week+4

Reading and writing definitions.

**Definitions**
A definition is a rethorical pattern you use to conceptualize words. Definitions usually have a term to be defined, a general class word and a characteristic or characteristics. Example A dog (term to be defined) is an animal (general class word) that barks has four legs and a tail. (characteristics)

=Assignment= 1. Now select 10 definitions from the on-line mathematics dictionary at [], [|http://www.math.com/school/glossary/glossindex.html], [], 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. Complex numbers (term to be defined) One can think of them as an ordered pair of numbers. (general class word) Complex numbers helped earlier mathematicians deal with the problem of taking the square root of a negative number. A complex number takes the form a + b*sqrt(-1), where a and b are real numbers. (characteristics)

2. Coordinates (term to be defined) A unique ordered pair of numbers (general class word) that identifies a point on the coordinate plane. The first number in the ordered pair identifies the position with regard to the x-axis while the second number identifies the position on the y-axis. (characteristics)

3. Correlation (term to be defined) A statistical measure (general class word) referring to the relationship between two random variables. It is a positive correlation when each variable tends to increase or decrease as the other does, and a negative or inverse correlation if one tends to increase as the other decreases. (characteristics)

4. Cube (term to be defined)A prism (general class word) with six square faces (characteristics)

5. Fibonacci numbers (term to be defined) A set of numbers (general class word) formed by adding the last two numbers to get the next in the series: 0, 1, 1, 2, 3, 5, 8, 13. Named for Leonardo of Pisa, an Italian mathematician of the Middle Ages, who called himself Fibonacci, short for filius Bonacci which means "son of Bonacci". The original problem he investigated in1202 A.D. was about how fast rabbits could breed under ideal circumstances. His research led to the construction of this unique set of numbers. (characteristics)

6. Infinity (term to be defined) Greater than any fixed counting number, or extending forever. (general class word) No matter how large a number one thinks of, infinity is larger than it. Infinity has no limits (characteristics)

7. Estimate (term to be defined)The best guess (general class word) arrived at after considering all the information given in a problem (characteristics)

8. Limit (term to be defined) The target value (general class word) that terms in a sequence of numbers are getting closer to. This limit is not necessarily ever reached the numbers in the sequence eventually get arbitrarily close to the limit (characteristics)

9. Percent (term to be defined) A ratio (general class word) that compares a number to one hundred. The symbol for percent is % (characteristics)

10. Graph (term to be defined)A visual representation of data (general class word) that displays the relationship among variables, usually cast along x and y axes. (characteristics)

2. __**Using your own words**__, write 5 definitions about any mathematical terms.

As soon as you have all these ready, please paste it in your wiki.

For additional information about writing definitions, please visit the following site (this is what I printed for the class) []

Triangle is a polygon of three sides, it is determinate by three noncollinear points called vertices.

Polinomial is a algebraic expression that has a finite number of variables and constants, it only use operations of addition, subtraction, multiplication and heightening with natural exponents.

Arithmetic is a part of the mathematics that study the formation of the numbers, how to express them, and the calculation, all the propierties and resolution of the problems derivaties from mathematics.

Algebra is a branch of the mathematics that use numbers, letters and characters to generalize different mathematical operations.

Geometry is a brach of the mathematics that is dedicated to the study of the propierties and measure of the figures in the space or in the plane.

Reading and writing descriptions

**Here we will read and write descriptions** =Description= A description is a writing form used to create an impression of an object, person, place, event, process, mechanism, etc. You can describe people, objects, animals, plants, or you can also describe how an event happened, how a mechanism operates, etcetera. In a description you find many ** adjectives ** which are the words that will characterize any thing you want to describe. __Example 1:__ In an **equilateral triangle**, all sides are of equal length. An equilateral triangle is also an equiangular polygon, i.e. all its internal angles are equal—namely, 60°; it is a regular polygon. This description was taken from the following web page: [] __Example 2:__ A polygon that is not convex is called **concave**.[|[2]] A concave polygon will always have an interior angle with a measure that is greater than 180 degrees. It is possible to cut a concave polygon into a set of convex polygons This description was taken from the following web page: []  =Assignment= [|__http://en.wikipedia.org/wiki/Fractal__]
 * I. In the text you will find when you click the link below, extract the first two paragraphs and please find all the characteristics of fractals and underline them. Also find the adjectives and circle them.Be careful ! ! ! **

