1 Definition
1.1 Objects 1.2 domain2 concept
2.1 pi 2.2 Structure 2.3 Space 2.4 2.6 base 2.5 Symbols 2.7 rigorous logic3 A Brief History
3.1 Origins 3.2 Evolution 3.3 3.4 Higher Elementary4 countries considered history
4.1 bud formation 4.3 4.2 4.5 Decline 4.6 prosperity and development 4.4 4.7 Europe 4.8 China incoming5 Chinese achievements: mathematical theorems
6 mathematics and science
7 math punctuation
8 mathematics culture
8.1 foreign famous saying 8.3 8.2 China International Journal9 learning methods
10 disciplines and subdisciplines grading distribution
1 defines mathematics is the study of the real world and the relationship between the number of spatial form a science. divided into elementary mathematics and advanced mathematics it in the scientific development and application of modern life and production very extensive study and research is essential to modern science and technology basic tools.introduction of mathematical symbols
with the words, mathematics is endless science Mathematics (Pinyin: shù xué; Greek: μαθηματικ; English: (Mathematics / abbreviation: Math), derived from the ancient Greek μθημα (máthēma), it has to learn, learning, scientific meaning, and in addition to a relatively narrow and technical sense - "Mathematics." even in its etymology, the meaning and its adjectives and Learning relevant, will also be used to index learn its plural form in English and in French plural form + es into mathématiques, can be traced back to the Latin neuter plural (Mathematica), the Cicero Translated from the Greek plural τα μαθηματικά (ta mathēmatiká). mathematics in ancient China called arithmetic, also known as arithmetic, and finally changed to mathematics from the content of mathematics is divided into three parts, part geometry, and the other part is the algebra , the last part is the analysis of learning (Calculus) Mathematics is the use of sign language studies quantity, structure, space model changes and concepts of a discipline. objects with the use of basic knowledge of mathematics is an integral part of life of individuals and groups of part of the basic concepts of its refinery back in ancient Egypt, Mesopotamia and ancient mathematics within the ancient Indian text within a matter of considerable see, and since then, its development would have a slight continuous progress, until 16 century Renaissance, with its combination of geometry and arithmetic form of analytic geometry, and the development of a more subtle calculus, because of new scientific discoveries and the relative role of generating mathematical knowledge has led to the acceleration of innovation, until today .
three-dimensional structure
Today, mathematics is used around the world in different fields, including science, engineering, medicine and economics. mathematical applications in these areas is often called Applied Mathematics , sometimes provoke new mathematical discoveries and lead to the development of a new discipline. mathematicians also study pure mathematics, which is the mathematics itself, without any practical application as the target. although many began to study pure mathematics, but then will found many applications. was founded in the 1930s in France Bourbaki school of thought: mathematics, at least pure mathematics, is the study of the theory of abstract structure. structure, that is, the initial concepts and axioms of deductive systems. Cloth school of thought There are three basic abstract structure: algebraic structures (groups, rings, fields, Georgia ......), coherent structure (partial order, total order ......), the topology (neighborhood, limit, connectivity, dimension ......) . areas of mathematical calculations on the needs of business, number of understanding between the number of systems, measuring land area and predict astronomical concepts which require roughly four kinds and quantity, structure, space, and change (ie arithmetic, algebra, geometry and analysis) on a wide range of areas such as mathematics relevant attached addition to the above main concern, there are also used to explore the core to other areas by the mathematical link between the child on the field: to logic, to set theory (basic), to different scientific the experience of mathematics (applied mathematics), and relatively modern to uncertainty rigorous learning .2 concept pi number of learning from a few, at the beginning of the familiar natural numbers and integers and are described in the arithmetic within the rational and irrational numbers Another area of research for its size, this leads to infinite cardinality and after another concept: the aleph numbers, which allows unlimited size can be made between the sets meaningful comparison.pi π
