Mathematics is an abstract field of knowledge that is built with the help of logical reasoning on concepts such as numbers, figures, structures and transformations. According to Berggren, JL, 2004, the discovery of mathematics at the time of Mesopotamia and Ancient Egypt, based on the many extant originals written by the scribe. Although the documents in the form of artifacts is not too much, but they are considered to be able to express mathematics in these times. Mathematical artifacts found indicates that the Mesopotamia has had many exceptional mathematical knowledge, even though they are still primitive mathematical and not deductively structured as it is now. Mathematics in Ancient Egypt can be learned from the artifacts found are then referred to as the Rhind Papyrus (edited the first time in 1877), has given an idea of how mathematics in ancient Egypt has been growing rapidly. Artifacts were found associated with mathematics-related areas such as the royal kingdom 3000 BC Sumerian, Akkadian and Babylonian regime (2000 BC), and the kingdom of Assyria (1000 BC), Persian (6-4 century BC), and Greece (century to 3-1 BC).
Math Lesson
In ancient Greece the least important mathematician noted that Thales and Pythagoras. Thales and Pythagoras pioneered thinking in the field of geometry, but Pythagoras who start doing or making mathematical proofs. Until the reign of Alexander the Great of Greece and thereafter, has recorded monumental work of Euclid's work in the form of a book entitled Elements (elements) which is the first geometry book compiled by deduction. Important treatise of the early period of Islamic mathematics much missing, so there are still unanswered questions about the relationship between the many early Islamic mathematics and mathematics from Greece and India. In addition, the number of relatively small number of documents that causes us difficulty to trace the extent of the role of Islamic mathematicians in the development of mathematics in Europe next. But clearly, Islamic mathematicians sizable donation in conjunction with the rise of modern thought emerged himpunanelah dark ages until around the 15th century BC himpunanelah.
The invention of the printing press printing in the modern era, which is about the 16th century, mathematicians have allowed each other to communicate more intensively, so as to publish works great. Up comes the Hilbert era who sought to create a system of mathematics as a single, complete and consistent. But the effort Hilbert then be broken or found mistakes by his own student named Godel stating that it was probably invented mathematics single, complete and consistent. Geometry and Algebra Problems ancient, can be found in the documents stored in Berlin. One of the problems is for example estimated length of the diagonal of a rectangle. They menggunakanhubungan between the long sides of the rectangle and then they find the shape of a right triangle. The relationship between the sides of a right-angled This became known as the Pythagorean Theorem. The Pythagorean theorem is actually been used for more than 1000 years before being discovered by Pythagoras.
The Babylonians had discovered sexagesimal number system which is then useful to perform calculations related to the sciences of astrology. Astronomers at the time of Babylon have been trying to predict an event by associating with astronomical phenomena such as lunar eclipses and planetary tipping point in the cycle (conjunction, opposition, stationary point, and the visibility of the first and last). They found the technique to calculate the position (expressed in degrees of latitude and longitude, measured relative to the track the apparent motion of the Sun yearly) with successively adding the appropriate terms in arithmetic progression. Mathematics in Ancient Egypt as well as due to the influence of Masopotamia and Babylon, but also influenced by the context of Egypt which has a wide stream and long live the Egyptian civilization. Problems arise because the public relations activities of the Egyptians face survive in natural conditions that can lead to conflict between them, such as how to define the boundary edge of paddy fields or himpunanelah Nile flood occurred that resulted in their land silted up to a few meters. From one of these cases later appeared notion or idea of the area, boundaries and forms. So in the days of Ancient Egypt, Geometry has grown rapidly as a branch of mathematics.
