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Movie Title Year Distributor Notes Rev Formats Any Time Any Place 1981 VCX Facial DRO Best of VCX Classics 2 2005 VCX 1 DO Centerfold Celebrities 2 1983 VEP Centerfold Celebrities 3 1983 VEP Hot Dallas Nights 1981 VCX Facial 1 DO Limited Edition Film 181 1982 AVC Limited Edition Film 183 1982 AVC Starship Eros 1979 Capa Productions BJOnly Facial that while interesting at first, could eventually bog them down.[53] Payment Within the Bureau, payment was decided upon by rank. As established in the year 1392, the top rank of Directors is paid sixteen piculs of rice per month. The Deputy Directors and Chiefs of the Five Agencies are allotted ten piculs per month, the Astronomers receive seven piculs, while both the Registrars and Chief Diviners have six and a half piculs. The Chiefs of the Clepsydras receive six piculs, and the Calendar Officers and Observers both have five and a half piculs. The lowest payment level goes to the Observers of the Sunrise and the Professors of the Clepsydras at five piculs per month.
Instruments Used by the Occupation Memorial The memorial was used by astronomers as a record keeper of anomalies, as the heavens are demonstrative of the effect of the ruler's actions. Originally, authors signed each contribution individually but that was eventually replaced by the official seal of the astronomical bureau.[54] Imperial Observatory The imperial observatory was a platform where the observations were made. It was first located just south of Nanjing, but late moved to Jiming Mountain city. However, in 1402 there was another platform created in the capital of Beijing.[55] Armillary Sphere (Ming China) The armillary sphere has three sets of rings that represent the celestial sphere. The first group contains fixed meridian, horizon, and equatorial rings. The second group contains ecliptic, solstitial, and equinoctial rings that turn as a unit. The inner group contains one meridian ring that moves around the celestial pole. These allow the astronomer to set a celestial object within their sights and judge distance.[56] The Simplified Instrument The simplified instrument serves a very similar purpose to the armillary sphere but has fewer parts. With only two sets of coordinates, this instrument has a larger range and vision than the armillary spheres.

Yuan Gnomon The Yuan Gnomon is a shadow casting instrument used to measure the position of the sun. However, it does not appear to be very accurate. A crucial aspect of this mechanism was that it was oriented along the north-south meridian line, which allowed it to show the local noon. While not included in the 1392 list of official instruments, in 1437 Huangfu Zhonghe included it, likely due less to its practicality and more to the ingenuity behind it.[57] Clepsydra The clepsydra, or water clock, was the most prevalent of time-keeping devices for astronomers. The clepsydra was also used as the official state time-keeping device. The Astronomical Bureau used a three chamber intake clepsydra, although there is no record of a water clock at Nanjing. It was not until the Bureau moved to Beijing that an official water hall was observed.[58] Outside Perspective Because of the ideological importance of astronomy regarding politics, and the lack of precision by the instruments, many people believed the observations were false.[59] Other recorded corruption such as accepting bribery, stealing, and not being punctual were also experienced.[60] This led to a strict policy of punishment if the astronomers were found to be corrupt. Punishments included such actions as dismissal, deprivation of salary, or even beatings.[60] Famous Chinese astronomers Gan De Guo Shoujing Shen Kuo Shi Shen Su Song Xu Guangqi Yu Xi Zhang Heng Mathematics in China emerged independently by the 11th century BC.[1] The Chinese independently developed a real number system that includes significantly large and negative numbers, more than one numeral systems (base 2 and base 10), algebra, geometry, number theory and trigonometry. In the Han Dynasty, the Chinese made substantial progress on finding the nth root of positive numbers and solving linear congruence equations.[2] The major texts from the period, The Nine Chapters on the Mathematical Art and the Book on Numbers and Computation gave detailed processes to solving various mathematical problems in daily life.[3] 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 and modular method for Diophantine equation, respectively.[4] The achievement of Chinese algebra reached its zenith in the 13th century, when Li Jingzhai invented tian yuán shù. 