Here are explained the history and development of the number (number theory) from the ancient time until being used now.
a. History of Ancient MathematicalAt first, in ancient times, many nations who reside along the major rivers. The Egyptians along the Nile in Africa, the people of Babylonia along the river Tigris and Eufrat, Hindu race along the river Indus and the Ganges, the Chinese people along the Huang Ho and the Yang Tze. Nations is in need of skills to deal with floods, drying the marshes, making irrigation to cultivate the land along the river into the agricultural area for the required practical knowledge, that knowledge and mathematical techniques together.History shows that the initial Math from people who reside along the river flow. They require calculations, removal of which can be used in accordance with the changing seasons. Necessary measuring instruments to measure Persil Persil-owned land. The increase of civilization requires evaluating the trade, finance and tax collection. For practical needs it is needed the numbers.The number was originally used only to remember the number, but in the long himpunanelah treasury specialists add mathematical symbols and the right words to define the number then becomes the subject of mathematics is essential for life and we can not pungkiri that in everyday life we will always meet with the name of, because the number is always required both in technology, science, economy or the world of music, philosophy and entertainment, and many other aspects of life.Number of previously used as a symbol to replace an object such as pebbles, twigs, each tribe or nation has its own way to describe the number in the form of symbols.In further development, the X ditemukanlah century Spanish manuscript that contains the number of symbols written by ancient Hindu-Arabic nations and style of writing that has been a symbol of the embryo of writing we used so far.
b. Development of Number Theory1) Number Theory Babylonia quarterBabylonian mathematics refers to the mathematics developed by the people of Mesopotamia (now Iraq) since the beginning of the Sumerian to the beginning of Hellenistic civilization. Called the "Babylonian Mathematics" because the main role of the area of Babylonia as the place to learn. At the time of Hellenistic civilization, Mathematics Babylonian Mathematics united with Greece and Egypt to raise the Greek Math. Then under Islamic Kekhalifahan, Mesopotamia, specialized Baghdad, once again became an important center of Islamic study Mathematics.Contrary to langkanya resources on Egyptian Mathematics, Babylonian Mathematical knowledge passed down from more than 400 plates of clay excavated since the 1850s. Written in nail plates while still wet clay, and baked in the oven or dried in the sun. Some of them were home-based work.Terdini mathematical proof is the work of the people writing the Sumerians, who developed an ancient civilization in Mesopotamia. They developed complex system of metrology since 3000 BC. From about 2500 BC to the face, the Sumerian people write multiplication tables on clay plates and dealing with geometrical exercises and sharing issues. Terdini Trail system also refers to the number of Babylonia during this period.Most of the clay plates are known to originate from the years 1800 until 1600 BC, and covers the topics of fractions, algebra, quadratic and cubic equations, and calculation of the number of regular, inverse multiplication, and the number of prime twins.Plates also include multiplication tables and linear equation solving methods and quadratic equations. 7289 BC Babylonia plates give the approximate to √ 2 accurate to five decimal places.Babylonian mathematics was written using a system of sexagesimal (base-60). From here down the use of 60 seconds to a minute, 60 minutes to an hour, and 360 (60 x 6) degrees to a circle rotation, the use of seconds and minutes on the arc of a circle represents the fraction of degrees. Also, unlike the Egyptians, Greeks, and Roman, Babylonian people have a system where the true value, where the numbers are written in the left column specifies the value that is larger, as in the decimal system
2) Theoretical Number In Ancient Egypt EthnicsEgyptian mathematics refers to mathematics written in the language of Egypt. Since civilization Hellenistic Egyptians melt with math math Greek and Hellenistic Babylonia who raised Math. Continues the study of mathematics in Egypt under the Islamic Caliphate as a part of Islamic mathematics, when Arabic became the written language of Egyptian intellectuals.Egypt's mathematical writings is how long is the Sheet Rhind (sometimes also called "Ahmes Sheet" by the author), is estimated to originate from 1650 BC, but probably the sheet is a copy of older documents from the Central Government, namely the years 2000-1800 BC . User instruction sheet is for students Arithmetic and geometry. In addition to providing extensive formula and methods of multiplication, sharing, and processing breakdown, is also a proof sheet for other mathematical knowledge, including composite and prime numbers; Arithmetic average, geometric, and harmonic and simple understanding of the Sieve of Eratosthenes and theory of perfect (ie, number 6).The sheet also includes how to solve linear equations of the line order Arithmetic and geometry.Other important Egyptian mathematical manuscripts are sheets Moscow, also from the Middle Kingdom period, dated about 1890 BC. This script contains the word or question about the story, which perhaps is intended as entertainment.
