Historical development of mathematics Part II (Still Continues)

Egypt Mathematician. Mathematics developed by the Egyptians refer to mathematics written in the language of Egypt. Since the hellenistic civilization, because the Greek had a change in the life sciences, it has since replaced Greek as the language of the Egyptian language written for the educated Egyptians, and since that Egyptian mathematics merged with Greek and Babylonian mathematics that evokes hellenistic mathematics. Assessment of mathematics in Egypt continued under the leadership of Islam as a form of development and mathematics education from Islam, so that Arabic became the written language of Egyptian intellectuals. (Source: from http://google.com/images)

In the Wikipedia site, mention writing the longest Egyptian mathematics was Rhind Gazette (sometimes referred to as "Ahmes Gazette" by the author), supposedly from the year 1650 BC, but maybe it is a copy sheet of the documents that are older than that of the Middle Kingdom 2000-1800 years BC. It is a manual instruction sheet for students arithmetic and geometry. In addition to providing extensive formulas and ways of multiplication, partially, and workmanship fractions, it is also a proof sheet for other mathematical knowledge, including composite and prime numbers; the average arithmetic, geometry, and harmonics, and a simple understanding of the Sieve of Eratosthenes and perfect number theory (ie, number 6). Sheet also shows you how to solve linear equations also ranks first order arithmetic and geometry. 

Also three geometrical elements in the piece is written in the simplest discussion implies Rhind on analytic geometry: (1) first, to obtain an accurate approximation of less than one percent, (2) second, the efforts of ancient squared circle, and (3) Third, the use of cotangent earliest.

Other important Egyptian mathematical texts is a sheet of Moscow, also from the Middle Kingdom era, beginning about 1890 BC. This text contains the word or question about the story, which perhaps is intended as entertainment. One matter that is deemed to have a special method to resolve is the calculation of a room built like a pyramid. And after finally growing research note, sheet Berlin (approx. 1300 BC) indicates that ancient Egyptians could solve algebraic equations of order two.

Greek Mathematician. Greek mathematics refers to mathematics written in Greek between 600 BC to 300 AD Greek mathematicians lived in cities along the eastern Mediterranean, from Italy to North Africa, but they dibersatukan by the same culture and language. Greek mathematician in the period after Alexander the Great is sometimes called Hellenistic mathematics. 

Greek mathematics is more weighty than the mathematics developed by its predecessor cultures. All pre-Greek mathematical texts that are still preserved shows the use of inductive reasoning, ie, repeated observations are used to establish a rule of thumb. In contrast, the Greek mathematicians use deductive reasoning. The Greeks used logic to derive conclusions from definitions and axioms, and use of mathematical rigor to prove it.

Believed to be commenced by the Greek mathematician Thales of Miletus (about 624 to 546 BC) and Pythagoras of Samos (about 582 to 507 BC). Although the disputed expansion of their influence, they may be inspired by Egyptian and Babylonian Mathematics. According to legend, Pythagoras safari to Egypt to learn mathematics, geometry, and astronomy from Egyptian priests. 

Thales used geometry to solve problems calculating the height of the pyramids and the distance the boat from the shoreline. He is credited as the first to use deductive reasoning to be applied to geometry, with the lower four corollary of the theorem of Thales. The result, he is considered the first true mathematician and the first person to produce mathematical discovery. Pythagoras founded the school of Pythagoras, who claimed that mathematic is the master of the universe and the motto is "all is number". The school of Pythagoras who roll the term "mathematics", and it is they who set about mathematical assessment. The school of Pythagoras regarded as the inventor of the first proof of the theorem of Pythagoras, though note that the theorem has a long history, even with evidence of irrational numbers. 

Eudoxus (about 408 BC to 355 BC) developed the method of exhaustion, a stub of the modern Integral. Aristotle (about 384 BC to 322 BC) began to write the laws of logic. Euclid (about 300 BC) is the earliest example of the format still used in mathematics today, namely definitions, axioms, theorems, and proofs. He also reviews the cone. His book, Elements, known in all the educated people in the West until the mid-20th century. In addition to the well-known theorem of geometry, such as the Pythagorean theorem, Elements includes a proof that the square root of two is irrational and there are infinitely many prime numbers. Sieve of Eratosthenes (about 230 BC) was used to find prime numbers. 

Archimedes (about 287 BC to 212 BC) of Syracuse using the method of exhaustion to calculate the area under the arc of a parabola with the summation of an infinite sequence, and provide a fairly accurate approximation of Pi. He also reviewed the spiral up to its name, volume formulas rotate objects, and the pilot system to express extremely large numbers. 

