text:
Chinese mathematics

Mathematics emerged independently in China by the 11th century BCE. The Chinese independently developed a real number system that includes significantly large and negative numbers, more than one numeral system (binary and decimal), algebra, geometry, number theory and trigonometry.

Since the Han dynasty, as diophantine approximation being a prominent numerical method, the Chinese made substantial progress on polynomial evaluation. Algorithms like regula falsi and expressions like continued fractions are widely used and have been well-documented ever since. They deliberately find the principal nth root of positive numbers and the roots of equations. The major texts from the period, The Nine Chapters on the Mathematical Art and the Book on Numbers and Computation gave detailed processes for solving various mathematical problems in daily life. All procedures were computed using a counting board in both texts, and they included inverse elements as well as Euclidean divisions. The texts provide procedures similar to that of Gaussian elimination and Horner's method for linear algebra. The achievement of Chinese algebra reached a zenith in the 13th century during the Yuan dynasty with the development of tian yuan shu.

As a result of obvious linguistic and geographic barriers, as well as content, Chinese mathematics and the mathematics of the ancient Mediterranean world are presumed to have developed more or less independently up to the time when The Nine Chapters on the Mathematical Art reached its final form, while the Book on Numbers and Computation and Huainanzi are roughly contemporary with classical Greek mathematics. Some exchange of ideas across Asia through known cultural exchanges from at least Roman times is likely. Frequently, elements of the mathematics of early societies correspond to rudimentary results found later in branches of modern mathematics such as geometry or number theory. The Pythagorean theorem for example, has been attested to the time of the Duke of Zhou. Knowledge of Pascal's triangle has also been shown to have existed in China centuries before Pascal, such as the Song-era polymath Shen Kuo.

Pre-imperial era
Shang dynasty (1600–1050 BC). One of the oldest surviving mathematical works is the I Ching, which greatly influenced written literature during the Zhou dynasty (1050–256 BC). For mathematics, the book included a sophisticated use of hexagrams. Leibniz pointed out, the I Ching (Yi Jing) contained elements of binary numbers.

Since the Shang period, the Chinese had already fully developed a decimal system. Since early times, Chinese understood basic arithmetic (which dominated far eastern history), algebra, equations, and negative numbers with counting rods. Although the Chinese were more focused on arithmetic and advanced algebra for astronomical uses, they were also the first to develop negative numbers, algebraic geometry, and the usage of decimals.

Math was one of the Six Arts students were required to master during the Zhou dynasty (1122–256 BCE). Learning them all perfectly was required to be a perfect gentleman, comparable to the concept of a "renaissance man". Six Arts have their roots in the Confucian philosophy.

The oldest existent work on geometry in China comes from the philosophical Mohist canon c. 330 BCE, compiled by the followers of Mozi (470–390 BCE). The Mo Jing described various aspects of many fields associated with physical science, and provided a small wealth of information on mathematics as well. It provided an 'atomic' definition of the geometric point, stating that a line is separated into parts, and the part which has no remaining parts (i.e. cannot be divided into smaller parts) and thus forms the extreme end of a line is a point. Much like Euclid's first and third definitions and Plato's 'beginning of a line', the Mo Jing stated that "a point may stand at the end (of a line) or at its beginning like a head-presentation in childbirth. (As to its invisibility) there is nothing similar to it." Similar to the atomists of Democritus, the Mo Jing stated that a point is the smallest unit, and cannot be cut in half, since 'nothing' cannot be halved." It stated that two lines of equal length will always finish at the same place," while providing definitions for the comparison of lengths and for parallels," along with principles of space and bounded space. It also described the fact that planes without the quality of thickness cannot be piled up since they cannot mutually touch. The book provided word recognition for circumference, diameter, and radius, along with the definition of volume.

The history of mathematical development lacks some evidence. There are still debates about certain mathematical classics. For example, the Zhoubi Suanjing dates around 1200–1000 BC, yet many scholars believed it was written between 300 and 250 BCE. The Zhoubi Suanjing contains an in-depth proof of the Gougu Theorem, a special case of the Pythagorean theorem) but focuses more on astronomical calculations. However, the recent archaeological discovery of the Tsinghua Bamboo Slips, dated c. 305 BCE, has revealed some aspects of pre-Qin mathematics, such as the first known decimal multiplication table.

The abacus was first mentioned in the second century BC, alongside 'calculation with rods' (suan zi) in which small bamboo sticks are placed in successive squares of a checkerboard.

Qin dynasty
Not much is known about Qin dynasty mathematics, or before, due to the burning of books and burying of scholars, circa 213–210 BC. Knowledge of this period can be determined from civil projects and historical evidence. The Qin dynasty created a standard system of weights. Civil projects of the Qin dynasty were significant feats of human engineering. Emperor Qin Shi Huang ordered many men to build large, life-sized statues for the palace tomb along with other temples and shrines, and the shape of the tomb was designed with geometric skills of architecture. It is certain that one of the greatest feats of human history, the Great Wall of China, required many mathematical techniques. All Qin dynasty buildings and grand projects used advanced computation formulas for volume, area and proportion.

Qin bamboo cash purchased at the antiquarian market of Hong Kong by the Yuelu Academy, according to the preliminary reports, contains the earliest epigraphic sample of a mathematical treatise.

Han dynasty
In the Han dynasty, numbers were developed into a place value decimal system and used on a counting board with a set of counting rods called rod calculus, consisting of only nine symbols with a blank space on the counting board representing zero. Negative numbers and fractions were also incorporated into solutions of the great mathematical texts of the period. The mathematical texts of the time, the Book on Numbers and Computation and Jiuzhang suanshu solved basic arithmetic problems such as addition, subtraction, multiplication and division. Furthermore, they gave the processes for square and cubed root extraction, which eventually was applied to solving quadratic equations up to the third order. Both texts also made substantial progress in Linear Algebra, namely solving systems of equations with multiple unknowns. The value of pi is taken to be equal to three in both texts. However, the mathematicians Liu Xin (d. 23) and Zhang Heng (78–139) gave more accurate approximations for pi than Chinese of previous centuries had used. Mathematics was developed to solve practical problems in the time such as division of land or problems related to division of payment. The Chinese did not focus on theoretical proofs based on geometry or algebra in the modern sense of proving equations to find area or volume. The Book of Computations and The Nine Chapters on the Mathematical Art provide numerous practical examples that would be used in daily life.

Book on Numbers and Computation
The Book on Numbers and Computation is approximately seven thousand characters in length, written on 190 bamboo strips. It was discovered together with other writings in 1984 when archaeologists opened a tomb at Zhangjiashan in Hubei province. From documentary evidence this tomb is known to have been closed in 186 BC, early in the Western Han dynasty. While its relationship to the Nine Chapters is still under discussion by scholars, some of its contents are clearly paralleled there. The text of the Suan shu shu is however much less systematic than the Nine Chapters, and appears to consist of a number of more or less independent short sections of text drawn from a number of sources.

The Book of Computations contains many perquisites to problems that would be expanded upon in The Nine Chapters on the Mathematical Art. An example of the elementary mathematics in the Suàn shù shū, the square root is approximated by using false position method which says to "combine the excess and deficiency as the divisor; (taking) the deficiency numerator multiplied by the excess denominator and the excess numerator times the deficiency denominator, combine them as the dividend." Furthermore, The Book of Computations solves systems of two equations and two unknowns using the same false position method.

The Nine Chapters on the Mathematical Art
The Nine Chapters on the Mathematical Art dates archeologically to 179 CE, though it is traditionally dated to 1000 BCE, but it was written perhaps as early as 300–200 BCE. Although the author(s) are unknown, they made a major contribution in the eastern world. Problems are set up with questions immediately followed by answers and procedure. There are no formal mathematical proofs within the text, just a step-by-step procedure. The commentary of Liu Hui provided geometrical and algebraic proofs to the problems given within the text.

The Nine Chapters on the Mathematical Art was one of the most influential of all Chinese mathematical books and it is composed of 246 problems. It was later incorporated into The Ten Computational Canons, which became the core of mathematical education in later centuries. This book includes 246 problems on surveying, agriculture, partnerships, engineering, taxation, calculation, the solution of equations, and the properties of right triangles. The Nine Chapters made significant additions to solving quadratic equations in a way similar to Horner's method. It also made advanced contributions to fangcheng, or what is now known as linear algebra. Chapter seven solves system of linear equations with two unknowns using the false position method, similar to The Book of Computations. Chapter eight deals with solving determinate and indeterminate simultaneous linear equations using positive and negative numbers, with one problem dealing with solving four equations in five unknowns. The Nine Chapters solves systems of equations using methods similar to the modern Gaussian elimination and back substitution.

The version of The Nine Chapters that has served as the foundation for modern renditions was a result of the efforts of the scholar Dai Zhen. Transcribing the problems directly from Yongle Encyclopedia, he then proceeded to make revisions to the original text, along with the inclusion his own notes explaining his reasoning behind the alterations. His finished work would be first published in 1774, but a new revision would be published in 1776 to correct various errors as well as include a version of The Nine Chapters from the Southern Song that contained the commentaries of Lui Hui and Li Chunfeng. The final version of Dai Zhen's work would come in 1777, titled Ripple Pavilion, with this final rendition being widely distributed and coming to serve as the standard for modern versions of The Nine Chapters. However, this version has come under scrutiny from Guo Shuchen, alleging that the edited version still contains numerous errors and that not all of the original amendments were done by Dai Zhen himself.

