Curve Classification Essay

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In mathematics, the curve generally is an object similar to a straight line, but it does not require to be straight. This speaks to the straight line is a special case of the curve or curves with a curvature of 0. The two-dimensional or three-dimensional Euclidean space curves are interesting subjects for most of the scientists. Many mathematical subjects were assigned to the different meanings depending on the field of study, so the precise meaning depends on the context of referring to them. However, the meaning is the specific example of a more general definition. For example, the curve is a topological space that locally homeomorphic mapping into a straight line. In daily language, this means that the curve is the set of points at the sufficiently …show more content…
It is based on the distillation characteristics of each function the curve is divided into two main branches: Random and Determinate. The Random is composed of three small branches. The first branch is Fractal. In mathematics, Fractal is defined as is a geometric object, usually folded shape in all magnification ratio, and can be split into parts: each part looks like the whole, but at a smaller magnification ratio. Such a fractal has infinite detail, these details can have the self-uniform structure in the different magnification ratio. In many cases, can generate fractals by repeating a mathematical form, according to the regression. From fractal first mentioned in 1975 by Benoit Mandelbrot, fractals derived from Latin meaning "broken." Previously, these structures called "curve demons". For the defining characteristic of a fractal, it looks easy with intuitive, extremely difficult to require precise and concise of mathematics. Mandelbrot defined fractal as "a set in which the dimensional Hausdorff greater than the topological dimension." Hausdorff dimension is a concept born to measure the size of a fractal, it is usually not a natural number. A classification drawings on two-dimensional paper format can start with the properties of objects in three-dimensional space, and Hausdorff can have between two-dimensional and three-dimension. For a fully automatic distribution uniform format, dimensional Hausdorff will be equal …show more content…
Definition of Determinate is having exact and discernible limits or form. There are four main branches: Algebraic, Integral, Transcendental, Piecewise Continuous. In mathematics, algebraic is a finite combination of numbers and symbols by using the operation of addition, subtraction, multiplication, division, raising to a power, and extracting a root. Therefore, the algebraic function defined by the root of a polynomial equation. Hence, rational and irrational are two branches of an algebraic function. The rational function is a fraction and has the property that both its numerator and denominator are polynomial. So, the polynomial is the function written as form f (x) = a_0+a_1 x+a_2 x^2+⋯+a_n x^n with a_1,a_2,…,a_n are real number and n is non-negative number. The irrational function is the independent variable x under the root symbol of a rational function. It is written in the form f (x) = √(n&g(x) ) with g (x) is a rational function. Such as Algebraic, Integration is also a form of curves. Definite integrals are defined as the area S is limited by the curve y = f (x) and the horizontal axis, with x running from a to b. Can understand simple as an area integral or generalized area. Assuming should take a flat area covered by straight lines, we just divide it into the thumbnail image simpler and already know how to calculate the area, such as triangles, squares, trapezoids, rectangles, etc. Subsequent consider a more complex picture in which

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