The first scientific approach seeks pi value of people is perhaps Archimedes, draw accurate to two decimal places the value of π. mathematician Liu Hui in the comment " Nine Chapters on Arithmetic "is obtained by cutting circle approximation of π. draw. mathematician and astronomer Zu through hard work, his first time in the world history of mathematics will be pi (π) values calculated to seven decimal places, ie between 3.1415926 to 3.1415927. structure and function of many shown with a collection of other mathematical objects all have implicit structure structural properties of these objects are discussed in groups, rings, and other body that is itself an abstract system of this object. This is the realm of abstract algebra In this there is a very important concept, namely vector and generalized to vector spaces and studied in linear algebra. vector mathematics research combines three basic areas: volume, structure and spatial The vector analysis will be extended to a fourth of its basic areas, namely changes in Spacegeometry
derived from the European Space Research geometry. Trigonometry is a combination of space and number, and contains a very famous Pythagorean theorem. now more promotion of space research to a more high-dimensional geometry, non-Euclidean geometry and topology. count and space analytic geometry, differential geometry and algebraic geometry have a very important role in differential geometry has a fiber bundle and the manifold computing concepts in algebra Geometry has a solution set of polynomial equations, such as geometric objects such as a description, a combination of numbers and spatial concepts; also has a topological group study, a combination of structure and space. Lie been used to study space, structure, and changes based on order clear mathematical foundation, mathematical logic and set theory and other areas have been developed out of the German mathematician Cantor (1845-1918) pioneered set theory, boldly, "infinity" march, in order to give the various branches of mathematics to provide a solid foundation while the content itself is quite rich, proposed the existence of actual infinity for the future development of mathematics has made an invaluable contribution.surface of revolution
set theory in the early 1900s has gradually penetrated into the various branches of mathematics, became a theory, measure theory, topology and mathematical sciences indispensable tool in the early 20th century the world's greatest mathematician Hilbert spread in Germany Cantor's ideas, called him "a mathematician's paradise" and "the most amazing product of mathematical thinking." British philosopher Bertrand Russell hailed the work of Cantor "This era can boast the most tremendous work." logical-mathematical logic to focus on the mathematical axioms placed on a solid framework, and to study the results of this structure. On its own, it is not Godel second incompleteness theorem of origin, and this is perhaps the most widely circulated logical outcome - there is always one that can not be proven true theorems of modern logic is divided into recursion theory, model theory and proof theory, and theoretical computer science and is closely linked sex. symbol in ancient China may be the world's first operator to raise one of the symbols used, the time of its invention, a non-sophisticated in modern notation, simple expressions may depict the complex concept. This is an image that is Simple equations arising from our most used today are mathematical symbols to the 16th century before it was invented. Prior to this, mathematics was written out of the text, which is a development of mathematics will be locked painstaking process. nowadays Mathematical symbols makes it easier for experts to control for the purpose, but a bit overwhelming for beginners but often this it is extremely compressed: a small amount of symbol contains a large number of messages. as music notation in general, today there is a clear mathematical symbols grammar and writing is difficult in other ways message encoding. rigorous mathematical language also find it difficult for beginners How to make these words have a more precise than ordinary language meaning. has vexed the beginner, words such as open and domain In mathematics has a special meaning. mathematical terms are also included as embryos and integrability other proper nouns, but the use of these special symbols and proprietary terminology has its reasons: mathematics requires more precision than everyday language of mathematics home language and logic of this on the accuracy requirements referred to as "strict."trigonometric