Calculation of pi
Problems in The Nine Chapters on the Mathematical Art take pi to be equal to three in calculating problems related to circles and spheres, such as spherical surface area. There is no explicit formula given within the text for the calculation of pi to be three, but it is used throughout the problems of both The Nine Chapters on the Mathematical Art and the Artificer's Record, which was produced in the same time period. Historians believe that this figure of pi was calculated using the 3:1 relationship between the circumference and diameter of a circle. Some Han mathematicians attempted to improve this number, such as Liu Xin, who is believed to have estimated pi to be 3.154. Later, Liu Hui attempted to improve the calculation by calculating pi to be 3.141024. Liu calculated this number by using polygons inside a hexagon as a lower limit compared to a circle. Zu Chongzhi later discovered the calculation of pi to be 3.1415926 < π < 3.1415927 by using polygons with 24,576 sides. This calculation would be discovered in Europe during the 16th century.

There is no explicit method or record of how he calculated this estimate.

Division and root extraction
Basic arithmetic processes such as addition, subtraction, multiplication and division were present before the Han dynasty. The Nine Chapters on the Mathematical Art take these basic operations for granted and simply instruct the reader to perform them. Han mathematicians calculated square and cube roots in a similar manner as division, and problems on division and root extraction both occur in Chapter Four of The Nine Chapters on the Mathematical Art. Calculating the square and cube roots of numbers is done through successive approximation, the same as division, and often uses similar terms such as dividend (shi) and divisor (fa) throughout the process. This process of successive approximation was then extended to solving quadratics of the second and third order, such as $$x^2+a=b$$, using a method similar to Horner's method. The method was not extended to solve quadratics of the nth order during the Han dynasty; however, this method was eventually used to solve these equations.

Linear algebra
The Book of Computations is the first known text to solve systems of equations with two unknowns. There are a total of three sets of problems within The Book of Computations involving solving systems of equations with the false position method, which again are put into practical terms. Chapter Seven of The Nine Chapters on the Mathematical Art also deals with solving a system of two equations with two unknowns with the false position method. To solve for the greater of the two unknowns, the false position method instructs the reader to cross-multiply the minor terms or zi (which are the values given for the excess and deficit) with the major terms mu. To solve for the lesser of the two unknowns, simply add the minor terms together.

Chapter Eight of The Nine Chapters on the Mathematical Art deals with solving infinite equations with infinite unknowns. This process is referred to as the "fangcheng procedure" throughout the chapter. Many historians chose to leave the term fangcheng untranslated due to conflicting evidence of what the term means. Many historians translate the word to linear algebra today. In this chapter, the process of Gaussian elimination and back-substitution are used to solve systems of equations with many unknowns. Problems were done on a counting board and included the use of negative numbers as well as fractions. The counting board was effectively a matrix, where the top line is the first variable of one equation and the bottom was the last.

Liu Hui's commentary on The Nine Chapters on the Mathematical Art
Liu Hui's commentary on The Nine Chapters on the Mathematical Art is the earliest edition of the original text available. Hui is believed by most to be a mathematician shortly after the Han dynasty. Within his commentary, Hui qualified and proved some of the problems from either an algebraic or geometrical standpoint. For instance, throughout The Nine Chapters on the Mathematical Art, the value of pi is taken to be equal to three in problems regarding circles or spheres. In his commentary, Liu Hui finds a more accurate estimation of pi using the method of exhaustion. The method involves creating successive polygons within a circle so that eventually the area of a higher-order polygon will be identical to that of the circle. From this method, Liu Hui asserted that the value of pi is about 3.14. Liu Hui also presented a geometric proof of square and cubed root extraction similar to the Greek method, which involved cutting a square or cube in any line or section and determining the square root through symmetry of the remaining rectangles.

Three Kingdoms, Jin, and Sixteen Kingdoms
In the third century Liu Hui wrote his commentary on the Nine Chapters and also wrote Haidao Suanjing which dealt with using Pythagorean theorem (already known by the 9 chapters), and triple, quadruple triangulation for surveying; his accomplishment in the mathematical surveying exceeded those accomplished in the west by a millennium. He was the first Chinese mathematician to calculate π=3.1416 with his π algorithm. He discovered the usage of Cavalieri's principle to find an accurate formula for the volume of a cylinder, and also developed elements of the infinitesimal calculus during the 3rd century CE. In the fourth century, another influential mathematician named Zu Chongzhi, introduced the Da Ming Li. This calendar was specifically calculated to predict many cosmological cycles that will occur in a period of time. Very little is really known about his life. Today, the only sources are found in Book of Sui, we now know that Zu Chongzhi was one of the generations of mathematicians. He used Liu Hui's pi-algorithm applied to a 12288-gon and obtained a value of pi to 7 accurate decimal places (between 3.1415926 and 3.1415927), which would remain the most accurate approximation of π available for the next 900 years. He also applied He Chengtian's interpolation for approximating irrational number with fraction in his astronomy and mathematical works, he obtained $$\tfrac{355}{113}$$ as a good fraction approximate for pi; Yoshio Mikami commented that neither the Greeks, nor the Hindus nor Arabs knew about this fraction approximation to pi, not until the Dutch mathematician Adrian Anthoniszoom rediscovered it in 1585, "the Chinese had therefore been possessed of this the most extraordinary of all fractional values over a whole millennium earlier than Europe".

Along with his son, Zu Geng, Zu Chongzhi applied the Cavalieri's principle to find an accurate solution for calculating the volume of the sphere. Besides containing formulas for the volume of the sphere, his book also included formulas of cubic equations and the accurate value of pi. His work, Zhui Shu was discarded out of the syllabus of mathematics during the Song dynasty and lost. Many believed that Zhui Shu contains the formulas and methods for linear, matrix algebra, algorithm for calculating the value of π, formula for the volume of the sphere. The text should also associate with his astronomical methods of interpolation, which would contain knowledge, similar to our modern mathematics.

A mathematical manual called Sunzi mathematical classic dated between 200 and 400 CE contained the most detailed step by step description of multiplication and division algorithm with counting rods. Intriguingly, Sunzi may have influenced the development of place-value systems and place-value systems and the associated Galley division in the West. European sources learned place-value techniques in the 13th century, from a Latin translation an early-9th-century work by Al-Khwarizmi. Khwarizmi's presentation is almost identical to the division algorithm in Sunzi, even regarding stylistic matters (for example, using blank spaces to represent trailing zeros); the similarity suggests that the results may not have been an independent discovery. Islamic commentators on Al-Khwarizmi's work believed that it primarily summarized Hindu knowledge; Al-Khwarizmi's failure to cite his sources makes it difficult to determine whether those sources had in turn learned the procedure from China.

In the fifth century the manual called "Zhang Qiujian suanjing" discussed linear and quadratic equations. By this point the Chinese had the concept of negative numbers.

Tang dynasty
By the Tang dynasty study of mathematics was fairly standard in the great schools. The Ten Computational Canons was a collection of ten Chinese mathematical works, compiled by early Tang dynasty mathematician Li Chunfeng (李淳風 602–670), as the official mathematical texts for imperial examinations in mathematics. The Sui dynasty and Tang dynasty ran the "School of Computations".

Wang Xiaotong was a great mathematician in the beginning of the Tang dynasty, and he wrote a book: Jigu Suanjing (Continuation of Ancient Mathematics), where numerical solutions which general cubic equations appear for the first time.

The Tibetans obtained their first knowledge of mathematics (arithmetic) from China during the reign of Nam-ri srong btsan, who died in 630.

The table of sines by the Indian mathematician, Aryabhata, were translated into the Chinese mathematical book of the Kaiyuan Zhanjing, compiled in 718 AD during the Tang dynasty. Although the Chinese excelled in other fields of mathematics such as solid geometry, binomial theorem, and complex algebraic formulas, early forms of trigonometry were not as widely appreciated as in the contemporary Indian and Islamic mathematics.

Yi Xing, the mathematician and Buddhist monk was credited for calculating the tangent table. Instead, the early Chinese used an empirical substitute known as chong cha, while practical use of plane trigonometry in using the sine, the tangent, and the secant were known. Yi Xing was famed for his genius, and was known to have calculated the number of possible positions on a go board game (though without a symbol for zero he had difficulties expressing the number).

Song and Yuan dynasties
Northern Song dynasty mathematician Jia Xian developed an additive multiplicative method for extraction of square root and cubic root which implemented the "Horner" rule. Four outstanding mathematicians arose during the Song dynasty and Yuan dynasty, particularly in the twelfth and thirteenth centuries: Yang Hui, Qin Jiushao, Li Zhi (Li Ye), and Zhu Shijie. Yang Hui, Qin Jiushao, Zhu Shijie all used the Horner-Ruffini method six hundred years earlier to solve certain types of simultaneous equations, roots, quadratic, cubic, and quartic equations. Yang Hui was also the first person in history to discover and prove "Pascal's Triangle", along with its binomial proof (although the earliest mention of the Pascal's triangle in China exists before the eleventh century AD). Li Zhi on the other hand, investigated on a form of algebraic geometry based on tiān yuán shù. His book; Ceyuan haijing revolutionized the idea of inscribing a circle into triangles, by turning this geometry problem by algebra instead of the traditional method of using Pythagorean theorem. Guo Shoujing of this era also worked on spherical trigonometry for precise astronomical calculations. At this point of mathematical history, a lot of modern western mathematics were already discovered by Chinese mathematicians. Things grew quiet for a time until the thirteenth century Renaissance of Chinese math. This saw Chinese mathematicians solving equations with methods Europe would not know until the eighteenth century. The high point of this era came with Zhu Shijie's two books Suanxue qimeng and the Jade Mirror of the Four Unknowns. In one case he reportedly gave a method equivalent to Gauss's pivotal condensation.

Qin Jiushao (c. 1202 – 1261) was the first to introduce the zero symbol into Chinese mathematics." Before this innovation, blank spaces were used instead of zeros in the system of counting rods. One of the most important contribution of Qin Jiushao was his method of solving high order numerical equations. Referring to Qin's solution of a 4th order equation, Yoshio Mikami put it: "Who can deny the fact of Horner's illustrious process being used in China at least nearly six long centuries earlier than in Europe?" Qin also solved a 10th order equation.

