nd century BCE, its latest stage being from the 2nd century CE. This book is one of the earliest surviving mathematical texts from China, the first being Suan shu shu and Zhoubi Suanjing, it lays out an approach to mathematics that centres on finding the most general methods of solving problems, which may be contrasted with the approach common to ancient Greek mathematicians, who tended to deduce propositions from an initial set of axioms. Entries in the book take the form of a statement of a problem, followed by the statement of the solution, an explanation of the procedure that led to the solution; these were commented on by Liu Hui in the 3rd century. The full title of The Nine Chapters on the Mathematical Art appears on two bronze standard measures which are dated to 179 CE, but there is speculation that the same book existed beforehand under different titles.
Most scholars believe that Chinese mathematics and the mathematics of the ancient Mediterranean world had developed more or less independently up to the time when the Nine Chapters reached its final form. The method of chapter 7 was not found in Europe until the 13th century, the method of chapter 8 uses Gaussian elimination before Carl Friedrich Gauss. There is the mathematical proof given in the treatise for the Pythagorean theorem; the influence of The Nine Chapters assisted the development of ancient mathematics in the regions of Korea and Japan. Its influence on mathematical thought in China persisted until the Qing Dynasty era. Liu Hui wrote a detailed commentary on this book in 263, he analyses the procedures of the Nine Chapters step by step, in a manner, designed to give the reader confidence that they are reliable, although he is not concerned to provide formal proofs in the Euclidean manner. Liu's commentary is of great mathematical interest in its own right. Liu credits the earlier mathematicians Zhang Cang and Geng Shouchang with the initial arrangement and commentary on the book, yet Han Dynasty records do not indicate the names of any authors of commentary, as they are not mentioned until the 3rd century.
The Nine Chapters is an anonymous work, its origins are not clear. Until recent years, there was no substantial evidence of related mathematical writing that might have preceded it, with the exception of mathematical work by those such as Jing Fang, Liu Xin, Zhang Heng and the geometry clauses of the Mozi of the 4th century BCE; this is no longer the case. The Suàn shù shū or writings on reckoning is an ancient Chinese text on mathematics seven thousand characters in length, written on 190 bamboo strips, it was discovered together with other writings in 1983 when archaeologists opened a tomb in Hubei province. It is among the corpus of texts known as the Zhangjiashan Han bamboo texts. From documentary evidence this tomb is known to have been closed in 186 BCE, early in the Western Han dynasty. While its relationship to the Nine Chapters is still under discussion by scholars, some of its contents are paralleled there; the text of the Suàn shù shū is however much less systematic than the Nine Chapters.
The Zhoubi Suanjing, a mathematics and astronomy text, was compiled during the Han, was mentioned as a school of mathematics in and around 180 CE by Cai Yong. Contents of The Nine Chapters are. Areas of fields of various shapes, such as rectangles, triangles and circles. Liu Hui's commentary includes a method for calculation of π and the approximate value of 3.14159. 粟米 Sumi - Millet and rice. Exchange of commodities at different rates. 衰分 Cuifen - Proportional distribution. Distribution of commodities and money at proportional rates. 少廣 Shaoguang - Reducing dimensions. Finding the diameter or side of a shape given its volume or area. Division by mixed numbers. 商功 Shanggong - Figuring for construction. Volumes of solids of various shapes. 均輸 Junshu - Equitable taxation. More advanced word problems on proportion, involving work and rates. 盈不足 Yingbuzu - Excess and deficit. Linear problems solved using the principle known in the West as the rule of false position. 方程 Fangcheng - The two-sided reference. Problems of agricultural yields and the sale of animals that lead to systems of linear equations, solved by a principle similar to Gaussian elimination.
勾股 Gougu - Base and altitude. Problems involving the principle known in the West as the Pythagorean theorem. Abridged English translation: Florian Cajori: Arithmetic in Nine Sections, 1893. Abridged English translation: Lam Lay Yong: Jiu Zhang Suanshu, An Overview, Archive for History of Exact Science, 1994 Springer Verlag. A full translation and study of the Nine Chapters and Liu Hui's commentary is available in SHEN Kangshen "The Nine Chapters on the Mathematical Art" Oxford 1999. ISBN 0-19-853936-3 A French translation with detailed scholarly addenda and a critical edition of the Chinese text of both the book and its commentary is Chemla and Shuchun Guo