rigorous mathematical proof is a very important and fundamental part of Mathematicians want their theorems to systematic reasoning to go by the axiom be deduced. This is to avoid false " theorem ", according to the unreliable intuitive, and this case in history there have been many examples in mathematics were expectations of rigor because of time difference: the Greeks expect a careful argument, but in Newton's era , the method used is less rigorous. Newton made in order to solve the problem definition to the nineteenth century was re-analyzed with caution and formal proof to deal with. Today, mathematicians are constantly arguing rigorous computer-assisted proof degrees when measured at a large number of difficult to verify, it also proved to be effective in rigorous hard to say because the age difference, but also erase a lot of knowledge, but the math never forgotten, never spread wisdom originated .3 Brief History of Mathematics, originated in the production of early human activity. was one of six arts in ancient China (Liu Yi called "numbers"), also ancient Greek scholars as the starting point of philosophy, "knowledge based", from ματθημα (máthema) ( "science, knowledge, learning"). Evolutionadditive derived from simple abstract ideas
about the evolution of mathematical abstraction can be seen as sustainable development or extension of the theme, while the eastern and western cultures also used a different angle, the European civilization developed geometry, while China developed similar to the now general arithmetic algebraic The first one is about the concept of abstract numbers (our count chips), its two apples and two oranges between a the same kind of thing perception is a major breakthrough in human thought in addition to how to count the actual cognitive quantity of material, prehistoric humans also learn how to count the number of abstract substances, such as time - days, seasons and years. arithmetic ( subtraction, multiplication and division) is also naturally produced. ancient monument also confirmed the then existing [1] the knowledge you need further writing or other digital recording systems, such as wood or operator Inca empire used to store data The Chip in history there were many and divergent number system from the beginning of the historical era, the main principle of mathematics is to do astronomy, the rational allocation of crop land, taxation and trade and other related multi-computing, in order to to understand the relationship between numbers, to measure land, and to predict astronomical events and the formation of these needs can simply be summarized as math right quantity, structure, space, and time studies. elementary (Lv. 1 Math) of AD 200 Liu Wei years annotation "Nine Chapters on Arithmetic," and after the Tang Dynasty, AD 600 years ago to form the "count by ten book", marking the establishment of a complete system of arithmetic Western Europe through the Renaissance to the 16th century it, elementary algebra, and trigonometry and other elementary mathematics has been largely complete, but no concept of limit, known as fuzzy mathematics, we can not give him a definition, it is not necessary. Higher (Lv. 2 Math) 17 century variable concepts of production so that people began to study changes in the quantity and amount of mutual relations between each other and graphics transform the study of classical mechanics of the process, a combination of geometric precision thinking calculus method is found. along with the natural sciences and technology, further development for the study of mathematics arising basis and mathematical logic, set theory began to slowly develop .4 countries considered ancient history of mathematics mathematics, is the ancient Chinese science an important subject, according to the characteristics of the development of mathematics in ancient China can be divided into five periods : bud; system formation; development; prosperity and integration of Western mathematics. bud primitive stage, private ownership and exchange of goods produced, the number and shape of the concept has been further developed, Yangshao period pottery, has carved above symbols indicating 1234. to primitive stage, has begun to use text symbols instead of Jieshengjishi the Xi'an Banpo pottery available 1 ~ 8 dots composed of equilateral triangles and squares for the 100 small squares pattern , Banpo Ruins of houses are round and square base in order to draw a circle for the parties to determine straight, people also created rules, moment, accurate, rope and other mapping and measurement tools. According to "Historical Records summer of the century "records, Yu flood have been using these tools. quotient mid, Oracle has been produced in a decimal number and notation, with the largest number of thirty thousand; Meanwhile, Yin with ten Heavenly Stems and twelve Earthly Branches composed six decades, Yi Chou, Bing Yin, Dingmao other 60 names to remember 60 days of the date; in the Zhou Dynasty, again previously yin yang symbol represents eight kinds of things that constitute the gossip develop sixty-four Gua, which means that 64 kinds of things.Zhou Bi Suan Jing