Pascal's triangle was first illustrated in China by Yang Hui in his book Xiangjie Jiuzhang Suanfa (詳解九章算法), although it was described earlier around 1100 by Jia Xian. Although the Introduction to Computational Studies (算學啓蒙) written by Zhu Shijie (fl. 13th century) in 1299 contained nothing new in Chinese algebra, it had a great impact on the development of Japanese mathematics.

Ceyuan haijing
Ceyuan haijing, or Sea-Mirror of the Circle Measurements, is a collection of 692 formula and 170 problems related to inscribed circle in a triangle, written by Li Zhi (or Li Ye) (1192–1272 AD). He used Tian yuan shu to convert intricated geometry problems into pure algebra problems. He then used fan fa, or Horner's method, to solve equations of degree as high as six, although he did not describe his method of solving equations. "Li Chih (or Li Yeh, 1192–1279), a mathematician of Peking who was offered a government post by Khublai Khan in 1206, but politely found an excuse to decline it. His Ts'e-yuan hai-ching (Sea-Mirror of the Circle Measurements) includes 170 problems dealing with[...]some of the problems leading to polynomial equations of sixth degree. Although he did not describe his method of solution of equations, it appears that it was not very different from that used by Chu Shih-chieh and Horner. Others who used the Horner method were Ch'in Chiu-shao (ca. 1202 – ca.1261) and Yang Hui (fl. ca. 1261–1275).

Jade Mirror of the Four Unknowns
The Jade Mirror of the Four Unknowns was written by Zhu Shijie in 1303 AD and marks the peak in the development of Chinese algebra. The four elements, called heaven, earth, man and matter, represented the four unknown quantities in his algebraic equations. It deals with simultaneous equations and with equations of degrees as high as fourteen. The author uses the method of fan fa, today called Horner's method, to solve these equations.

There are many summation series equations given without proof in the Mirror. A few of the summation series are:

$$1^2 + 2^2 + 3^2 + \cdots + n^2 = {n(n + 1)(2n + 1)\over 3!}$$ $$1 + 8 + 30 + 80 + \cdots + {n^2(n + 1)(n + 2)\over 3!} = {n(n + 1)(n + 2)(n + 3)(4n + 1)\over 5!}$$

Mathematical Treatise in Nine Sections
The Mathematical Treatise in Nine Sections, was written by the wealthy governor and minister Ch'in Chiu-shao (c. 1202 – c. 1261) and with the invention of a method of solving simultaneous congruences, it marks the high point in Chinese indeterminate analysis.

Magic squares and magic circles
The earliest known magic squares of order greater than three are attributed to Yang Hui (fl. ca. 1261–1275), who worked with magic squares of order as high as ten. "The same "Horner" device was used by Yang Hui, about whose life almost nothing is known and who work has survived only in part. Among his contributions that are extant are the earliest Chinese magic squares of order greater than three, including two each of orders four through eight and one each of orders nine and ten." He also worked with magic circle.

Trigonometry
The embryonic state of trigonometry in China slowly began to change and advance during the Song dynasty (960–1279), where Chinese mathematicians began to express greater emphasis for the need of spherical trigonometry in calendar science and astronomical calculations. The polymath and official Shen Kuo (1031–1095) used trigonometric functions to solve mathematical problems of chords and arcs. Joseph W. Dauben notes that in Shen's "technique of intersecting circles" formula, he creates an approximation of the arc of a circle s by s = c + 2v2/d, where d is the diameter, v is the versine, c is the length of the chord c subtending the arc. Sal Restivo writes that Shen's work in the lengths of arcs of circles provided the basis for spherical trigonometry developed in the 13th century by the mathematician and astronomer Guo Shoujing (1231–1316). Gauchet and Needham state Guo used spherical trigonometry in his calculations to improve the Chinese calendar and astronomy. Along with a later 17th-century Chinese illustration of Guo's mathematical proofs, Needham writes:

"Guo used a quadrangular spherical pyramid, the basal quadrilateral of which consisted of one equatorial and one ecliptic arc, together with two meridian arcs, one of which passed through the summer solstice point...By such methods he was able to obtain the du lü (degrees of equator corresponding to degrees of ecliptic), the ji cha (values of chords for given ecliptic arcs), and the cha lü (difference between chords of arcs differing by 1 degree)."

Despite the achievements of Shen and Guo's work in trigonometry, another substantial work in Chinese trigonometry would not be published again until 1607, with the dual publication of Euclid's Elements by Chinese official and astronomer Xu Guangqi (1562–1633) and the Italian Jesuit Matteo Ricci (1552–1610).

Ming dynasty
After the overthrow of the Yuan dynasty, China became suspicious of Mongol-favored knowledge. The court turned away from math and physics in favor of botany and pharmacology. Imperial examinations included little mathematics, and what little they included ignored recent developments. Martzloff writes: "At the end of the 16th century, Chinese autochthonous mathematics known by the Chinese themselves amounted to almost nothing, little more than calculation on the abacus, whilst in the 17th and 18th centuries nothing could be paralleled with the revolutionary progress in the theatre of European science. Moreover, at this same period, no one could report what had taken place in the more distant past, since the Chinese themselves only had a fragmentary knowledge of that. One should not forget that, in China itself, autochthonous mathematics was not rediscovered on a large scale prior to the last quarter of the 18th century." Correspondingly, scholars paid less attention to mathematics; preeminent mathematicians such as Gu Yingxiang and Tang Shunzhi appear to have been ignorant of the 'increase multiply' method. Without oral interlocutors to explicate them, the texts rapidly became incomprehensible; worse yet, most problems could be solved with more elementary methods. To the average scholar, then, tianyuan seemed numerology. When Wu Jing collated all the mathematical works of previous dynasties into The Annotations of Calculations in the Nine Chapters on the Mathematical Art, he omitted Tian yuan shu and the increase multiply method. Instead, mathematical progress became focused on computational tools. In 15 century, abacus came into its suan pan form. Easy to use and carry, both fast and accurate, it rapidly overtook rod calculus as the preferred form of computation. Zhusuan, the arithmetic calculation through abacus, inspired multiple new works. Suanfa Tongzong (General Source of Computational Methods), a 17-volume work published in 1592 by Cheng Dawei, remained in use for over 300 years. Zhu Zaiyu, Prince of Zheng used 81 position abacus to calculate the square root and cubic root of 2 to 25 figure accuracy, a precision that enabled his development of the equal-temperament system.

In the late 16th century, Matteo Ricci decided to published Western scientific works in order to establish a position at the Imperial Court. With the assistance of Xu Guangqi, he was able to translate Euclid's Elements using the same techniques used to teach classical Buddhist texts. Other missionaries followed in his example, translating Western works on special functions (trigonometry and logarithms) that were neglected in the Chinese tradition. However, contemporary scholars found the emphasis on proofs — as opposed to solved problems — baffling, and most continued to work from classical texts alone.

Qing dynasty
Under the Kangxi Emperor, who learned Western mathematics from the Jesuits and was open to outside knowledge and ideas, Chinese mathematics enjoyed a brief period of official support. At Kangxi's direction, Mei Goucheng and three other outstanding mathematicians compiled a 53-volume work titled Shuli Jingyun ("The Essence of Mathematical Study") which was printed in 1723, and gave a systematic introduction to western mathematical knowledge. At the same time, Mei Goucheng also developed to Meishi Congshu Jiyang [The Compiled works of Mei]. Meishi Congshu Jiyang was an encyclopedic summary of nearly all schools of Chinese mathematics at that time, but it also included the cross-cultural works of Mei Wending (1633–1721), Goucheng's grandfather. The enterprise sought to alleviate the difficulties for Chinese mathematicians working on Western mathematics in tracking down citations.

In 1773, the Qianlong Emperor decided to compile the Complete Library of the Four Treasuries (or Siku Quanshu). Dai Zhen (1724–1777) selected and proofread The Nine Chapters on the Mathematical Art from Yongle Encyclopedia and several other mathematical works from Han and Tang dynasties. The long-missing mathematical works from Song and Yuan dynasties such as Si-yüan yü-jian and Ceyuan haijing were also found and printed, which directly led to a wave of new research. The most annotated works were Jiuzhang suanshu xicaotushuo (The Illustrations of Calculation Process for The Nine Chapters on the Mathematical Art ) contributed by Li Huang and Siyuan yujian xicao (The Detailed Explanation of Si-yuan yu-jian) by Luo Shilin.

Western influences
In 1840, the First Opium War forced China to open its door and look at the outside world, which also led to an influx of western mathematical studies at a rate unrivaled in the previous centuries. In 1852, the Chinese mathematician Li Shanlan and the British missionary Alexander Wylie co-translated the later nine volumes of Elements and 13 volumes on Algebra. With the assistance of Joseph Edkins, more works on astronomy and calculus soon followed. Chinese scholars were initially unsure whether to approach the new works: was study of Western knowledge a form of submission to foreign invaders? But by the end of the century, it became clear that China could only begin to recover its sovereignty by incorporating Western works. Chinese scholars, taught in Western missionary schools, from (translated) Western texts, rapidly lost touch with the indigenous tradition. Those who were self-trained or in traditionalist circles nevertheless continued to work within the traditional framework of algorithmic mathematics without resorting to Western symbolism. Yet, as Martzloff notes, "from 1911 onwards, solely Western mathematics has been practised in China."

In modern China
Chinese mathematics experienced a great surge of revival following the establishment of a modern Chinese republic in 1912. Ever since then, modern Chinese mathematicians have made numerous achievements in various mathematical fields.

