The history of Algebra

The history of algebra began in ancient Egypt and Babylon, where people learn to solve linear (ax = b) and quadratic (ax ^ 2 + bx = c) equation, sertapersamaan indeterminate as x ^ 2 + y ^ 2 = z ^ 2, where some known to be involved. The ancient Babylonians could solve quadratic equations with the same procedure. They also could solve some indeterminate equations.
The Alexandrian mathematicians Hero of Alexandria and Diophantus continued the tradition of Egypt and Babylon, but Diophantus book Arithmetica is in a much higher level and provide solutions surprise many difficult indeterminate equations.Ancient knowledge of the equation solution in turn found a home early in the Islamic world, where it was known as "the science of restoration and balancing." (Arabic for the restoration, al-jabru, is the root of the word algebra). In the 9th century, the Arab mathematician al-Khwarizmi wrote one of the first Arab algebra, a systematic description of the basic theory of equations, with both examples and evidence. At the end of the 9th century, the Egyptian mathematician Abu Kamil had stated and proved the basic laws and identities of the algebra and solve complex problems such as finding x, y, and z so that x + y + z = 10, x ^ 2 + y ^ 2 = z ^ 2, and xz = y ^ 2.
Ancient civilizations write algebraic expressions using only occasional abbreviations, but by medieval Islamic mathematicians able to talk about arbitrary high powers are unknown x, and worked out basic algebra polynomials (without yet using modern symbolism). This includes the ability to multiply, divide, and find the square root of a polynomial and knowledge-binomial theorem. Persian mathematician, astronomer, and poet Omar Khayyam showed how to express roots of cubic equations by line segments obtained by conic sections, but he could not find a formula for the roots. A Latin translation of Al-Khwarizmi's Algebra appeared in the 12th century. At the beginning of the 13th century, the great Italian mathematician Leonardo Fibonacci achieved close approach to the solution of the cubic equation x ^ 3 + 2 x ^ 2 + cx = d. Because Fibonacci had traveled in the land of Islam, he probably used the Arab approximation method.
At the beginning of the 16th century, Italian mathematician Scipione del Ferro, Niccolo Tartaglia, and Gerolamo Cardano solved the general cubic equation in terms of the constants appearing in the equation. Cardano's pupil, Ludovico Ferrari, soon find the right solution for the equation of the fourth degree (quartic lihatpersamaan), and as a result, mathematicians for the next few centuries trying to find a formula for the roots of equations of degree five or higher. At the beginning of the 19th century, however, the Norwegian mathematician Niels Abel and French mathematician Evariste Galoismembuktikan that no such formula does not exist.
An important development in algebra in the 16th century was the introduction of a symbol for the unknown and to the power of algebra and operations. As a result of these developments, Book III of géométrie La (1637), written by French philosopher and mathematician Rene Descartes, looks like a modern algebra text. Descartes' most significant contribution to mathematics, however, was the invention of analytic geometry, which reduces the problem solving algebraic geometry for solutions. His geometry text also contains the essence of the course on the theory of equations, including the so-called reign marks to count the number of so-called Descartes (positive) and "wrong" (negative) "correct" the root of an equation. Work continued through the 18th century on the theory of equations, but not published until 1799 is evidence, by the German mathematician Carl Friedrich Gauss, who showed that himpunaniap himpunanidaknya polynomial equation has one root in the complex plane (see Number: Complex Numbers).
At the time of Gauss, algebra had entered the modern phase.Attention shifted from solving polynomial equations to study the structure of the axioms of abstract mathematical systems based on the behavior of mathematical objects, such as complex numbers, which is encountered when learning math equation polinomial.Dua example of such a system algebraic group (see Group) and quaternions, which share properties properties of number systems but also depart from them in important ways.The group began as a system of permutations and combinations of the roots of a polynomial, but they became one of the major unifying concepts of mathematics of the 19th century. Important to study their contribution made by the French mathematician Galois and Augustin Cauchy, British mathematician Arthur Cayley, and the Norwegian mathematician Niels Abel and Sophus Lie. Quaternions invented by British mathematician and astronomer, William Rowan Hamilton, who extended the arithmetic of complex numbers to quaternions as complex number is the form a + bi, quaternions are of the form a + bi + cj + dk.
Soon himpunanelah Hamilton's invention, the German mathematician Hermann Grassmann began investigating vector.Despite the abstract character, the American physicist JW Gibbs recognized in vector algebra for physicists major utility systems, such as Hamilton acknowledges the usefulness quaternions.Widespread influence of the abstract approach that led to George Boole writes Legal Thought (1854), care of the basic algebra of logic. Since then, modern algebra is also called abstract algebra.
Sources:
http://www.algebra.com/algebra/about/history/

