May 22, at 5: May 26, at 1: Piper Watsky June 2, at 1:
Ancient Greece[ edit ] The Greek mathematician Menaechmus solved problems and proved theorems by using a method that had a strong resemblance to the use of coordinates and it has sometimes been maintained that he had introduced analytic geometry.
His application of reference lines, a diameter and a tangent is essentially no different from our modern use of a coordinate frame, where the distances measured along the diameter from Def analytical essay point of tangency are the abscissas, and the segments parallel to the tangent and intercepted between the axis and the curve are the ordinates.
He further developed relations between the abscissas and the corresponding ordinates that are equivalent to rhetorical equations of curves.
However, although Apollonius came close to developing analytic geometry, he did not manage to do so since he did not take into account negative magnitudes and in every case the coordinate system was superimposed upon a given curve a posteriori instead of a priori.
That is, equations were determined by curves, but curves were not determined by equations. Coordinates, variables, and equations were subsidiary notions applied to a specific geometric situation. Descartes made significant progress with the methods in an essay titled La Geometrie Geometryone of the three accompanying essays appendices published in together with his Discourse on the Method for Rightly Directing One's Reason and Searching for Truth in the Sciences, commonly referred to as Discourse on Method.
This work, written in his native French tongue, and its philosophical principles, provided a foundation for calculus in Europe. Initially the work was not well received, due, in part, to the many gaps in arguments and complicated equations. Only after the translation into Latin and the addition of commentary by van Schooten in and further work thereafter did Descartes's masterpiece receive due recognition.
Although not published in his lifetime, a manuscript form of Ad locos planos et solidos isagoge Introduction to Plane and Solid Loci was circulating in Paris injust prior to the publication of Descartes' Discourse.
The key difference between Fermat's and Descartes' treatments is a matter of viewpoint: Fermat always started with an algebraic equation and then described the geometric curve which satisfied it, whereas Descartes started with geometric curves and produced their equations as one of several properties of the curves.
It was Leonhard Euler who first applied the coordinate method in a systematic study of space curves and surfaces. Coordinate systems Illustration of a Cartesian coordinate plane. Four points are marked and labeled with their coordinates: In analytic geometry, the plane is given a coordinate system, by which every point has a pair of real number coordinates.
Similarly, Euclidean space is given coordinates where every point has three coordinates. The value of the coordinates depends on the choice of the initial point of origin. There are a variety of coordinate systems used, but the most common are the following: Cartesian coordinate system The most common coordinate system to use is the Cartesian coordinate systemwhere each point has an x-coordinate representing its horizontal position, and a y-coordinate representing its vertical position.
Polar coordinates in a plane [ edit ] Main article: Cylindrical coordinates in a space [ edit ] Main article: Spherical coordinates in a space [ edit ] Main article: The names of the angles are often reversed in physics.
Solution set and Locus mathematics In analytic geometry, any equation involving the coordinates specifies a subset of the plane, namely the solution set for the equation, or locus.
In general, linear equations involving x and y specify lines, quadratic equations specify conic sectionsand more complicated equations describe more complicated figures. This is not always the case: In three dimensions, a single equation usually gives a surfaceand a curve must be specified as the intersection of two surfaces see belowor as a system of parametric equations.
Lines and planes[ edit ] Lines in a Cartesian plane or, more generally, in affine coordinatescan be described algebraically by linear equations.
In two dimensions, the equation for non-vertical lines is often given in the slope-intercept form:NEWTON, ISAAC (vetconnexx.comhorpe, England, 25 December ; vetconnexx.com, England, 20 March ) mathematics, dynamics, celestial mechanics, astronomy, optics, natural.
i took this class online. book required but i passed without a book with a b. i missed 2 assignments a disscuss (50) and a paper( pts).
the class is points and its a quiz/discussion due every 2 weeks and maybe easy word essays! i would def take again. Mass media is the most powerful tool used by the ruling class to manipulate the masses.
It shapes and molds opinions and attitudes and defines what is normal and acceptable. This article looks at the workings of mass media through the theories of its major thinkers, its power structure and the techniques it uses, in order [ ].
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