the first century BC, "Zhou Bi Suan Jing" said the early Western Zhou Dynasty moment measurements with high, deep, wide, far way, citing Gougu Xing hook three, shares four, five and chord ring moments can circle are examples. "Book of Rites" article mentioned in the Western Zhou Dynasty nobility had to learn from the age of nine and counting the number of ways they want Shouli, music, archery , riding, writing, arithmetic training, as "six arts" one of the few has started to become specialized courses on the occasion of the Spring and Autumn, counsel has been universal application, counsel notation has been made to use a decimal value, this notation number method development of mathematics in the world there is a landmark. Measurement of mathematics in this period the production has wide application in mathematics is also a corresponding increase in the Warring States Period contending also promote the development of mathematics, especially for proof and some propositions controversy directly related to mathematics. masters think after abstract nouns after their original concept with different entities, they proposed "Moment parties, rules can not be a circle", the "freshman" (infinity) is defined as "to Big no outside "," small one "(infinitesimal) is defined as" to small without internal "(similar to today's calculus infinity and infinitesimal). also proposed a" foot of the whip, whichever half day, eternal inexhaustible "and other proposition is that the name comes from the Mohist things, names from different aspects and different depths of the reactants. Mohists give some mathematical definitions, such as round, square, flat, straight, sub (tangent), end (point) etc. (equivalent to simple geometry). Mohists disagree "foot of the whip," the proposition, put forward a "non-half" to refute the proposition: the line segment divided by half and half to go on infinitely, then he will appear a can not be divided "non-half", the "non-half" is the point. masters thesis discusses the finite length can be divided into an infinite sequence of Mohist this proposition is that the infinite variations and segmentation results and Mohist's mathematical definitions and mathematical propositions discussions on the mathematical theory of ancient China's development is of great significance. formationNine Chapters on Arithmetic
Han is rising period of feudal society, economy and culture have developed rapidly. ancient Chinese mathematical system is formed in this period,R4i DS, it is the main indicator is the arithmetic has become an specialized disciplines, as well as the "Nine Chapters on Arithmetic" to represent the mathematical writings appeared. "Nine Chapters on Arithmetic" is the Warring States, Qin, Han feudal society founded and consolidation period summary of the development of mathematics, mathematics achievement of its terms, called is the world famous mathematical example scores four operations, today have surgery (the West said three rate method), open squares and open cube (including numerical solution of quadratic equations), insufficient surplus surgery (the West called dual tried), a variety of area and volume formulas, linear equations solution, positive and negative numbers subtraction operation rules Gougu Xing solution (especially the Pythagorean theorem Pythagorean numbers and seek ways), etc., the level is very high which Equations for positive and negative Number subtraction rule on the development of mathematics in the world is far ahead. their characteristics, it forms a center to counsel, and ancient Greek mathematics completely different independent system. "Nine Chapters on Arithmetic" There are several notable features : using disaggregated set of chapters in the form of mathematical problems; formula are from the counsel notation developed; in arithmetic, algebra, and few involve graphic nature; emphasis on the application, the lack of theoretical explanations, etc. Finally a book in the Eastern Han Dynasty the early years of the "Nine Chapters on Arithmetic", excluding the Warring States period in contending that appear and Mohist attention definitions and logical discussion with the then emphasis on production and life are closely combined math problem and its solution, which is the social The development is entirely consistent. "Nine Chapters on Arithmetic" In the Sui and Tang dynasties had spread to Korea, Japan, and became mathematics textbooks in these countries at the time and it's some of the achievements made as a decimal value, now have surgery, surgery such as insufficient