Some famous modern ethnic Chinese mathematicians include:

 * Shiing-Shen Chern was widely regarded as a leader in geometry and one of the greatest mathematicians of the 20th century and was awarded the Wolf Prize for his contributions to mathematics.
 * Ky Fan made contributions to fixed point theory, in addition to influencing nonlinear functional analysis, which have found wide application in mathematical economics and game theory, potential theory, calculus of variations, and differential equations.
 * Shing-Tung Yau, a Fields Medal laureate, has influenced both physics and mathematics, and he has been active at the interface between geometry and theoretical physics and subsequently awarded the for his contributions.
 * Terence Tao, a Fields Medal laureate and child prodigy of Chinese heritage, was the youngest participant in the history of the International Mathematical Olympiad at the age of 10, winning a bronze, silver, and gold medal. He remains the youngest winner of each of the three medals in the Olympiad's history.
 * Yitang Zhang, a number theorist who established the first finite bound on gaps between prime numbers.
 * Chen Jingrun, a number theorist who proved that every sufficiently large even number can be written as the sum of either two primes, or a prime and a semiprime, which is now called Chen's theorem. His work was important for research of Goldbach's conjecture.

People's Republic of China
In 1949, at the beginning of the founding of the People's Republic of China, the government paid great attention to the cause of science although the country was in a predicament of lack of funds. The Chinese Academy of Sciences was established in November 1949. The Institute of Mathematics was formally established in July 1952. Then, the Chinese Mathematical Society and its founding journals restored and added other special journals. In the 18 years after 1949, the number of published papers accounted for more than three times the total number of articles before 1949. Many of them not only filled the gaps in China's past, but also reached the world's advanced level.

During the chaos of the Cultural Revolution, the sciences declined. In the field of mathematics, in addition to Chen Jingrun, Hua Luogeng, Zhang Guanghou and other mathematicians struggling to continue their work. After the catastrophe, with the publication of Guo Moruo's literary "Spring of Science", Chinese sciences and mathematics experienced a revival. In 1977, a new mathematical development plan was formulated in Beijing, the work of the mathematics society was resumed, the journal was re-published, the academic journal was published, the mathematics education was strengthened, and basic theoretical research was strengthened.

An important mathematical achievement of the Chinese mathematician in the direction of the power system is how Xia Zhihong proved the Painleve conjecture in 1988. When there are some initial states of N celestial bodies, one of the celestial bodies ran to infinity or speed in a limited time. Infinity is reached, that is, there are non-collision singularities. The Painleve conjecture is an important conjecture in the field of power systems proposed in 1895. A very important recent development for the 4-body problem is that Xue Jinxin and Dolgopyat proved a non-collision singularity in a simplified version of the 4-body system around 2013.

In addition, in 2007, Shen Weixiao and Kozlovski, Van-Strien proved the Real Fatou conjecture: Real hyperbolic polynomials are dense in the space of real polynomials with fixed degree. This conjecture can be traced back to Fatou in the 1920s, and later Smale posed it in the 1960s. The proof of Real Fatou conjecture is one of the most important developments in conformal dynamics in the past decade.

IMO performance
In comparison to other participating countries at the International Mathematical Olympiad, China has highest team scores and has won the all-members-gold IMO with a full team the most number of times.

In education
The first reference to a book being used in learning mathematics in China is dated to the second century CE (Hou Hanshu: 24, 862; 35,1207). We are told that Ma Xu, who is a youth c. 110, and Zheng Xuan (127–200) both studied the Nine Chapters on Mathematical procedures. Christopher Cullen claims that mathematics, in a manner akin to medicine, was taught orally. The stylistics of the Suàn shù shū from Zhangjiashan suggest that the text was assembled from various sources and then underwent codification.

title: Chinese mathematics


text:
Tsanko Dyustabanov

Tsanko Hristov Dyustabanov (Цанко Христов Дюстабанов; (May 13, 1844 – June 15, 1876) was a Bulgarian revolutionary and participant in the April uprising of 1876.

Dyustabanov was born in Gabrovo in today's Bulgaria, which was then part of the Ottoman Empire. He attended the Gabrovo School and was fluent in French and Turkish, he later studied at Robert College in Istanbul in 1872-1873.

Though not a supporter of the revolutionary campaign in the struggle for national liberation, Dyustabanov gradually became active in the social and political life of Gabrovo. In 1875, he was elected trustee of the school and member of the District court. As such he organized a petition to the Ottoman government with demands such as the recognition of the Bulgarian language as a second official language in the empire alongside Turkish.

Dyustabanov joined the local revolutionary committee and assisted the preparation of the April Uprising of 1876. He led a cheta (detachment) when the uprising broke out and fought with Ottoman posses in the regions of Batoshevo, Kravenik and Novo Selo. He was seriously wounded and arrested. Dyustabanov was sentenced to death and hanged in Veliko Tarnovo June 15, 1876.

license: Creative Commons - Attribution Share-Alike - https://creativecommons.org/licenses/by-sa/4.0/

title: Tsanko Dyustabanov


text: User talk:130.13.153.39

title: User talk:130.13.153.39


text:
Cúscraid

Cúscraid (Cúscraid Mend Macha; var. Cumscraid ) ( pronunciation guides: /'ku:skrid m'eN 'maxa / /cŏŏs'crĭ/  /KOOS-kridh/ (Paddy Brown) ) known by the epithet Mend Macha (the "stammerer" or "inarticulate one" of Macha), is a son of Conchobar mac Nessa in the Ulster Cycle of Irish mythology.

When he first took arms he led a foray against Connacht. He was met on the border by the Connacht hero Cet mac Mágach, who wounded him in the throat (or tip of the tongue) with a spear, giving him his speech impediment.

The three most popular heroes with the women of Ulster were Cúscraid, Cúchulainn and Conall Cernach. The women imitated the peculiarity of the hero they loved the most: Cúscraid's fans stammered, Conall's crooked their necks, and Cúchulainn's squinted one eye in imitation of his warp spasm.

After Conchobar's death, the Ulstermen invited his eldest son Cormac Cond Longas to succeed him as king of Ulster, but Cormac was killed before he could take the throne. It was then offered to Conall Cernach, who refused, recommending his foster-son Cúscraid instead, and Cúscraid became king.

title: Cúscraid


text:
Talk:Wechsler Adult Intelligence Scale

Wechsler Adult Intelligence Scale—Fourth Edition (WAIS–IV) by David Wechsler, Statistics Solutions
Used as a general test the intelligence, the Wechsler Adult Intelligence Scale –Fourth Edition (WAIS-IV) was developed to assess cognitive ability for adults. This instruments aids in examining the relationship between intellectual functional and memory. A common purpose for the WAIS is for educational planning and placement with older adolescents and adults.

The test includes 11 subtests with various types of format. Approximately 60 to 90 minutes is required for completion.

Reliability and Validity
The Wechsler Adult Intelligence is a well-established scale and it has fairly high consistency. Over a two to twelve week time period, the test-retest reliabilities ranged from 0.70 (7 subscales) to 0.90 (2 subscales). Inter-scorer coefficients were very high, all being above 0.90. According to the test manual, the instrument targets three areas: psychoeducational disability, neuropsychiatric and organic dysfunction, and giftedness. The WAIS correlated highly with the Stanford-Binet IV test (0.88) and had high concordance with various measures: memory, language, dexterity, motor speed, attention, and cognitive ability.

Obtaining the WAIS-IV
Pearson Assessments

Administration, Analysis and Reporting
Statistics Solutions consists of a team of professional methodologists and statisticians that can assist the student or professional researcher in administering the survey instrument, collecting the data, conducting the analyses and explaining the results.

Dissertations Using the Wechsler Adult Intelligence Scale
Below is a list of dissertations that use the WAIS-IV. The full version of these dissertations can be found using ProQuest.

Hershberger, K. A. (1997). The relationship between conceptually similar subtests of the wechsler adult intelligence scale-revised and the career ability placement survey with a vocational rehabilitation sample. University of Cincinnati.

Meyer, M. P. (2000). Use of the wechsler abbreviated scale of intelligence in a vocational rehabilitation sample. University of Cincinnati.

New column for table in the "Index scores and scales" section
Any objection to duplicating the time info from the "Description" column into a new column vith values: "untimed", "timed", "time-limited" (or abbreviations such as U/T/TL with a legend) for ease of reference? If you think it's worth adding, would you want color backgrounds in addition to the text (and if so, which colors), or text only? If no one objects, I plan to do it whenever I think of it again or 2 months after the first reply, whichever comes first. The Crab Who Played With The Sea (talk) 14:25, 28 November 2021 (UTC)

Wiki Education assignment: PSYC 115 General Psychology
— Assignment last updated by RealSpill27 (talk) 19:11, 29 September 2023 (UTC)

Contributing to WAIS-III and WAIS-IV
We will use the Test Review source on the Fourth edition of the intelligence scale to add citations and additional information to the paragraph in the article that covers that edition. For example, a lot of the information in this section had no citations to it so if the information already in the article matches information from the source we will add a citation in those spots.

We plan on adding specific information to the WAIS-III section about how education and background can affect the scores of specific individuals. We also plan on adding some citations to this section because it does not include a lot of them. We just added one sentence citing some new major contributors to WAIS-III.

--Chillykangaroo06 (talk) 20:43, 20 November 2023 (UTC)

title: Talk:Wechsler Adult Intelligence Scale


text:
Charles-Louis Hanon

Charles-Louis Hanon (2 July 1819 – 19 March 1900) was a French piano pedagogue and composer. He is best known for his work The Virtuoso Pianist in 60 Exercises, which is still used today for modern piano teaching, but over the years the method has also faced criticisms. He was born in Renescure, France in 1819, and died in Boulogne-sur-Mer in 1900.

Biography
Charles-Louis Hanon was born in northern France in the village of Renescure on July 2, 1819. Trained as an organist by a local teacher, it is not known if he received more advanced musical education. At age 27, he moved a short distance west from Renescure to Boulogne-sur-Mer where he lived with his brother François who was also a musician.

Music was never the exclusive focus of Hanon's life: he was also a devout Roman Catholic, a Third Order Franciscan and a member of the Society of St. Vincent de Paul.