In a relatively short time (maybe only a century or less), a method developed by the Babylonians and Ancient Masir have come into the hands of the Greeks. For example, Hipparchus (second century BC) preferred approach to geometric Greek predecessors, but then he uses the method of Mesopotamia and adopted the style sexagesimal. Through the Greeks were forwarded to Arab scientists in the Middle Ages and from there to Europe, where it remained prominent in mathematical astronomy during the Renaissance and early modern period. To this day remain in use minutes and seconds to measure time and angles. Aspects of Babylonian mathematics that has come to Greece has increased the quality of the mathematical work with not only believe denganbentuk-physical form only, melainan gained confidence through mathematical proofs. The principles of the Pythagorean theorem sudal known since the days of Babylon which is about a thousand years before the Greek era, began to be proven mathematically by Pythagoras in Ancient Greece.
In Ancient Greece, during the period from about 600 BC to 300 BC, known as the classical period of mathematics, mathematics changed from practical functions into a coherent structure of deductive knowledge. Change the focus of practical problem solving to the knowledge of the truth and the development of a general mathematical objects mathematical theories transform into a discipline. The Greeks showed concern for the logical structure of mathematics. The followers of Pythagoras were trying to find the exact
The length of the hypotenuse of a right triangle. But they can not find a certain number of the same scale that applies to all the sides of the triangle. It is then known as Incommensurability issue, namely the scale is not the same in order to obtain a certain number for the hypotenuse. If forced to use the same scale (or commensurabel) then in the end they found that the length of the hypotenuse is not an integer but irrational numbers.
Achievements of the Ancient Greeks is a monumental work of Euclid on geometry axiomatic. The main source for reconstructing pre-Euclidean named Euclid's book Elements (elements), where most of the content is still relevant and used until the present. Element consists of 13 volumes. Book I deals with congruence of triangles, properties of parallel lines, and relationship area of triangles and parallelograms; Book II sets kehimpunanaraan associated with boxes, rectangles, and triangles; Book III contains properties Circles, and Book IV contains polygon in a circle. Most of the contents of Book I-III are the works of Hippocrates, and the content of Book IV can be attributed to Pythagoras, so it can be understood that the book element has its history to centuries before. Book V outlines a general theory of proportion, which is a theory that does not require restrictions on the amount of worth. This general theory derived from Eudoxus.
In theory, Book VI describes the rectilinear nature and generalization of the theory of congruence in Book I. Book VII-IX contains what the Greeks called "arithmetic," the theory of integers. This includes the properties of numerical proportion, the greatest divisor, common multiples, and primes (Book VII); propositions in numerical progression and square (Book VIII), and the specific outcomes, such as unique factorization into primes in the existence of an infinite number of primes, and the formation of a "perfect" numbers, ie numbers equal to the number of divisors (Book IX). In some form, originating from Theaetetus Book VII and Book VIII of Archytas. X book presents the theory of irrational lines and comes from the work of Theaetetus and Eudoxus. Xiberisi book about waking up the space; Book XII prove theorems on the ratio of a circle, the ratio of the ball, and the volume of pyramids and cones. Heritage of Greek mathematics, especially in geometry, is huge. From the early period of Greek people set goals in terms of mathematics is not practical procedures but as a theoretical discipline is committed to developing a general proposition, and a formal demonstration. The range and diversity of their findings, especially those of the SM-3 centuries, geometry has become the subject matter for ages himpunanelah, although the tradition is transmitted to the Middle Ages and the Renaissance is incomplete and flawed.
The rapid rise of mathematics in the 17th century was based in part on the renewal of the ancient mathematics and mathematics in Greek era. Mechanics from Galileo and calculations made Kepler and Cavalieri, a direct inspiration for the Archimedes. The study of geometry by Apollonius and Pappus stimulated by new approaches in geometry-for example, by Descartes developed analytic and projective theory of Girard Desargues.
Resurrection of mathematics in the 17th century along with the rise of the thinking of the philosopher as an anti-thesis of a dark age where truth is dominated by the Church. Then Copernicus is a groundbreaking figure who challenged the view of the Church that the earth as the center of the universe, and in return he expressed the idea that the Earth but not the sun that is the center of the solar system, while the surrounding earth. This revival era became known as the Modern Age, which is characterized by the emergence of figures as well as mathematicians philosophical thinkers like Immanuel Kant, Rene Descartes, David Hume, Galileo, Kepler, Cavalieri
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