surplus also spread to India and Arabia, and spread to Europe via India and Arabia, and promote new developments in the world of mathematics. development of the Wei, Jin Period metaphysics appears, is not bound Confucian classics, thought more active; it's long debate win, but also the use of logical thinking, analytical argumentation, which are conducive to improving mathematical theory. Wu Zhao Shuang note "Zhou Bi Suan Jing", Han early Wei Xu Yuezhuan "Nine Chapters on Arithmetic" Note, Wei Jin end early Liu Hui essays, "Nine Chapters on Arithmetic" note, "Nine Chapters weight difference map" all appear in this period. Zhao Shuang Liu Hui's work with mathematical system in ancient China has laid a theoretical foundation. Zhao Shuang theorems of mathematics in ancient China and and the derivation formula proved one of the earliest mathematicians which he "Zhou Bi Suan Jing" book supplement of the "Pythagorean round side view and Notes" and "Hidaka chart and note" is very important mathematical literature in "Pythagorean Round Square and note" in which he proposed to prove the Pythagorean theorem reconciliation Gougu Xing chord diagram of five formulas; in the "Hidaka chart and note", he graphically area prove the universal application of the Han Dynasty weight difference formula Zhao Shuang's work is of a groundbreaking development of mathematics in ancient China occupies an important position. Liu Hui and Zhao Shuang about the same time, he inherited and developed the Warring States period and Mohist thought, advocated for some particular mathematical terms important mathematical concepts give a strict definition that must be carried out on the mathematical knowledge "reasoning" in order to make concise rigorous mathematical works, which will help readers of his "Nine Chapters on Arithmetic" note not only of the "Nine Chapters on Arithmetic" approach, formulas and theorems for general explanation and derivation, but also in the process of discourse has great development. Liu Hui create cutting circle, the idea of using the ultimate proof formula for area of a circle, and the first method considered by theoretical circumference was 157 / 50 and 3927/1250. Liu Hui segmentation method with infinite proved right angle bevel angle tetrahedron with constant volume ratio of 2:1, to solve the general three-dimensional volume of the key issues in proving the square pyramid, cylinder, cone, round table volume, the Liu Hui volume of a sphere is proposed to solve the right way.Zu
Eastern Jin Dynasty, Chinese long period of war and the state of North-South divide. Zu father's work is the economic and cultural southward after the development of mathematics southern representative work, they are Liu Hui Note "Nine Chapters on Arithmetic", based on the traditional mathematical greatly step forward. their mathematical work are: calculate pi ~ 3.1415927 3.1415926 between; proposed Zu Geng principle; proposed quadratic and cubic equations method etc. Presumably, Zu Liu Hui cutting circle method, based on the calculated inscribed regular 6144-gon and n 12288-gon to obtain this result, he has a new way to get pi two fractional value, ie about rate 22/7 and close ratio 355/113. Zuchongzhi this work, making China the pi calculation, than Western leader about a thousand years; Zu's son Zu Geng summarizes Liu Hui of the work, that "power potential both with the plot intolerance "that the two high-dimensional, if any of its high level of cross-sectional area equal, the two dimensional volume equal, which is the famous Zu Geng axiom Zu Geng apply this axiom to solve the Liu Hui unresolved ball volume formula Emperor ambitious, massive construction projects, the objective is to promote the development of mathematics. Tang Dynasty WANG Xiao Tong's "Ji Gu Suan Jing", focuses on civil engineering, earthwork calculations, engineering division, as well as warehouses and acceptance cellar computational problems, reflecting this period mathematical situations. WANG Xiao-tong without using mathematical symbols in the case, stand out the digital cubic equation, not only solved the social needs, but also for the subsequent Tianyuan surgery to establish the foundation. Moreover, the traditional The Gougu Xing solution, WANG Xiao-tong cubic equation is solved numerically.island Suan Jing