3) Theory of Numbers In India EthnicsSulba sutras (about 800-500 BC) is the geometry of the writings of using irrational numbers, prime numbers, the order of three cubic root; calculate the square root of 2 to a portion of one hundred thousand; provide a wide circle construction method approaches the square given, solving linear and quadratic equations; develop Pythagorean triples algebraically, and provide numerical evidence for the statement and the Pythagorean theorem.About the 5th century BC to formulate rules of Sanskrit grammar using the same notation with modern mathematical notation, and using meta rules, transformations, and recursion. Pingala (about the 3rd century until the first century BC) in the pamphlet prosodynya use in accordance with the number of binary systems. Pembahasannya about kombinatorika compatible with a basic version of the binomial theorem. Pingala paper also contains a basic idea of the number of Fibonacci.At about the 6th century BC, Pythagoras developed a group of properties is complete (perfect number), the number bersekawan (amicable number), the number of prime (prime number), the number of triangles (triangular number), the number of squares (square number), the number of hexagons (pentagonal number) and the numbers of polygon (figurate numbers) to another. One of the features of the famous triangle until now called Pythagorean triple, ie: aa + bb = cc of discovery through the calculation of the broad area of square sides are the sides of the triangular square with sloping sides (hypotenosa) is c, and the other side is a and b. Other findings were very popular until now is the classification of prime and composite numbers.The number of prime is a positive integer greater than one that does not have positive factors except 1 and the number itself.Positive number other than one and the other prime number called a composite number. Historical records show that the problem of prime numbers has attracted the attention of mathematicians for thousands of years, especially with regard to how many prime numbers and how the formula can be used to find and make a list of prime numbers.With the expansion of literacy and numeracy systems, methods and procedures developed are aritmetis for track work, particularly to address the general problem, through specific measures, which clearly referred to the algorithm. First the algorithm worked by Euclid.At around 4 century BC, Euclid developed the concepts of geometry and the theory of policy. Book VII of Euclid to take an algorithm to find the Greatest Federation factor of two positive integers using a technique or procedure that efficiently, through a finite number of steps. Word comes from the algorism algorithm.At the time of Euclid, the term is not known. Algorism said came from the name of a famous Muslim and the author of 825 in M., which is Abu Ja'far Mohammed ibn Musa al-Khowarizmi. The end of his name (Al-Khowarizmi), inspired the birth of the term Algorism. Algorithm in terms of vocabulary at the beginning of most of the computer revolution, that is the end of 1950.In the 3rd century BC, marked by a number of theoretical development work Erathosthenes, now known as Screening Erastosthenes (The Sieve of Erastosthenes). In the next six centuries, Diopanthus published a book called Arithmetika, which discusses solving the equations in whole numbers and rational number, in the form of a symbol (not the form / up geometrically, as developed by Euclid). With the work of this symbol, referred to as one of Diopanthus founder of algebra.
4) Theory of Numbers The History of Time (AD)Early rise of modern number theory pioneered by Pierre de Fermat (1601-1665), Leonhard Euler (1707-1783), JL Lagrange (1736-1813), AM Legendre (1752-1833), Dirichlet (1805-1859), Dedekind (1831-1916), Riemann (1826-1866), Giussepe Peano (1858-1932), Poisson (1866-1962), and Hadamard (1865-1963). As a prince of mathematics, Gauss was so entranced to the theory of beauty and charm, and to melukiskannya, it mentions the theory of numbers as the queen of mathematics.At this time, the theory is not only expanding the extent of the concept, but also much applied in many fields of science and technology. This can be seen on the utilization of the concept of the method of lines code, cryptography, computer, and so forth.
c. History of Zero FiguresIntroduced as the number of zeros, and as a symbol to fill the empty space the first time by al-Khwarizmi. Zero (0) is in the English language that could mean zero is empty or blank.Around the year 300 BC the Babylonian had started with two slashes (/ /) to indicate an empty place, an empty column in Abacus. This symbol provides an easy way to determine the place of a symbol. Zero is very useful and is a symbol that describes an empty spot in Abacus, a column with stones placed at the bottom. Its purpose is to ensure that these items are in the right places, the number zero does not have a numeric value of its own.At zero computer can harm the system, because there is no zero mean. Whatever the number multiplied by zero the result is not there. Well this is confusing the calculation operations. Note that this example:0 = 0 (zero equal to zero, true)0 x 3 = 0 x 89 (both zero multiplied by a number, because it will be worth zero)(0 x 3) / 0 = (0 x 89) / 0 (a number divided by the number of the same, will be worth it)3 = 89 (???, these results are confusing)Zero conflict with one of the key principles of western philosophy, a dictum which terhujam roots in the philosophy of numbers and the importance grows Phythagoras of Zeno's paradox. the Cosmos Greek erected on pillars: there is no vacancy.December = Greek cosmos created by Phytagoras, Aristotle and are still enduring Ptolemeus himpunanelah Greek civilization collapse. In this cosmos there is no unavailable. Therefore, most of the two Millennium western people not willing to accept zero.Frightening consequences. The absence of zero inhibits the development of mathematics, science and hinder innovation even more dangerous, demoralize removal system.
Resources:http://eduklinik.info/2010/11/20/sejarah-teori-bilangan/http://translate.google.co.id/translate?hl=id&langpair=en|id&u=http://en.wikipedia.org/wiki/Number
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