Download Assignment - FrancisLarreal

Assignment
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,” 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.
A fractal often has the following features:
 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).
 It has a simple and recursive definition.
1. There is a definition of fractals there. Please identify it and identify its components.
Term to be defined will be underlined.
General class will be in green.
Characteristics will be in orange.
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,” a property called self-similarity.
2. There is a description there, please identify it and tell me how you found it. What helped you
when locating it.
Professor Ferrari: I will copy the two paragraphs here and I will
underline the description, because I think there are some
characteristics written in both of them.
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,” 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.
A fractal often has the following features:
 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).
 It has a simple and recursive definition.
II: Now write a description of any mathematical word or topic.


Vector spaces are collections of vectors where two proposals are true:
For each vector x in the vector space, Ax is in the vector space to, being A any real
number.
For every x and y in the vector space, x+y is also in the vector space.
A straight line is a vector space. For every vector (or pair of vectors) of it , this two
proposals are valid. A plane is also a vector space.
To describe a vector space means to define as many vectors (X 1, X2,X3,...,Xn) as needed so
every single vector in the vector space can be described as a multiple of any of these vectors, or as
a combination of two or more of them. The is minimun quantity of vectors needed to describe the
whole space are independent from each other, and all of them conform the basis of the space. The
quantity of vectors in the basis is said to be the dimension of the space. Thus, every vector in a
plane can be described by combinating two different vectors defined previously; the basis are those
two vectors, and the dimension of any plane is two.
As a vector space is a collection of elementes, some functions must be specifically defined
to vectors. Function of vectors, defined from one vector space to another, are named linear maps.
In these functions, vectors that are transformed into multiples of themselves are named eigenvectors, and the scalar numbers that multiplied them in the transformation are named eigen-values.