feudal rulers inherit the Sui Dynasty Tang Dynasty, 656 years of the establishment of mathematics at Imperial College Hall, a PhD and assistant operator, 30 students from other compilation Taishiling Chunfeng comment " The Ten count "as a mathematics student textbooks Museum, Ming examinations were also considered these operators shall prevail. Chunfeng such codification of the" The Ten count, "the preservation of mathematical classics, the mathematical aspects of research literature it makes sense to give "Zhou Bi Suan Jing", "Nine Chapters on Arithmetic" and "island Suan Jing"'s comments, it is helpful to the reader. Sui and Tang dynasties, the calendar needs, day mathematicians founded quadratic function interpolation method to enrich the contents of ancient Chinese mathematics. chip count is the major computational tools in ancient China, one of which has a simple, image, concrete, etc., but there are also a large cloth chip footprint, logistics speed easily when playing with errors caused by errors and other shortcomings, so very early reforms which Tai count, appearances count, three are considered and abacus abacus with beads groove, is technically important reforms, especially " abacus ", it inherits the contemplated five liters decimal system with the advantages of bit values, but also to overcome the count and set the aspect contemplated raising inconvenient drawback is obvious superiority, but because at that time multiplication algorithm is still not carried out in a row. counting beads also did not wear stalls, convenient to carry, it is still not widely used. Tang metaphase, commercial prosperity, figures increased, urgently requires reform calculation method from the "Book of Tang" and other literature left to count the book titles, you can The algorithm is mainly seen reforms to simplify multiplication, division algorithm, algorithms reforms Tang multiplication and division can be performed in a row operations, applicable both to counsel, but also for the abacus. boom 960 years, the establishment of the Northern Song dynasty ends Five Dynasties and Ten Kingdoms separatist situation. Song of agriculture, handicrafts, commerce unprecedented prosperity, scientific and technological advances, gunpowder, the compass, printing three great inventions is in this case economic upsurge widely .1084 annual provincial first secretary times printed publication of "The Ten count", 1213 Martin roll out again for turning moment these are mathematical development to create good conditions from 11 to 14 century, about 300 years, there have been a number of famous mathematicians and mathematical works, such as Jia constitution of the "Yellow Emperor IX algorithm Xicao," Liu Yi's "discussing ancient roots," Horner's "Number Nine Chapters" Li Ye's "cyclometry Sea Mirror" and "Yi Gu speech segment." , Yang Hui's "Detailed IX algorithm," "Daily algorithm" and "Pascal's algorithm," Zhu Shijie's "mathematics enlightenment", "four yuan Yu Kam", etc., many areas have reached the peak of ancient mathematics, some of which was also the world's mathematical achievements peak.Pascal's Triangle
From the open square, open cube to four times more than prescribing, is a leap in understanding, to achieve this leap is Jia Xian. Pascal in "Nine Chapters on Algorithms compile class "contains Jia Xian" increase by Kaiping method "," increase multiplicative open method "; in the" Detailed IX algorithm "contained Jia constitution 'prescribing practices bare" map, "increase multiplicative method for solving inexpensive grass" and with the increase multiplicative method to open fourth side open example of these records can be determined according to the constitution has been found that two Jia coefficient table, creating the increase multiplicative method to open this two mathematics achievement for the entire Song significant impact, including JIA Gazette Pascal triangle triangle than in the West long before 600 years. increased by the open method is extended to digital high-order equation (including the case of a negative coefficient) solution is Liu Yi. "Pascal's algorithm" and "Rebellion than the class multiplication and division McNair Law" volumes, introduced the original book 22 quadratic and a quartic equation, which is multiplied with the open method of solution increased more than three times the earliest examples of high-order equation. Horner is a high-order equations for the synthesizer, he "Number Nine Chapters" and collected 21 opened with increase multiplicative method for solving equations of higher (maximum number is 10) issues in order to accommodate increased by open method calculation procedures, Horner provisions of the constant term is negative, the higher equation method is divided into various types, when a non-integer roots of the equation,R4i 3DS, Horner taken to continue rooting decimal, or reduce the powers of the root transformation equation coefficients of the denominator, numerator constant to represent the non-integer portion of the root , which is "Nine Chapters on Arithmetic" and Liu Hui Note the development of processing methods irrational numbers in rooting second digits, Horner also proposes a coefficient constant except for the root