=Fractal=

From Wikipedia, the free encyclopedia
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. Characteristics: orange color. Adjectives: violet color.  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). <span style="color: #b2a1c7; font-family: 'Times New Roman','serif'; font-size: 12pt; mso-ansi-language: EN; mso-fareast-font-family: 'Times New Roman'; mso-fareast-language: ES; mso-themecolor: accent4; mso-themetint: 153;">Natural <span style="color: #f79646; font-family: 'Times New Roman','serif'; font-size: 12pt; mso-ansi-language: EN; mso-fareast-font-family: 'Times New Roman'; mso-fareast-language: ES; mso-themecolor: accent6;"> 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. <span style="color: black; font-family: 'Times New Roman','serif'; font-size: 12pt; mso-ansi-language: EN; mso-fareast-font-family: 'Times New Roman'; mso-fareast-language: ES; mso-themecolor: text1;"> However, not all <span style="color: #b2a1c7; font-family: 'Times New Roman','serif'; font-size: 12pt; mso-ansi-language: EN; mso-fareast-font-family: 'Times New Roman'; mso-fareast-language: ES; mso-themecolor: accent4; mso-themetint: 153;">self-similar <span style="color: black; font-family: 'Times New Roman','serif'; font-size: 12pt; mso-ansi-language: EN; mso-fareast-font-family: 'Times New Roman'; mso-fareast-language: ES; mso-themecolor: text1;"> objects are fractals—for example, the <span style="color: #b2a1c7; mso-themecolor: accent4; mso-themetint: 153; text-decoration: none; text-underline: none;">[|real] [| line] (a <span style="color: #b2a1c7; font-family: 'Times New Roman','serif'; font-size: 12pt; mso-ansi-language: EN; mso-fareast-font-family: 'Times New Roman'; mso-fareast-language: ES; mso-themecolor: accent4; mso-themetint: 153;">straight <span style="color: #b2a1c7; mso-themecolor: accent4; mso-themetint: 153; text-decoration: none; text-underline: none;">[|Euclidean] <span style="color: black; font-family: 'Times New Roman','serif'; font-size: 12pt; mso-ansi-language: EN; mso-fareast-font-family: 'Times New Roman'; mso-fareast-language: ES; mso-themecolor: text1;"> line) is formally <span style="color: #b2a1c7; font-family: 'Times New Roman','serif'; font-size: 12pt; mso-ansi-language: EN; mso-fareast-font-family: 'Times New Roman'; mso-fareast-language: ES; mso-themecolor: accent4; mso-themetint: 153;">self-similar <span style="color: black; font-family: 'Times New Roman','serif'; font-size: 12pt; mso-ansi-language: EN; mso-fareast-font-family: 'Times New Roman'; mso-fareast-language: ES; mso-themecolor: text1;"> but fails to have other fractal characteristics; for instance, it is <span style="color: #b2a1c7; font-family: 'Times New Roman','serif'; font-size: 12pt; mso-ansi-language: EN; mso-fareast-font-family: 'Times New Roman'; mso-fareast-language: ES; mso-themecolor: accent4; mso-themetint: 153;">regular <span style="color: black; font-family: 'Times New Roman','serif'; font-size: 12pt; mso-ansi-language: EN; mso-fareast-font-family: 'Times New Roman'; mso-fareast-language: ES; mso-themecolor: text1;"> enough to be described in <span style="color: #b2a1c7; font-family: 'Times New Roman','serif'; font-size: 12pt; mso-ansi-language: EN; mso-fareast-font-family: 'Times New Roman'; mso-fareast-language: ES; mso-themecolor: accent4; mso-themetint: 153;">Euclidean <span style="color: black; font-family: 'Times New Roman','serif'; font-size: 12pt; mso-ansi-language: EN; mso-fareast-font-family: 'Times New Roman'; mso-fareast-language: ES; mso-themecolor: text1;"> terms.
 * <span style="font-family: 'Times New Roman','serif'; font-size: 12pt; mso-ansi-language: EN; mso-fareast-font-family: 'Times New Roman'; mso-fareast-language: ES;">It has a fine structure at arbitrarily small scales.
 * <span style="font-family: 'Times New Roman','serif'; font-size: 12pt; mso-ansi-language: EN; mso-fareast-font-family: 'Times New Roman'; mso-fareast-language: ES;">It is too irregular to be easily described in traditional [|Euclidean geometric] language.
 * <span style="font-family: 'Times New Roman','serif'; font-size: 12pt; mso-ansi-language: EN; mso-fareast-font-family: 'Times New Roman'; mso-fareast-language: ES;">It is [|self-similar] (at least approximately or [|stochastically] ).
 * <span style="font-family: 'Times New Roman','serif'; font-size: 12pt; mso-ansi-language: EN; mso-fareast-font-family: 'Times New Roman'; mso-fareast-language: ES;">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]]
 * <span style="font-family: 'Times New Roman','serif'; font-size: 12pt; mso-ansi-language: EN; mso-fareast-font-family: 'Times New Roman'; mso-fareast-language: ES;">It has a simple and [|recursive definition].