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,[5] such as the Song dynasty Chinese polymath Shen Kuo. A man in black armor standing in front of a rocket, attached to a stick, with the stick being held up by two X-shaped wooden brackets. History of science and technology in China Inventions Four Great InventionsDiscoveries By subject MathematicsAstronomyCalendarUnits of measurementCartographyGeographyPrintingCeramicsMetallurgyCoinageAlchemyTraditional medicine herbologyAgriculture sericultureSilk industryArchitecture classic gardensbridgesTransport navigationMilitary naval By era HanTangSongYuanPeople's Republic agriculturespace vte Contents 1 Early Chinese mathematics 2 Qin mathematics 3 Han mathematics 3.1 Suan shu shu 3.2 The Nine Chapters on the Mathematical Art 3.3 Calculation of pi 3.4 Division and root extraction 3.5 Linear algebra 3.6 Liu Hui's commentary on The Nine Chapters on the Mathematical Art 4 Mathematics in the period of disunity 5 Tang mathematics 6 Song and Yuan mathematics 6.1 Algebra 6.1.1 Ceyuan haijing 6.1.2 Jade Mirror of the Four Unknowns 6.1.3 Mathematical Treatise in Nine Sections 6.1.4 Magic squares and magic circles 6.2 Trigonometry 7 Ming mathematics 8 Qing dynasty 9 Western influences 9.1 Western mathematics in modern China 10 Mathematics in the People's Republic of China 10.1 Performance at the IMO 11 Mathematical texts 12 Mathematics in education 13 See also 14 References 14.1 Citations 14.2 Sources 15 External links Early Chinese mathematics Visual proof for the (3, 4, 5) triangle as in the Zhoubi Suanjing 500–200 BC. Oracle bone script numeral system counting rod place value decimal Simple mathematics on oracle bone script date back to the 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.[citation needed] 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 (only Chinese geometry) and the usage of decimals. Math was one of the Liù Yì (??) or Six Arts, students were required to master during the Zhou Dynasty (1122–256 BC). Learning them all perfectly was required to be a perfect gentleman, or in the Chinese sense, 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 of c. 330 BC, compiled by the followers of Mozi (470–390 BC). 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.[6] 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."[7] 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.[7] It stated that two lines of equal length will always finish at the same place,[7] while providing definitions for the comparison of lengths and for parallels,[8] along with principles of space and bounded space.[9] It also described the fact that planes without the quality of thickness cannot be piled up since they cannot mutually touch.[10] The book provided word recognition for circumference, diameter, and radius, along with the definition of volume.[11] 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 300–250 BC. 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 BC, has revealed some aspects of pre-Qin mathematics, such as the first known decimal multiplication table.[12] 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.[13] Qin mathematics 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 Shihuang (???) ordered many men to build large, lifesize 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 mathematics Further information: Science and technology of the Han Dynasty § Mathematics and astronomy The Nine Chapters on the Mathematical Art. 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 chousuan, consisting of only nine symbols with a blank space on the counting board representing zero.[2] Negative numbers and fractions were also incorporated into solutions of the great mathematical texts of the period.[3] The mathematical texts of the time, the Suàn shù shu and the Jiuzhang suanshu solved basic arithmetic problems such as addition, subtraction, multiplication and division.[3] Furthermore, they gave the processes for square and cubed root extraction, which eventually was applied to solving quadratic equations up to the third order.[4] Both texts also made substantial progress in Linear Algebra, namely solving systems of equations with multiple unknowns.[14] The value of pi is taken to be equal to three in both texts.[15] 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.[3] Mathematics was developed to solve practical problems in the time such as division of land or problems related to division of payment.[16] 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.[17] The Book of Computations and The Nine Chapters on the Mathematical Art provide numerous practical examples that would be used in daily life.[17] Suan shu shu The Suàn shù shu (Writings on Reckoning or The Book of Computations) is an ancient Chinese text on mathematics approximately seven thousand characters in length, written on 190 bamboo strips.[18] 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.[3] 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.[18] The Book of Computations contains many perquisites to problems that would be expanded upon in The Nine Chapters on the Mathematical Art.[18] An example of the elementary mathematics in the Suàn shù shu, the square root is approximated

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