of the second digit of the trial division, which Horner's method than in the West as early as the first 500 years of the Yuan Dynasty astronomer Wang Xun, GuoShouJing etc. in the "THE HISTORY" and solve the problem of three interpolation function. Horner in the "push Zhuishu Star" title, Zhu Shijie in the "Four Elements Kam, "" If the elephant tricks "problem mentioned interpolation method (they call Zhaocha surgery), Zhu Shijie get a four function interpolation formula with Tianyuan (equivalent to x) as an unknown symbol, standing out higher-order equation , the ancient technique known as Tianyuan, which is China first introduced the history of mathematics symbols, and use symbolic computation to solve the problem of establishing high-order equation. earliest extant writings Tianyuan Li Ye's "cyclometry sea mirror." from Tianyuan extended to binary, ternary and quaternary high-order simultaneous equations, is yet another outstanding mathematician Song creation. has been transmitted, and the creation of this outstanding systematic exposition is Zhu Shijie of the "four yuan Yu Kam . "four yuan Yu Kam
Zhu Shijie higher quaternion representation of simultaneous equations is developed on the basis Tianyuan up, he put on a constant central, four dollars each time Power on the up, down, left, and right directions, the other on the four quadrants. Zhu Shijie's greatest contribution is to present four yuan elimination method, the method is to first select one yuan for the unknown, the other element consisting of As this unknown polynomial coefficients, fitted to a number of one yuan higher order equation, and then multiply the destructive method of application interoperability gradual elimination of this unknown Repeat this step can eliminate the other unknowns, the final increase multiplicative method for solving open, which is a linear significant development solution method group, than in the West similar way as early as 400 years. Gougu Xing solution in the Song and Yuan Dynasties there are new developments, Zhu Shijie in the "mathematics enlightenment" volume and made known to hook chord, chords and solving Gougu Xing shares approach complements the "Nine Chapters on Arithmetic" deficiencies. Li Ye in the "cyclometry Sea Mirror" Pythagorean Yung Yuan for a detailed study of the issue, to get nine Yung Yuan formula, greatly enriched the content of geometry in ancient China Given that the angle between the ecliptic and the equator and the sun from the winter solstice to the vernal equinox longitude I run arc, arc I seek ascension and declination in degrees, is a solution of spherical right triangle problem, the traditional calendar is calculated by interpolation Yuan Dynasty Wang Xun, GuoShouJing other solution is to use traditional Gougu Xing, Shen Kuo Yuan with surgery and Tianyuan will solve this problem, but they get is an approximate formula, the result is not precise enough, but their entire projection step is correct correct, from a mathematical sense, this approach opens up the pathway leading to spherical trigonometry in ancient China computing technology is the culmination of the reform in Song and Yuan Dynasties. Yuan, Ming and historical literature contains a wealth of practical arithmetic bibliography of this period, their number is more than the Tang Dynasty, the main contents of the reform is still multiplication and division with algorithms reforms, abacus beads may have occurred in the Northern Song Dynasty, but as if both the modern abacus abacus beads, another set of improved algorithms and formulas, then they should say that it finalized in the Yuan Dynasty and Yuan mathematics prosperity, social and economic development and the inevitable result of the development of science and technology is the inevitable result of the development of traditional mathematics. Moreover, mathematicians scientific thought and mathematical thinking is also very important. Song mathematicians are in varying degrees, as opposed to the number of ancient Chinese philosophy of mysticism. Horner Though there have been claims of Mathematics and yin and yang from the same source, but he later realized that "pass the gods." math does not exist, only "by the World Service class all things" mathematics; Morrow in the "four yuan Yu Kam," the preface's "illusion of real use to ask real virtual" represents a highly abstract thinking way of thinking; Pascal's study of the structure on the aspect graph reveals the essence of Luoshu, forcefully criticized as the number mysticism, all of which is undoubtedly an important factor in promoting the development of mathematics. fading from the Ming Dynasty, China began to enter the late feudal society, feudal rule who implement totalitarian rule, advocacy idealist philosophy, the implementation of stereotyped examination system in this case, in addition to the abacus, the gradual decline of the development of mathematics. incoming Renaissance, Europe has been widely developed geometry, algebraic form Analytic theory to solve geometric problems. 