It is known from an 1869 article that Hanon was involved with a monastic order called the "Brothers of the Christian Schools". Founded in the 17th century by Saint John Baptist de la Salle, the schools run by the order provide free instruction to poor children. One such school was established in Boulogne-sur-Mer in approximately 1815 by Léon de Chanlaire and Father Benoît-Agathon Haffreingue; free music instruction was offered there by 1830.

The Virtuoso Pianist
Piano students all over the world know of Hanon's famous training exercises. Both Sergei Rachmaninoff and Josef Lhévinne claimed Hanon to be the secret of why the Russian piano school delivered an explosion of virtuosi in their time, for the Hanon exercises have been obligatory for a long time throughout Russian conservatories; there were special examinations at which one had to know all exercises by heart, to be played in all keys at high speed.

Although most respected pedagogues and pianists acknowledge the value of Hanon's exercises, they have their detractors. Some critics have questioned the merits of the independent finger technique which the exercises seek to cultivate, with some pedagogues, such as Abby Whiteside, considering them to be actively harmful.

It has become a custom in some music schools to hold a Hanon Marathon, in which the exercises are played competitively, the Church Street School for Music and Art being the first to have coined the term and hold the event.

Other works and derivatives
Hanon also wrote 50 instructional pieces, Méthode Élémentaire de Piano, and a collection of 50 Ecclesiastical Chants. Charles Nunzio wrote Hanon for Accordion, a two-volume set of exercises for piano accordion based on a similar philosophy, which has recently been reissued in an updated edition.

A Hanon for guitar and bass have also been written.

title: Charles-Louis Hanon


text:
Demigod (band)

Demigod are a Finnish death metal band formed in 1990 in Loimaa, Finland. The band's debut album Slumber of Sullen Eyes is highly regarded in the heavy metal community. Terrorizer included it in their list of "40 death metal albums that you must hear", commenting: "It is with this often overlooked classic that one of the greatest love stories of all time unfolded: Florida's pummeling groove meets Sweden's buzzsaw guitar work in a union so deliciously evil it could move the hardest of bangers to tears of joy."

History
Demigod was a popular group in the death metal underground of the 1990s; however, despite a steady status and a healthy number of gigs, the band split up in the mid-90s. Demigod re-formed in 1998 and was eventually signed by Spikefarm, a sublabel of major Finnish metal record company Spinefarm, who released the band's second album Shadow Mechanics.

Somewhere between 2002 and 2006, this co-operation came to an end, and the band recorded the follow-up to Shadow Mechanics without a label. The recordings were finished in the summer of 2006, and the album was released by the band's own label, Open Game Productions, in 2007. Since late 2007, worldwide distribution has been handled by the Spanish label Xtreem Music, leaving only the Scandinavian market for the band's own label. Xtreem Music has also re-released the debut album, previously long out of print.

In 2012, Esa Linden and several of the other "Slumber of Sullen Eyes" members took part in several reunion shows. After the string of shows was brought to a close, the band intended to begin writing another album.

Current

 * Esa Lindén - vocals (1990-1994, 1997-2001, 2010-present), guitar (1990-1993)
 * Jussi Kiiski - guitars (1991-2008, 2010-present)
 * Tuomas Karppinen - guitars (2007-2008, 2010-present)
 * Sami Vesanto - bass (1993-2008, 2010-present)
 * Tuomo Latvala - drums (2002-2008, 2010-present)

Former

 * Seppo Taatila - drums (1990-2002)
 * Tero Laitinen - bass (1990-1993), guitar (1994-2007)
 * Mika Haapasalo - guitar (1992), vocals (1994-1997)
 * Tuomas Ala-Nissilä - vocals (2001-2008)
 * Ali Leiniö - vocals (2001)

Discography

 * Unholy Domain (Demo, 1991)
 * Slumber of Sullen Eyes (1992)
 * Shadow Mechanics (Spikefarm, 2002)
 * Let Chaos Prevail (Open Game/Xtreem, 2007)

title: Demigod (band)


text:
Talk:Charles-Louis Hanon

Comments
There's a lot of controversy about the merits of Hanon's exercises. The article just says that these have become "standard" for "modern piano teachers" but it's more complex than that.

I've added a sentence or two, but it would be good to have an extended section about their whole use and POVs about them. I'll do more when I get time. I'm still feeling traumatised at the very concept of a Hanon Marathon. Urgh! Kisch

I only know this: after a few minutes of warming up by Hanon's exercices, it's so much easier to handle a Bach fugue! Try it yourself: your hands feel a lot faster and more flexible and the piano keys feel a lot lighter! And i believe i'm in good company if Horowitz liked it too, obscure critics notwithstanding...
 * The exercises have their own article, which is much longer. Further explanation and opinions should be added there. Meanwhile, it would be nice to have more information on Hanon himself, like biographical information, or if he wrote anything else. Rigadoun (talk) 19:49, 20 September 2007 (UTC)

I think I have found a compromise which satisfies both the Hanon groupies and the Hanon detractors, vis I play the half of the exercise which works mainly on the RH with that hand, and vice-versa. This gives the hands 50% exercise and 50% rest. I'm also trying to keep a beautiful tone as I play them. I would have been sad to let them go completely because they really do work magic in the fingers. John160251 (talk) 22:18, 15 January 2008 (UTC)

Assessment comment
Substituted at 11:22, 29 April 2016 (UTC)

External links modified
Hello fellow Wikipedians,

I have just modified one external link on Charles-Louis Hanon. Please take a moment to review my edit. If you have any questions, or need the bot to ignore the links, or the page altogether, please visit this simple FaQ for additional information. I made the following changes:
 * Added archive https://web.archive.org/web/20111205132321/http://www.how-to-play-bass.com/bass-hanon.html to http://www.how-to-play-bass.com/bass-hanon.html

When you have finished reviewing my changes, you may follow the instructions on the template below to fix any issues with the URLs.

Cheers.— InternetArchiveBot  (Report bug) 01:46, 3 August 2017 (UTC)

Reference Link 1 does not work
Clicking on Reference 1 brings up a Not Found link. Bread2u (talk) 21:01, 25 February 2018 (UTC)

CF Hanon listed at Redirects for discussion
An editor has asked for a discussion to address the redirect CF Hanon. Please participate in the redirect discussion if you wish to do so.  Onel 5969  TT me 19:04, 8 June 2019 (UTC)

C.F. Hanon listed at Redirects for discussion
An editor has asked for a discussion to address the redirect C.F. Hanon. Please participate in the redirect discussion if you wish to do so.  Onel 5969  TT me 19:06, 8 June 2019 (UTC)

title: Talk:Charles-Louis Hanon


text:
Fedelm Noíchrothach

Fedelm Noíchrothach ("nine times beautiful"), also known as Fedelm Noíchride ("nine-hearts" or "fresh-heart"), is a daughter of Conchobar mac Nessa in the Ulster Cycle of Irish mythology. She married Cairbre Nia Fer, king of Tara, but was unfaithful to him. She enjoyed a tryst with Cúchulainn at the beginning of the Táin Bó Cuailnge (Cattle Raid of Cooley), although the text has been clumsily altered to say that Cúchulainn's lover was Fedelm's handmaid. She later left her husband for Conall Cernach.

title: Fedelm Noíchrothach


text:
File:Tetras and Pentas.jpg

Tetras and Pentas

Source
Yılmaz, Zeki. Türk Mûsıkîsi Dersleri. (2001). ISBN 975-95729-1-5.

Links to
Maqam

title: File:Tetras and Pentas.jpg


text:
Category:Animal intelligence

Animal intelligence is the study about the origins of animal intelligence by studying the mental processes of other species. The basic premise of this research is that we need to understand the processes of association and learning in other animals in order to understand how human culture, art, religion, mathematics and more may have developed.

title: Category:Animal intelligence


text:
Paragus

Paragus is a genus of hoverflies.

Species

Subgenus: Afroparagus Vujić & Radenković, 2008
 * P. borbonicus Macquart, 1842

Subgenus: Pandasyopthalmus Stuckenberg, 1954

 * P. ascoensis Goeldlin, 1981
 * P. atratus Meijere, 1906
 * P. basilewskyi Doesburg, 1955
 * P. chalybeatus Hull, 1964
 * P. coadunatus Rondani, 1847
 * P. dolichocerus Bezzi, 1915
 * P. gracilis Stuckenberg, 1954
 * P. haemorrhous Meigen, 1822
 * P. jozanus Matsumura, 1916
 * P. longiventris Loew, 1858
 * P. marshalli Bezzi, 1915
 * P. minutus Hull, 1964
 * P. naso Stuckenberg, 1954
 * P. nasutus Bezzi, 1915
 * P. nigrocoeruleus Hull, 1949
 * P. politus Wiedemann, 1830
 * P. punctatus Hull, 1949
 * P. tibialis (Fallén, 1817)

Subgenus: Paragus Latreille, 1804
 * P. bicolor (Fabricius, 1794)
 * P. bispinosus Vockeroth, 1986
 * P. cooverti Vockeroth, 1986
 * P. quadrifasciatus Meigen, 1822
 * P. variabilis Vockeroth, 1986

Subgenus: Serratoparagus Vujić & Radenković, 2008
 * P. crenulatus Thompson, 1869
 * P. pusillus Stuckenberg, 1954

In need of organisation

 * P. absidatus Goeldlin, 1971
 * P. albifrons (Fallén, 1817)
 * P. albipes Gimmerthal, 1842
 * P. ambalaensis Sodhi & Singh, 1991
 * P. angustifrons Loew, 1863
 * P. angustistylus Vockeroth, 1986
 * P. arizonensis Vockeroth, 1986
 * P. asiaticus Peck, 1979
 * P. bradescui Stanescu, 1981
 * P. cinctus Schiner & Egger, 1853
 * P. clausseni Mutin, 1999
 * P. compeditus Wiedemann, 1830
 * P. constrictus Simic, 1986
 * P. dauricus Mutin, 1999
 * P. finitimus Goeldlin, 1971
 * P. flammeus Goeldlin, 1971
 * P. glumaci Vujic, Simic & Radenkovic, 1999
 * P. hermonensis Kaplan, 1981
 * P. hyalopteri Marcos-Garcia & Rojo, 1994
 * P. kitincheevi Barkalov & Goguzokov, 2001
 * P. kopdagensis Claussen, 1997
 * P. leleji Mutin, 1985
 * P. longistylus Vockeroth, 1986
 * P. majoranae Rondani, 1857
 * P. medeae Stanescu, 1991
 * P. oltenicus Stanescu, 1877
 * P. oltenicus Stanescu, 1977
 * P. pecchiolii Rondani, 1857
 * P. punctulatus Zetterstedt, 1838
 * P. romanicus Stanescu, 1992
 * P. sexarcuatus Bigot, 1862
 * P. strigatus Meigen, 1822
 * P. vandergooti Marcos-Garcia, 1986

title: Paragus


text:
Category:Italian DOC

This is a category for Italian wine DOCs (Denominazione di origine controllata), the second-highest level of Italian wine "appellations".