 * <span style="font-family: 'Times New Roman','serif'; font-size: 12pt; mso-ansi-language: EN; mso-fareast-font-family: 'Times New Roman'; mso-fareast-language: ES;">It has a <span style="color: #b2a1c7; font-family: 'Times New Roman','serif'; font-size: 12pt; mso-ansi-language: EN; mso-fareast-font-family: 'Times New Roman'; mso-fareast-language: ES; mso-themecolor: accent4; mso-themetint: 153;">fine <span style="font-family: 'Times New Roman','serif'; font-size: 12pt; mso-ansi-language: EN; mso-fareast-font-family: 'Times New Roman'; mso-fareast-language: ES;"> structure at arbitrarily <span style="color: #b2a1c7; font-family: 'Times New Roman','serif'; font-size: 12pt; mso-ansi-language: EN; mso-fareast-font-family: 'Times New Roman'; mso-fareast-language: ES; mso-themecolor: accent4; mso-themetint: 153;">small <span style="font-family: 'Times New Roman','serif'; font-size: 12pt; mso-ansi-language: EN; mso-fareast-font-family: 'Times New Roman'; mso-fareast-language: ES;"> scales.
 * <span style="font-family: 'Times New Roman','serif'; font-size: 12pt; mso-ansi-language: EN; mso-fareast-font-family: 'Times New Roman'; mso-fareast-language: ES;">It is too <span style="color: #b2a1c7; font-family: 'Times New Roman','serif'; font-size: 12pt; mso-ansi-language: EN; mso-fareast-font-family: 'Times New Roman'; mso-fareast-language: ES; mso-themecolor: accent4; mso-themetint: 153;">irregular <span style="font-family: 'Times New Roman','serif'; font-size: 12pt; mso-ansi-language: EN; mso-fareast-font-family: 'Times New Roman'; mso-fareast-language: ES;"> to be easily described in traditional <span style="color: #b2a1c7; font-family: 'Times New Roman','serif'; font-size: 12pt; mso-ansi-language: EN; mso-fareast-font-family: 'Times New Roman'; mso-fareast-language: ES; mso-themecolor: accent4; mso-themetint: 153; msoansilanguage: EN; msofareastfontfamily: 'Times New Roman'; msofareastlanguage: ES; msothemecolor: accent4; msothemetint: 153; text-decoration: none; textunderline: none;">[|Euclidean geometric] <span style="font-family: 'Times New Roman','serif'; font-size: 12pt; mso-ansi-language: EN; mso-fareast-font-family: 'Times New Roman'; mso-fareast-language: ES;"> language.
 * <span style="font-family: 'Times New Roman','serif'; font-size: 12pt; mso-ansi-language: EN; mso-fareast-font-family: 'Times New Roman'; mso-fareast-language: ES;">It is <span style="color: #b2a1c7; font-family: 'Times New Roman','serif'; font-size: 12pt; mso-ansi-language: EN; mso-fareast-font-family: 'Times New Roman'; mso-fareast-language: ES; mso-themecolor: accent4; mso-themetint: 153; msoansilanguage: EN; msofareastfontfamily: 'Times New Roman'; msofareastlanguage: ES; msothemecolor: accent4; msothemetint: 153; text-decoration: none; textunderline: none;">[|self-similar] <span style="font-family: 'Times New Roman','serif'; font-size: 12pt; mso-ansi-language: EN; mso-fareast-font-family: 'Times New Roman'; mso-fareast-language: ES;"> (at least approximately or <span style="color: #b2a1c7; font-family: 'Times New Roman','serif'; font-size: 12pt; mso-ansi-language: EN; mso-fareast-font-family: 'Times New Roman'; mso-fareast-language: ES; mso-themecolor: accent4; mso-themetint: 153; msoansilanguage: EN; msofareastfontfamily: 'Times New Roman'; msofareastlanguage: ES; msothemecolor: accent4; msothemetint: 153; text-decoration: none; textunderline: none;">[|stochastically] <span style="font-family: 'Times New Roman','serif'; font-size: 12pt; mso-ansi-language: EN; mso-fareast-font-family: 'Times New Roman'; mso-fareast-language: ES;">).
 * <span style="font-family: 'Times New Roman','serif'; font-size: 12pt; mso-ansi-language: EN; mso-fareast-font-family: 'Times New Roman'; mso-fareast-language: ES;">It has a <span style="color: #b2a1c7; mso-themecolor: accent4; mso-themetint: 153; text-decoration: none; text-underline: none;">[|Hausdorff] [| dimension] which is <span style="color: #b2a1c7; font-family: 'Times New Roman','serif'; font-size: 12pt; mso-ansi-language: EN; mso-fareast-font-family: 'Times New Roman'; mso-fareast-language: ES; mso-themecolor: accent4; mso-themetint: 153;">greater <span style="font-family: 'Times New Roman','serif'; font-size: 12pt; mso-ansi-language: EN; mso-fareast-font-family: 'Times New Roman'; mso-fareast-language: ES;">than its <span style="color: #b2a1c7; mso-themecolor: accent4; mso-themetint: 153; text-decoration: none; text-underline: none;">[|topological] [| dimension] (although this requirement is not met by [|space-filling curves] such as the <span style="color: #b2a1c7; mso-themecolor: accent4; mso-themetint: 153; text-decoration: none; text-underline: none;">[|Hilbert] [|curve] ). [|[4]]
 * <span style="font-family: 'Times New Roman','serif'; font-size: 12pt; mso-ansi-language: EN; mso-fareast-font-family: 'Times New Roman'; mso-fareast-language: ES;">It has a simple and <span style="color: #b2a1c7; mso-themecolor: accent4; mso-themetint: 153; text-decoration: none; text-underline: none;">[|recursive] [|definition].