16th century, Western geometry gradually introduced into China, and China's ancient arithmetic combine to make China Western Mathematical Research and blend the emergence of a situation; Opium War, modern mathematics began to spread into China, China will be transferred to a mathematical study of ancient arithmetic, geometry and mathematics of modern Western-oriented period. Eurasia from the Han Dynasty Silk Road China Unicom began to Ming Dynasty, the commodity economy gradually development, prosperity and development of this business is adapted to the popularity of abacus early Ming "Qui-phase four of the right words miscellaneous word" and "Luban wooden Sutra", suggesting that the abacus has been very popular former children learn reading textbooks, which the abacus as a family essential items included in the general wood furniture handbook.abacus
With the popularity of the abacus, abacus algorithms and formulas tend to improve gradually, such as Wang Su and Cheng Dawei to increase and improve the hit return, from a pithy formula; XU Xin Lu and Cheng Dawei increase Add, subtract formulas and division widely used normalized addition, in order to achieve the abacus arithmetic all formulas of; Zhu Zai moisture and Cheng Dawei to counsel open squares and open cube method is applied to the abacus, Cheng Dawei with Abacus Solutions Digital quadratic, cubic equations, etc. Cheng Dawei's writings circulated widely at home and abroad, a significant influence. 1582, the Italian missionary Matteo Ricci to China, in 1607, he met with Xu Guangqi translated "geometry "former six volumes," Measuring the Dhamma "volume, and Li algae Compile" Won Yung than justice "and" Tong Wen count means ".1629, Xu was rites appointed governor repair calendar, under his auspices, the compiler" Chongzhen almanac " 137 volumes. "Chongzhen almanac" is to introduce the European astronomer Tycho's geocentric theory as the mathematical basis of this doctrine, Greek geometry, trigonometry several European Yushan, and Napier count chips, such as Galileo proportional regulation also introduce computational tools come in the incoming mathematics, the greatest impact is "Geometry". "Euclid" is the Chinese translation of the first mathematical writings, most mathematical terms are first, many of which still follow. Xu Guangqi that it "without doubt", "Do not change", "no one universally improper learn". "Euclid" is the Ming and Qing dynasties mathematician math book required reading for their research work influential. Second, is the most widely used trigonometry, trigonometry introduce Western writings have "big test", "cut round eight lines Table" and "measure all righteousness". "big test" is mainly explained triangle eight lines (sine, cosine, tangent, cotangent, secant, cosecant, versine, I vector) the nature of the manufacturing methods and the use of tables Table method. "measure all righteousness", apart from some "big test" the missing plane triangle, the more important is the plot of the sum and difference formulas and spherical trigonometry, all of which, at the time the calendar with the translation work is with the use of. 1646, the Polish missionary to China Mooney Court, following his study of Western science has Xue Feng oak, Fang Tong etc. Mooney Court after the death of Xue Feng oak According to their study, compiled, "calendar learned through", trying to digest France Sifa up. "calendar learned through" the main content of the mathematics scale logarithmic tables, "proportional four-wire new table "and" Triangle algorithm. "the first two books is to introduce the British mathematician invented upgrading of Napier and Briggs logarithm after a book except" Chongzhen almanac "describes a spherical triangle, there are half-angle formula , semi-arc formula Deshi proportional, proportional Nessler etc. Fang Tong "written several derivative" logarithmic theory explained. logarithmic incoming is very important, it is in calendar calculations are applied immediately Qing beginners study experiences and write books and Western mathematics has handed down a lot, have a greater impact Xi elaborated, "graphic", Mei Wending "Mei's books series to" (of which 13 kinds of mathematical works of 40 volumes), the annual Xi Yao, "Inspection", etc. Mei Wending is the culmination of those who focus on Western mathematics his traditional mathematics of Linear Equations, Gougu Xing solution and demand high power of positive root methods, collation and research, so that