See also Category:Italian DOCG for the level above DOC.

title: Category:Italian DOC


text:
User talk:169

Welcome!

Hello,, and welcome to Wikipedia! Thank you for your contributions. I hope you like the place and decide to stay. Here are a few good links for newcomers: I hope you enjoy editing here and being a Wikipedian! Please sign your name on talk pages using four tildes (~~); this will automatically produce your name and the date. If you need help, check out Where to ask a question, ask me on my talk page, or place   on your talk page and someone will show up shortly to answer your questions. Again, welcome! --Eleassar777 09:24, 19 Feb 2005 (UTC)
 * The five pillars of Wikipedia
 * How to edit a page
 * Help pages
 * Tutorial
 * How to write a great article
 * Manual of Style

Please stop removing content from Wikipedia; it is considered vandalism. If you want to experiment, please use the sandbox. Thank you. --Eleassar777 09:24, 19 Feb 2005 (UTC)

Semi-automated template substitution

 * This page was modified to semi-automatically substitute templates using Pathoschild's template list. // Tawker 17:43, 12 February 2006 (UTC)

title: User talk:169


text:
Lugaid Riab nDerg

Lugaid Riab nDerg ("the red-striped") or Réoderg ("Red Sky"), son of the three findemna, triplet sons of Eochu Feidlech, and their sister Clothru was, according to medieval Irish legend and historical tradition, a High King of Ireland.

Conception
Lugaid was conceived of incest. The night before the three findemna, Bres, Nár and Lothar, made war for the High Kingship against their father in the Battle of Druimm Criaich, their sister Clothru, concerned that her brothers could die without heirs, seduced all three of them, and a son, Lugaid, was conceived. His epithet came from two red stripes around his neck and waist, dividing him into three: above the neck he resembled Nár; from the neck to the waist he resembled Bres; and from the waist down he resembled Lothar. Incest features further in Lugaid's story: he slept with Clothru himself, conceiving Crimthann Nia Náir.

Rise to power
The Lebor Gabála Érenn says he came to power after a five-year interregnum following the death of Conaire Mór (six years according to the Annals of the Four Masters). His foster-father, the Ulster hero Cúchulainn, split the Lia Fáil (coronation stone at Tara which roared when the rightful king stood or sat on it) with his sword when it failed to roar under Lugaid. It never roared again except under Conn of the Hundred Battles.

Conflicts
The wizard of Ethne, daughter of Eochu Feidlech, prophesied that the son of Ethne's sister Clothru would kill her (Ethne). Therefore Ethne fled to Cruachan in the East to give birth to her son, but Lugaid chased her there and drowned her; he then cut her son, Furbaide Fer-benn (described as having two horns on his temples) from her womb. Later at the age of 17 Furbaide sought revenge against Lugaid for his mother's death, and killed Clothru, for which Lugaid killed Furbaide on a mountaintop called Sliab Uillean. Certain elements of this story bear a resemblance to the prophecy of Lugh Lamhfhada, son of Ethniu, who was predicted to kill his grandfather Balor of the Evil-Eye.

Marriage
His wife was Derbforgaill, a daughter of the king of Lochlann (Scandinavia), who had fallen in love with Cúchulainn from afar and come to Ireland with a handmaiden in the form of a pair of swans, linked by a golden chain, to seek him out. Cúchulainn and Lugaid were at Loch Cuan (Strangford Lough) and saw them fly past. Cúchulainn, at Lugaid's urging, shot a slingstone which hit Derbforgaill, penetrating her womb, and the two women fell on the beach in human form. Cúchulainn saved Derbforgaill's life by sucking the stone from her side, and she declared her love for him, but because he had sucked her side he could not marry her – evidently, he had violated some geis or taboo. Instead, he gave her to Lugaid. They married and had children.

Deaths of Derbforgaill and Lugaid
One day in deep winter, the men of Ulster made pillars of snow, and the women competed to see who could urinate the deepest into the pillar and prove herself the most desirable to men. Derbforgaill's urine reached the ground, and the other women, out of jealousy, attacked and mutilated her, gouging out her eyes and cutting off her nose, ears, and hair. Lugaid noticed that the snow on the roof of her house had not melted, and realised she was close to death. He and Cúchulainn rushed to the house, but Derbforgaill died shortly after they arrived, and Lugaid died of grief. Cúchulainn avenged them by demolishing the house the women were inside, killing 150 of them.

Alternatives
For Lugaid Réoderg, an alternative tradition exists that he met his death at the hands of the Trí Rúadchinn Laigen, the "Three Reds of the Laigin" also involved in the death of Conaire Mór. Lucius Gwynn suggested that what may have happened is an earlier King of Tara known as Lugaid Réoderg may have become confused with a separate and minor character from the Ulster Cycle associated with Cúchulainn. T. F. O'Rahilly, on the other hand, believed the epithet Riab nDerg to simply be a corruption of the earlier Réoderg, meaning something like "of the red sky", and does not believe them to be distinct legendary figures (see below).

Further analysis
The view advanced by O'Rahilly was that Lugaid Riab nDerg is yet another emanation of the heroic mytho-dynastic figure Lugaid, closely associated with the prehistoric Érainn, a population of late Iron Age Ireland who provide Irish legend with its earliest known Kings of Tara. One of their most notable representatives in that office is Lugaid's immediate predecessor, Conaire Mór.

Specifically, O'Rahilly believed Lugaid Riab nDerg to be the double of Lugaid mac Con Roí, whose alternative epithet was mac Trí Con "son of Three Hounds", and who himself is to some extent identical with Lugaid Mac Con. The last, usually known simply as Mac Con "Hound's Son", is an Érainn king matching Conaire Mór in importance in Irish legend. Another is Cú Roí mac Dáire, or simply Dáire, father of Lugaid mac Con Roí. A 'fourth' Lugaid and 'ancestor' of Mac Con was Lugaid Loígde.

Lugaid's reign
He had ruled for twenty, twenty-five or twenty-six years. The Lebor Gabála  synchronises his reign with that of the Roman emperor Claudius (AD 41–54). The chronology of Geoffrey Keating's Foras Feasa ar Éirinn dates his reign to 33–13 BC, that of the Annals of the Four Masters to 33–9 BC.

title: Lugaid Riab nDerg


text:
D&B Hoovers

D&B Hoovers was founded by Gary Hoover and Patrick Spain in 1990 as an American business research company that provided information on companies and industries through their primary product platform named "Hoover's". In 2003, it was acquired by Dun & Bradstreet and operated for a time as a wholly owned subsidiary. In 2017, the Hoover's product was re-branded D&B Hoovers. Dun & Bradstreet is headquartered in Jacksonville, Florida, US.

Origins and expansion
Hoovers was started in 1990 by Gary Hoover, Patrick J. Spain, Alan Chai, and Alta Campbell. Leading up to this, Hoover had founded the Bookstop book store chain, ultimately purchase by Barnes & Noble.[citation needed] Hoover's initially was called The Reference Press as it published reference books about companies.

The company grew rapidly under a business team led by Spain. This team included Carl Shepherd, Lynn Atchison, Elisabeth DeMarse, Jani Spede, Kris Rao, and Gordon Anderson, among others. Spain was CEO from 1993 to 2001, and chairman from 1994 to 2002.

Hoovers made an initial public offering on the NASDAQ exchange in 1999. The company then became a subsidiary of Dun & Bradstreet, which bought Hoover's for $119 million in 2003. After the acquisition of Avention by Dun & Bradstreet in 2017, the D&B Hoovers solution was launched, and replaced the existing Hoovers' product.

Operations
Dun & Bradstreet maintains a database of more than 330 million companies with 30,000 global data sources updated 5 million times per day. It combines Dun & Bradstreet's data with Avention's sales acceleration platform. Subscriptions are sold primarily to sales, marketing, and business development professionals seeking contact information for prospective customers. The database is used for lead generation, outreach, prepping for sales calls, researching companies, being alerted to changes in leadership, and acquiring new customers.

Besides publishing information through the D&B Hoovers product, information is also distributed via data feeds and third-party licensing agreements.

D&B Hoovers claims to offer proprietary business information through an online platform and integrated workflow solutions, houses data on more than 120 million business records across 1,000 industries.

title: D&B Hoovers


text:
Paper recycling

The recycling of paper is the process by which waste paper is turned into new paper products. It has a number of important benefits: It saves waste paper from occupying homes of people and producing methane as it breaks down. Because paper fibre contains carbon (originally absorbed by the tree from which it was produced), recycling keeps the carbon locked up for longer and out of the atmosphere. Around two-thirds of all paper products in the US are now recovered and recycled, although it does not all become new paper. After repeated processing the fibres become too short for the production of new paper, which is why virgin fibre (from sustainably farmed trees) is frequently added to the pulp recipe.

