Definition+&+Description

Revision definition 5pts. description 4 pts [[image:manger.gif]]
**I. Now select 5 definitions from the on-line mathematics dictionary at** [], [], [], or from any other math glossary or dictionary and copy them. Your job will be to identify: a. the term to be defined b. the general class word and c. the characteristics. 1) Addition (the term to be defined) : The operation, or process, (the general class word) of calculating the sum of two numbers or quantities (the characteristics) . . 2) Ciphers (the term to be defined) : are codes (the general class word), for writing secret messages (the characteristics). Two simple types are shift ciphers and affine ciphers. 3) Constant functions (the term to be defined): Functions (the general class word), that stay the same no matter what the variable does are called constant functions (the characteristics) . 4) Empty set (the term to be defined) : The empty set, Ø, is the set (the general class word) that has no members (the characteristics). 5) Obtuse angle (the term to be defined) : An angle (the general class word), whose measure is greater than 90 degrees (the characteristics).
 * II. Using your own words, write 1 definition about any mathematical terms.**

**Transformations of plane (or space)** (the term to be defined) **:** The transformations of the plane are sets of bijectiones of THE plane (the general class word) on itself (the characteristics). **III. In the text you will find when you click the link below, extract the first paragraph and please find all the characteristics of fractals and underline them. Also find the adjectives and circle them. Be careful ! ! !** A **fractal ** is "a rough or fragmented [|geometric shape] that can be split into parts, each of which is (at least approximately) a reduced-size copy of the whole,"[|[1]] a property called [|self-similarity]. Roots of mathematical interest on fractals can be traced back to the late 19th Century; however, the term "fractal" was coined by [|Benoît Mandelbrot] in 1975 and was derived from the [|Latin] //[|fractus] // meaning "broken" or "fractured." A mathematical fractal is based on an [|equation] that undergoes [|iteration], a form of [|feedback] based on [|recursion].[|[2]] A fractal often has the following features:[|[3]] Because they appear similar at all levels of magnification, fractals are often considered to be infinitely complex (in informal terms). Natural objects that approximate fractals to a degree include clouds, mountain ranges, lightning bolts, coastlines, snow flakes, various vegetables (cauliflower and broccoli), and animal coloration patterns. However, not all self-similar objects are fractals—for example, the [|real line] (a straight [|Euclidean] line) is formally self-similar but fails to have other fractal characteristics; for instance, it is regular enough to be described in Euclidean terms.
 * __It has__ a fine structure at arbitrarily small scales.
 * __It is__ too irregular to be easily described in traditional [|Euclidean geometric] language.
 * __It is__ [|self-similar] (at least approximately or [|stochastically]).
 * __It has__ a [|Hausdorff dimension] which is greater than its [|topological dimension] (although this requirement is not met by [|space-filling curves] such as the [|Hilbert curve]).[|[4]]
 * __It has__ a simple and [|recursive definition].

// 1. There is a definition of fractals there. Please identify it and identify its components. //  Definition : A fractal is "a rough or fragmented geometric shape that can be split into parts.  Term to be defined: a fractal   General class word: Fragmented geometric. Characteristics : Can be split into parts.

//2. There is a description there, please identify it and tell me how you found it. What helped you when locating it?// A fractal often has the following features:[|[3]]
 * It has a fine structure at arbitrarily small scales.
 * It is too irregular to be easily described in traditional [|Euclidean geometric] language.
 * It is [|self-similar] (at least approximately or [|stochastically]).
 * It has a [|Hausdorff dimension] which is greater than its [|topological dimension] (although this requirement is not met by [|space-filling curves] such as the [|Hilbert curve]).[|[4]]
 * //It has// a simple and [|recursive definition].

**IV. Now write a description of any mathematical word or topic.**

**Transformations of the plane (or space):** A transformation of the plane __is a set of bijective of plane on itself__ It is better written in your definition. here it is confusing. in others words, a transformation of the plane is a function that sends every point on the plane to a point in the same plane. That is functions of plane in the plane than __be__ ARE injective and surjective such that, the images of points covering the whole plane and each point different have different images