<span style="color: black; font-family: Calibri; mso-ansi-language: EN; mso-themecolor: text1; msoansilanguage: EN; msothemecolor: text1;">

1. There is a definition of fractals there. Please identify it and identify its components.

<span style="color: black; font-family: 'Times New Roman','serif'; font-size: 12pt; line-height: 115%; mso-ansi-language: EN; mso-bidi-language: AR-SA; mso-fareast-font-family: 'Times New Roman'; mso-fareast-language: ES; mso-themecolor: text1;">A fractal (term to be defined) is "a rough or fragmented [|geometric shape] (general class word) 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]. (characteristics)

2. There is a description there, please identify it and tell me how you found it. What helped you when locating it.

<span style="color: black; font-family: 'Times New Roman','serif'; font-size: 12pt; line-height: 115%; mso-ansi-language: EN; mso-bidi-language: AR-SA; mso-fareast-font-family: 'Times New Roman'; mso-fareast-language: ES; mso-themecolor: text1;">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] . <span style="font-family: 'Times New Roman','serif'; font-size: 12pt; mso-ansi-language: EN; mso-fareast-font-family: 'Times New Roman'; mso-fareast-language: ES;">I found the descriptions reading the thing that express the object.
 * <span style="font-family: 'Times New Roman','serif'; font-size: 12pt; mso-ansi-language: EN; mso-fareast-font-family: 'Times New Roman'; mso-fareast-language: ES;">It has a fine structure at arbitrarily small scales.
 * <span style="font-family: 'Times New Roman','serif'; font-size: 12pt; mso-ansi-language: EN; mso-fareast-font-family: 'Times New Roman'; mso-fareast-language: ES;">It is too irregular to be easily described in traditional [|Euclidean geometric] language.
 * <span style="font-family: 'Times New Roman','serif'; font-size: 12pt; mso-ansi-language: EN; mso-fareast-font-family: 'Times New Roman'; mso-fareast-language: ES;">It is [|self-similar] (at least approximately or [|stochastically] ).
 * <span style="font-family: 'Times New Roman','serif'; font-size: 12pt; mso-ansi-language: EN; mso-fareast-font-family: 'Times New Roman'; mso-fareast-language: ES;">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]]
 * <span style="font-family: 'Times New Roman','serif'; font-size: 12pt; mso-ansi-language: EN; mso-fareast-font-family: 'Times New Roman'; mso-fareast-language: ES;">It has a simple and [|recursive definition].
 * II: Now write a description of any mathematical word or topic.**

**Please visit the following link for more information.**
[]

<span style="color: black; font-family: 'Times New Roman','serif'; font-size: 12pt; mso-ansi-language: EN-US; mso-fareast-font-family: 'Times New Roman'; mso-fareast-language: ES;">The square is a geometrical figure formed by four straight lines of equal length, they are called sides, they form straight angles in the points where join the lines between them (the corners measure 90 degrees).