There are three categories of paper that can be used as feedstocks for making recycled paper: mill broke, pre-consumer waste, and post-consumer waste. Mill broke is paper trimmings and other paper scrap from the manufacture of paper, and is recycled in a paper mill. Pre-consumer waste is a material which left the paper mill but was discarded before it was ready for consumer use. Post-consumer waste is material discarded after consumer use, such as old corrugated containers (OCC), old magazines, and newspapers. Paper suitable for recycling is called "scrap paper", often used to produce moulded pulp packaging. The industrial process of removing printing ink from paper fibres of recycled paper to make deinked pulp is called deinking, an invention of the German jurist Justus Claproth.

Process
The process of waste paper recycling most often involves mixing used/old paper with water and chemicals to break it down. It is then chopped up and heated, which breaks it down further into strands of cellulose, a type of organic plant material; this resulting mixture is called pulp, or slurry. It is strained through screens, which remove plastic (especially from plastic-coated paper) that may still be in the mixture. It is then cleaned, de-inked (ink is removed), bleached, and mixed with water. Then it can be made into new recycled paper.

The share of ink in a wastepaper stock is up to about 2% of the total weight.

In the mid-19th century, there was an increased demand for books and writing material. Up to that time, paper manufacturers had used discarded linen rags for paper, but supply could not keep up with the increased demand. Books were bought at auctions for the purpose of recycling fiber content into new paper, at least in the United Kingdom, by the beginning of the 19th century.

Rationale for recycling
Industrialized paper making has an effect on the environment both upstream (where raw materials are acquired and processed) and downstream (waste-disposal impacts).

Today, 40% of paper pulp is created from wood (in most modern mills only 9–16% of pulp is made from pulp logs; the rest comes from waste wood that was traditionally burnt). Paper production accounts for about 35% of felled trees. Recycling one ton of newsprint saves about 1 ton of wood while recycling 1 ton of printing or copier paper saves slightly more than 2 tons of wood. This is because kraft pulping requires twice as much wood since it removes lignin to produce higher quality fibres than mechanical pulping processes. Relating tons of paper recycled to the number of trees not cut is meaningless, since tree size varies tremendously and is the major factor in how much paper can be made from how many trees. In addition, trees raised specifically for pulp production account for 16% of world pulp production, old growth forests 9% and second- and third- and more generation forests account for the balance. Most pulp mill operators practice reforestation to ensure a continuing supply of trees. The Programme for the Endorsement of Forest Certification (PEFC) and the Forest Stewardship Council (FSC) certify paper made from trees harvested according to guidelines meant to ensure good forestry practices.

Energy
Energy consumption is reduced by recycling, although there is debate concerning the actual energy savings realized. The Energy Information Administration claims a 40% reduction in energy when paper is recycled versus paper made with unrecycled pulp, while the Bureau of International Recycling (BIR) claims a 64% reduction. Some calculations show that recycling one ton of newspaper saves about 4000 kWh of electricity, although this may be too high (see comments below on unrecycled pulp). This is enough electricity to power a 3-bedroom European house for an entire year, or enough energy to heat and air-condition the average North American home for almost six months. Recycling paper to make pulp actually consumes more fossil fuels than making new pulp via the kraft process; these mills generate most of their energy from burning waste wood (bark, roots, sawmill waste) and byproduct lignin (black liquor). Pulp mills producing new mechanical pulp use large amounts of energy; a very rough estimate of the electrical energy needed is 10 gigajoules per tonne of pulp (2500 kW·h per short ton).

Landfill use
About 35% of municipal solid waste (before recycling) in the United States by weight is paper and paper products. 42.4% of that is recycled.

Water and air pollution
The United States Environmental Protection Agency (EPA) has found that recycling causes 35% less water pollution and 74% less air pollution than making virgin paper. Pulp mills can be sources of both air and water pollution, especially if they are producing bleached pulp. Modern mills produce considerably less pollution than those of a few decades ago. Recycling paper provides an alternative fibre for papermaking. Recycled pulp can be bleached with the same chemicals used to bleach virgin pulp, but hydrogen peroxide and sodium hydrosulfite are the most common bleaching agents. Recycled pulp, or paper made from it, is known as PCF (process chlorine free) if no chlorine-containing compounds were used in the recycling process.

Greenhouse gas emissions
Studies on paper and cardboard production estimate the emissions of recycling paper to be 0.2 to 1.5 kg CO₂-equivalent/kg material. This is about 70% of the CO₂ emissions connected with production of virgin material.

European Union
Paper recycling in Europe has a long history. The industry self-initiative European Recovered Paper Council (ERPC) was set up in 2000 to monitor progress towards meeting the paper recycling targets set out in the 2000 European Declaration on Paper Recycling. Since then, the commitments in the Declaration have been renewed every five years. In 2011, the ERPC committed itself to meeting and maintaining both a voluntary recycling rate target of 70% in the then E-27, plus Switzerland and Norway by 2015, as well as qualitative targets in areas such as waste prevention, ecodesign and research and development. In 2014, the paper recycling rate in Europe was 71.7%, as stated in the 2014 Monitoring Report.

United States
Recycling has long been practiced in the United States. In 1690, nearly a century before the American Revolution, the first paper mill to use recycled linen rags was established by the Rittenhouse family. In 1993, 300 years later, another milestone was reached when, for the first time, more paper was recycled than was landfilled.

By 1998, some 9,000 curbside recycling programs and 12,000 recyclable drop-off centers existed nationwide. As of 1999, 480 materials recovery facilities had been established to process the collected materials.

In 2008, the global financial crisis caused the price of old newspapers to drop in the U.S. from $130 to $40 per short ton ($140/t to $45/t) in October.

In 2018, paper and paperboard accounted for 67.39 million tons of municipal solid waste (MSW) generated in the U.S., down from more than 87.74 million tons in 2000. As of 2018, paper products are still the largest component of MSW generated in the United States, making up 23% by weight. While paper is the most commonly recycled material (68.2 percent of paper waste was recovered in 2018, up from 33.5 percent in 1990) it is being used less overall than at the turn of the century. As of 2018, paper accounted for a third of all recyclables collected in the US, by weight. The widespread adoption of the internet and email has led to a change in the composition of the waste paper stream, with junk mail becoming a larger part of the materials collected, as reading of newspapers and writing of personal letters declines.

India
After China put restrictions on waste imports in January 2018, much paper was being shipped to India. However, India's domestic recycling only produces 30% of the total paper demand.

Mexico
In Mexico, recycled paper, rather than wood pulp, was the principal feedstock in paper mills accounting for about 90% of raw materials in 2020.

South Africa
In 2018, South Africa recovered 1.285 million tonnes of recyclable paper products, putting the country's paper recovery rate at 71.7%. More than 90% of this recovered paper is used for the local beneficiation of new paper packaging and tissue.

Limitations and effects
Along with fibres, paper can contain a variety of inorganic and organic constituents, including up to 10,000 different chemicals, which can potentially contaminate the newly manufactured paper products. As an example, bisphenol A (a chemical commonly found in thermal paper) has been verified as a contaminant in a variety of paper products resulting from paper recycling. Groups of chemicals as phthalates, phenols, mineral oils, polychlorinated biphenyls (PCBs) and toxic metals have all been identified in paper material. Although several measures might reduce the chemical load in paper recycling (e.g., improved decontamination, optimized collection of paper for recycling), even completely terminating the use of a particular chemical (phase-out) might still result in its circulation in the paper cycle for decades.

title: Paper recycling


text:
Michael Costa (conductor)

Sir Michael Andrew Angus Costa (14 February 1808 – 29 April 1884) was an Italian-born conductor and composer who achieved success in England.

Biography
He was born as Michele Andrea Agniello Costa in Naples, into a family of Sephardic Jewish descent. He studied there with his father, at the Real Collegio di Musica, and later with Niccolò Antonio Zingarelli.

In his youth, as throughout his life, he wrote a great quantity of music, including operas, symphonies and cantatas, all of which has long since passed into oblivion. In 1829 he visited the Birmingham Music Festival to conduct Zingarelli's Cantata Sacra, a setting of some verses from Isaiah ch. xii. This was the occasion of his memorably inauspicious début. The intention was that Costa should rehearse and conduct the work; but J. B Cramer and Thomas Greatorex elbowed him out and was instead engaged as a tenor soloist in another concert. Unfortunately both the work and Costa's singing met with ferocious criticism: "[This cantata] is one of the most tame, insipid things we were ever doomed to hear: a heap of common-place trash from the first to the last note. After twaddling in B flat for half-an-hour, he ventures for a few bars into F, then returns to B, and there is an end." "As a singer [Costa] is far below mediocrity, and he does not compensate for his vocal deficiencies by his personal address, which is abundantly awkward. In the theatre while singing the air "Nel furor delle tempeste", [from Bellini's Il pirata] and accompanying himself, he had a narrow escape. The tempests proved contagious, and were beginning to manifest themselves in the galleries, and had he remained but a few moments longer on the stage, he would have witnessed a storm compared to which the roarings of his own Vesuvius would have seemed but a murmur." Nonetheless he decided to settle in England.

In 1830 he arrived in London, working at His Majesty's Theatre. Costa exerted real influence for change as a conductor at Her Majesty's and, later, at Covent Garden theatre, to which he seceded in 1847 after disagreements with the manager of Her Majesty's, Benjamin Lumley. His concern for discipline, accuracy, and ensemble was a novelty in its time and earned him the admiration both of Meyerbeer and Verdi. Despite this, he could not be claimed as a purist: his re-scoring of Handel's Messiah includes a part for cymbals. He was selected by Nicolo Paganini to conduct his London concerts when Paganini visited the city throughout the 1830’s.