The history of Parabola

Parabola studied by Menaechmus who was a disciple of Platoand Eudoxus. He attempted to duplicate the cube, namely to findthe cube that has twice the volume of a cube is given. Therefore he tried to solve x ^ 3 = 2 by the method of geometry.

Even the method of geometric construction of a ruler andcompass can not solve this (but Menaechmus did not know this).Menaechmus solved it by finding the intersection of twoparabolas x ^ 2 = y and y ^ 2 = 2 x

Euclid wrote about the dish and it was given its present name byApollonius. The focus of the parabola and the directory is offered by Pappus.
Pascal argued parabola as projections of circles and Galileoshowed that projectiles follow parabolic paths.

Gregory and Newton put forward as the property of a parabolathat bring parallel rays of light to focus.

Parabola with a pedal point as a pedal point is cissoid. Pedal of the parabola with focus as pedal point is a straight line. With afoot pedal directrix as it is right to point strophoid (an obliquestrophoid to himpunaniap another point of the directrix). Pedalwhen the pedal curve of the image focal point in the directrix isTrisectrix of Maclaurin.

Evolute Neile's parabola is a parabola. From that point on theevolute three normals can be drawn to a parabola, while only onenormal can be drawn to a parabola from a point below theevolute. If the focus of the parabola is taken as a center ofinversion, invert dish to cardioid. If the node is taken as a center of inversion parabolic, reverse parabolas keCissoid of Diocles.The caustic of a parabola with a beam perpendicular to the axis of the parabola is Tschirnhaus's Cubic.

sources:

http://www-history.mcs.st-and.ac.uk/Curves/Parabola.html
http://xsquared.wikispaces.com/Parabola+History

The History of Circle

The circle has existed since prehistoric times. Invention of the wheel is the fundamental discoveries of the nature of the circle.The Greeks regarded Egypt as the inventor of geometry. ScribeAhmes, the author of the Rhind papyrus, provides rules fordetermining the area of a circle corresponding to π = 256 / 81 or about 3.16.

The first theorem relating to the circle that is associated with Thales around 650 BC. Book III of Euclid's Elements deals withthe nature and problem of inscribing circles and polygonsescribing.

One of the problems of Greek mathematics is a matter of finding the square with the same area as a given circle. Some of the'famous curves in a stack was first studied in an attempt to solvethis problem. In 450 BC Anaxagoras was the first recoredmathematicians to study this problem.

Problem to find a wide circle of cause of integration. For a circlewith the formula given above this region π ^ 2 and the length of acurve is 2π.
Pedal circle is the cardioid if the pedal point on thecircumference and is taken limacon if the point on the circumference of the pedal instead.

caustic of a circle with a point on the circumference is a cardioidshine, while if the beam is parallel to the caustic nephroid.

Apollonius, in about 240 BC, effectively demonstrated that thebipolar equation r = kr 'is a system of coaxial circles as k varies.In the case of bipolar equation mr + nr ^ 2 ^ 2 = c ^ 2 is a circlewhose center dividing line segment between two fixed points of the system in the ratio of n to m.

sources:
http://www-history.mcs.st-and.ac.uk/Curves/Circle.html