Chinese Mathematics. Chinese mathematics beginning is different when compared with that from other parts of the world, so it makes sense when considered as a result of independent development. Mathematical writings are considered the oldest of the Chou Pei Suan Chinese Ching, dates to between 1200 BC to 100 BC, although the rate of 300 BC is also quite reasonable. 

This is a special note of the use of Chinese mathematics is a decimal positional notation system, which is also called "trunk number" in which different codes are used for numbers between 1 and 10, and other codes as powers of ten. Thus, the number 123 is written using the symbol for "1", followed by the symbol for "100", then the symbol for "2" followed by the symbol separately "10", followed by the symbol for "3". In this way, the number of the most advanced systems in the world at that time, may be used several centuries before the period before the development of AD and of course the Indian number system. Numbers rod allows the presentation of the desired number and allows the calculations carried out on the suan pan, or (Chinese abacus). Suan pan discovery date is uncertain, but the earliest writings dating from 190 AD, in the Additional Notes on the work of Xu Yue Picture Arts. 

The oldest preserved works on geometry in China comes from the canonical regulation philosophy Mohisme circa 330 BC, compiled by the followers of Mozi (470-390 BC). Mo Jing describes the various aspects of the many disciplines related to physics, and also provide a wealth of information a little math. 

In the year 212 BC, Emperor Qin Shǐ Huang (Shi Huang-ti) commanded all the books in the Qin Empire other than the officially recognized government must be burned. This decree is generally ignored, but the result of this command is so little information about ancient Chinese mathematics is maintained from the time before that. After the burning of books in the year 212 BC, the Han dynasty (202 BC-220 AD) produced works of mathematics which might be an extension of the works are now lost. Most important of all is the Nine Chapters on the Mathematical Art, full title of which comes from the year 179 AD, but as the manifestation under different titles. It consists of 246 questions involving the word agriculture, trade, construction geometry that describes the range of heights and comparison of dimensions for Chinese pagoda towers, engineering, surveying, and materials of a right triangle and π. He also used the Cavalieri principle on volume more than a thousand years before Cavalieri took them in the West. He created a mathematical proof for the Pythagorean theorem, and mathematical formulas for Gaussian elimination. Liu Hui commented on this work in the 3rd century AD.

India Mathematics. Earliest civilization of the Indian subcontinent was the Indus Valley Civilization which arise between the years 2600 and 1900 BC in the Indus River basin. Their cities are geometrically regular, but still maintained a mathematical document of civilization has not been found. 

Vedanta Math commenced in India since the Iron Age. Shatapatha Brahmana (approximately the 9th century BC), up to the value of π, and Sulba Sutras (about 800-500 BC) who is writing that uses the geometry of irrational numbers, prime numbers, and the rule of three cubic roots; counting square root of 2 to a portion of one hundred thousand; provide a wide circle construction method is given over to the square, solve linear and quadratic equations; develop Pythagorean triples algebraically, and provide numerical evidence for the statement and the Pythagorean theorem. 

Panini (roughly the 5th century BC) who formulated the rules of Sanskrit grammar. He uses the same notation with modern mathematical notation, and using meta rules, transformations, and recursion. Pingala (roughly the 3rd century until the first century BC) in his treatise on prosody using the devices corresponding to the binary number system. Discussion of the combinatorics meter corresponds to the basic version of the binomial theorem. Pingala works also contain a basic idea of ​​Fibonacci numbers (called mātrāmeru). 

Surya Siddhanta (about 400) introduced the trigonometric functions sine, cosine, sine and feedback, and put the rules that determine the true motion of celestial objects, which correspond to their actual position in the sky. Cosmological time cycles explained in the caption, which is a copy of earlier work, corresponding to an average year siderik 365.2563627 days, which is only 1.4 seconds longer than the modern value of 365.25636305 days. This work was translated into Arabic and Latin in the Middle Ages. 

Aryabhata, in the year 499, introduced versinus function, producing India's first trigonometric tables of sine, developed techniques and algorithms of algebra, infinitesimal, and differential equations, and obtained whole number solutions to linear equations by a method equivalent to the modern method, along together with calculations [[astronomy] are accurate based on the heliocentric system of gravitation. An Arabic translation of his work Aryabhatiya available since the 8th century, followed by a translation of Latin in the 13th century. He also gives the value of π corresponding to the 62832/20000 = 3.1416. In the 14th century, Madhava of Sangamagrama find Leibniz formula for pi, and, using the 21 tribes, to calculate the value of π as 3.14159265359. 

Sources from Wikipedia.org / mathematics