Costa became a naturalized Englishman and received a knighthood in 1869. He was conductor of the Philharmonic Society from 1846 to 1854, of the Sacred Harmonic Society from 1848, and of the Birmingham Triennial Music Festival from 1849 to 1882. He conducted at the Bradford (1853, 1856, and 1859) and Handel festivals (1857–1880), and the Leeds Festivals from 1874 to 1880. He also taught several musicians in England, including contralto Emma Albertazzi.

He died in 1884 in Hove and was buried at Kensal Green. His home at 59 Eccleston Square in Pimlico, London, is commemorated with a blue plaque.

Works
Amongst the works of Costa's maturity may be listed his ballets Kenilworth (1831), Une Heure à Naples (1832), Sir Huon (composed for Taglioni) in 1833 and the ballet Alma (1844, later revived as La fille du marbre). His opera Malek Adel was produced in Paris in 1837 and in London in 1844, as was his opera Don Carlos.

In 1855 Costa wrote the oratorio Eli, and in 1864 Naaman, both for Birmingham. Rossini's comment on the former was: "The good Costa has sent me an oratorio score and a Stilton cheese. The cheese was very good." An aria from Eli, "I will extol thee", was recorded in 1910 by the great British dramatic soprano Agnes Nicholls (1876–1959), and the quality of Costa's music can be judged on various CD re-masterings of this particular disc which have been issued in recent years.

Freemasonry
On 3 May 1848 Costa followed in his brother Raphael's footsteps by becoming an English Freemason in the Bank of England Lodge, No. 263, (London, England). In July 1849 the brothers (in both senses of the word) were Exhalted (Initiated) into the Royal Arch (another branch of Freemasonry) in Fidelity Chapter, No. 3. Costa was appointed Grand Organist of the United Grand Lodge of England in 1851 a post he occupied for two years.

The brothers were instrumental in establishing Mark Masonry in England by signing a petition sent to the Bon Accord Royal Arch Chapter (Aberdeen, Scotland) requesting that a Bon Accord Mark Lodge be established in London. The inaugural meeting of this Mark Lodge was held in the Radley Hotel, Bridge Street, Blackfriars, on 19 September 1851. At that meeting both were 'Advanced' (Initiated) to the 'honorable degree of Mark Master.' Mark Masonry in England and Wales later came under the jurisdiction of the Grand Lodge of Mark Master Masons but neither brother appears to have been involved in the creation of that body.

title: Michael Costa (conductor)


text:
Category:Animal cognition

Animal cognition is the title given to a modern approach to the mental capacities of non-human animals. It has developed out of comparative psychology, but has also been strongly influenced by the approach of ethology and behavioral ecology. Much of what used to be considered under the title of animal intelligence is now thought of under this heading.

title: Category:Animal cognition


text:
Hitch (film)

Hitch is a 2005 American romantic comedy film directed by Andy Tennant and starring Will Smith in the title role, along with Eva Mendes, Kevin James, and Amber Valletta. The film, which was written by Kevin Bisch, features Smith as Alex "Hitch" Hitchens, a professional "date doctor" who makes a living teaching men how to woo women. Unfortunately, while helping his latest client woo the woman of his dreams, he finds out that his game does not work on the gossip columnist with whom he is smitten.

Columbia Pictures released Hitch on February 11, 2005. The film received positive reviews from critics and was a box office hit, grossing $371.6 million worldwide, becoming the tenth highest-grossing film of 2005.

Plot
Alex "Hitch" Hitchens is a professional "date doctor" who coaches other men in the art of wooing women, with the main focus of having genuine long-term relationships. He is very successful at what he does.

While coaching one of his clients, Albert Brennaman—who is smitten with a client of his investment firm, celebrity Allegra Cole—Hitch finds himself falling for Sara Melas, a gossip columnist and cynical workaholic. While Albert and Allegra's relationship progresses, Hitch has difficulty connecting with Sara as none of his romantic methods work for her. Throughout the entire process, he keeps his career secret, claiming to be a generic "consultant".

Hitch meets with Vance Munson, a shallow misogynist attempting to get Hitch to help him land a one-night stand with Casey Sedgewick, Sara's coworker and best friend. Although Hitch refuses to help, Vance smugly misleads her into believing that he has used Hitch's services. After finding out Hitch's true identity, Sara publishes an exposé, causing Albert to vandalize a newsstand in rage and get arrested, Allegra to break up with Albert, and Hitch's reputation to suffer.

At a speed dating event that Hitch sneaks into, Sara and Casey confront him and cite Vance as their source. Hitch explains that not only did he refuse to work with him but also the extent to which women must protect themselves from men like Vance unintentionally makes establishing genuine relationships with good men difficult enough to create a demand for Hitch's services.

After receiving some criticism from Albert about treating love as a job instead of a legitimate feeling, Hitch then tries to salvage Albert and Allegra's relationship by confronting her. When she mentions how Albert's quirks won her over, Hitch realizes he does not do anything significant besides giving his clients confidence and allowing them to get the attention of the women they love. And most of his customers, particularly Albert, really were successful by just being themselves. Allegra reconciles with Albert, and Hitch and Sara repair their relationship.

Albert and Allegra get married. During the reception, Casey gives the Heimlich maneuver to an elderly woman who is choking on a grape, which endears her to the woman's attractive grandson (it is revealed the elderly woman was working with Hitch). A dance party then begins with Albert, Allegra, Sara, and Hitch, which ends with Albert accidentally ripping his pants open to do the splits.

Development
The working title of the film was The Last First Kiss, referring to a line that Hitch delivers to Albert, "Tomorrow night Allegra Cole could have her last first kiss."

Smith has said that actress Eva Mendes, a Latina, was offered the female lead because the producers were worried about the public's reaction if the part was played by a white actress, creating a studio fear of a potential interracial taboo, or a black actress, creating a studio fear that two black leads would alienate the white audiences. It was believed that a Latina and a black lead would sidestep the issue. Patton Oswalt was considered for the role of Albert Brennaman.

Filming
Filming took place between March and July 2004. Parts of the film were filmed in Morningside Heights, Manhattan, at Columbia University, at Ellis Island, in the Fulton Fish Market, at the Wall Street Bull and the North Cove Marina.

The production budget was $55–70 million.

Box office
Hitch was theatrically released on February 11, 2005. Sony expected the film to open to $35 million, but the film performed above expectations, opening to $43,142,214. It spent three consecutive weeks at the number 1 position in the North American box office. Its worldwide box office take totaled $371.6 million, making it the tenth highest-grossing film of 2005 and the third highest-grossing romantic comedy film, after My Big Fat Greek Wedding and What Women Want.

Home media
The film was released on June 14, 2005, on VHS and DVD by Sony Pictures Home Entertainment. It was one of the first films to employ Sony's ARccOS Protection copy protection. The film was also available on UMD (Universal Media Disc) for the Sony PSP (PlayStation Portable).

Critical response
On Rotten Tomatoes, the film has a rating of 69% based on 188 reviews, and an average review of 6.30/10. The site's critical consensus reads: "Despite Hitch's predictability, Will Smith and Kevin James win praise for their solid, warmhearted performances." On Metacritic, the film has a weighted average score of 58 out of 100, based on 36 critics, indicating "mixed or average reviews". Audiences polled by CinemaScore gave the film an average grade of "A" on an A+ to F scale.

Roger Ebert of the Chicago Sun-Times wrote: "The premise is intriguing, and for a time it seems that the Date Doctor may indeed know things about women that most men in the movies are not allowed to know, but the third act goes on autopilot just when the Doctor should be in." Brian Lowry of Variety wrote: "Considerably heavier on romance than comedy, Hitch stitches together relatively few laughs but generates enough goodwill and energy."

Remake
The film was remade in Hindi as Partner in 2007, which was also filed a lawsuit against the film's producers Sohail Khan and Parag Sanghvi, by Sony Pictures for copyright infringement. It was solved after Sony Pictures acquired the world's exclusive satellite rights of the film.

Music
Hitch: The Soundtrack was released on September 20, 2005, by Columbia Records. The album reached No. 5 on the Billboard Soundtrack Albums chart and No. 35 on the Billboard 200 chart.

Soundtrack
The soundtrack features artists such as Amerie, Kelly Rowland, Sleepy Brown, Big Boi, Earth, Wind & Fire, Mark Ronson, Martha Reeves and the Vandellas, Omarion, The O Jays, John Legend, The Temptations, Jimmy Cliff and Kevin Lyttle.

Rob Theakston of AllMusic gave the album a three out of five star rating noting that it "features a brilliant survey of soul and R&B over the past three decades." He also proclaimed "while the new tracks are impressive and enjoyable, it's this combination that makes Hitch an enjoyable listen, with something for everyone -- regardless of age -- to enjoy."

TV show
On October 22, 2014, it was announced that Overbrook Entertainment and Sony Pictures Television began work on a television series adaptation inspired by the film for Fox.

title: Hitch (film)


text: File:Hitch poster.JPG

title: File:Hitch poster.JPG


text:
Generalized canonical correlation

In statistics, the generalized canonical correlation analysis (gCCA), is a way of making sense of cross-correlation matrices between the sets of random variables when there are more than two sets. While a conventional CCA generalizes principal component analysis (PCA) to two sets of random variables, a gCCA generalizes PCA to more than two sets of random variables. The canonical variables represent those common factors that can be found by a large PCA of all of the transformed random variables after each set underwent its own PCA.

Applications
The Helmert-Wolf blocking (HWB) method of estimating linear regression parameters can find an optimal solution only if all cross-correlations between the data blocks are zero. They can always be made to vanish by introducing a new regression parameter for each common factor. The gCCA method can be used for finding those harmful common factors that create cross-correlation between the blocks. However, no optimal HWB solution exists if the random variables do not contain enough information on all of the new regression parameters.

title: Generalized canonical correlation