Reading+2

Pre-Reading
====Read the title and write a list of ten words you think you might find in the text. ====

====What do you know about the link between artwork and mathematics? Mention some examples. ====

So we know that mathematics are everywhere, as artwork are not the exception. In many artworks we can find the golden ratio, the golden rectangle and golden spiral. The golden ratio can be found in "El hombre de Vitrubio" by Leonardo Da Vinci. The golden rectangle can be found in "La Gioconda" by Leonardo Da Vinci and The golden spiral can be found in "Semitaza gigante volando con anexo inexplicable de cinco metros de longitud" by Salvador Dalí.

===During Reading and After Reading === ====1. Please click on the following link to read the article. ==== ====[] ====

====2. While reading, please locate the words you listed in the pre-reading and write a list of the ones you found in the text ====

====3. Please write what the following referents **(in bold letters)** refer to in the text: ====


 *  Mathematicians often rhapsodize about the austere elegance of a well-wrought proof. But math also has a simpler sort of beauty **that** is perhaps easier to appreciate ...

=That refers to "a simpler sort of beauty" =

**Where** refers to **"Joint Mathematics Meeting in San Diego"**
 * That beauty was richly on display at an exhibition of mathematical art at the Joint Mathematics Meeting in San Diego in January, ** where ** more than 40 artists showed their creations.

**It refers to "any point" This process refers to "moves any point to a different spot" It refers to "a pixel"**
 * A mathematical dynamical system is just any rule that determines how a point moves around a plane. Field uses an equation that takes any point on a piece of paper and moves **it** to a different spot. Field repeats **this process** over and over again—around 5 billion times—and keeps track of how often each pixel-sized spot in the plane gets landed on. The more often a pixel gets hit, the deeper the shade Field colors ** it .**

**Such complex behavior** refers to **"field"**
 * The reason mathematicians are so fascinated by dynamical systems is that very simple equations can produce very complicated behavior. Field has found that **such complex behavior** can create some beautiful images.

<span style="font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 12pt;">His refers to **"Robert Bosch"** That refers to **"Trivial problem"** It refers to **"a loop of string"** Itself refers to **"string"** One inside refers to **"region one of loop"** One outside refers to **"region two of loop"**
 * <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 12pt;">Robert Bosch, a mathematics professor at Oberlin College in Ohio, took ** his ** inspiration from an old, seemingly trivial problem ** that ** hides some deep mathematics. Take a loop of string and throw ** it ** down on a piece of papaer. It can form any shape you like as long as the string never touches or crosses **itself** . A theorem states that the loop will divide the page into two regions, **one inside** the loop and ** one outside **.

It is hard to imagine how it could do anything else, and if the loop makes a smoothly curving line, a mathematician would think that is obvious too. But if a line is very, very crinkly, **it** may not be obvious whether a particular point lies inside or outside the loop. Topologists, the type of mathematicians **who** study such things have managed to construct many strange, "pathological" mathematical objects with very surprising properties, so they know from experience that **you** shouldn't assume a proof is unnecessary in cases like **this one**. It refers to "the curving line" Who refers to "Topologists" You refers to "each person who reads the text" This one refers to "this case (the loop makes a smoothly curving line)"

===<span style="font-family: 'Palatino Linotype','Book Antiqua',Palatino,serif; font-size: 110%;">After reading the text, please answer the following questions **in your own words:** ===

<span style="font-family: 'Palatino Linotype','Book Antiqua',Palatino,serif; font-size: 110%;">1. What is a mathematical dynamical System? <span style="color: #800080; font-family: 'Comic Sans MS',cursive; font-size: 70%;">Is just any rule that determines how a point moves around a plane. Field uses an equation that takes any point on a piece of paper and moves it <span style="color: #800080; font-family: 'Comic Sans MS',cursive; font-size: 70%;">to a different spot <span style="font-family: 'Palatino Linotype','Book Antiqua',Palatino,serif; font-size: 110%;"> 2. Why does the image "Coral Star" get more and more complex? <span style="color: #800080; font-family: 'Palatino Linotype','Book Antiqua',Palatino,serif; font-size: 110%;">The reason is that very simple equations can produce very complicated behavior. Field has found that such complex behavior can create some beautiful images. In"Coral Star" does some peculiar things as it gets closer to the center (technically, the equation is discontinuous at the origin). <span style="font-family: 'Palatino Linotype','Book Antiqua',Palatino,serif; font-size: 110%;">3. Find a definition of the following words that fits in the text, please acknowledge the source: Loop, crinckly, string Loop : A sequence of instructions that repeats either a specified number of times or until a particular condition is met.http://www.answers.com/topic/loop Crinckly: any of several virus diseases of plants marked by crinkling of leaves.http://www.merriam-webster.com/dictionary/crinkly String: [|A] [|thread] [|or] [|cord] [|on] [|which] [|a] [|number] [|of] objects [|or] parts [|are] [|strung] [|or] [|arranged] [|in] [|close] [|and] [|orderly] [|succession;] [|hence,] [|a] [|line] [|or] [|series] [|of] things [|arranged] [|on] [|a] [|thread,] [|or] [|as] [|if] [|so] [|arranged;] [|a] [|succession;] [|a] [|concatenation;] [|a] [|chain;] [|as,] [|a] [|string] [|of] shells [|or] beads; [|a] [|string] [|of] [|dried] apples; [|a] [|string] [|of] [|houses;] [|a] [|string] [|of] arguments. []

4. Where did Robert Bosch take his inspiration from? Describe the source of his inspiration. The inspiration of Robert Bosch from an old, seemingly trivial problem that hides some deep mathematics.

5. What happened with Fathauer's arrangement? Why? The arrangement of Fathauer surprising is that he was just playing with various forms without noticing that what he was doing would result the triangle Sierpinski. The shape was approximating a pyramid, with triangular holes punched out.

6. How did Andrew Pike create the Sierpinski carpet?
 * "** To create a Sierpinski carpet, take a square, divide it in a tic-tac-toe pattern, and take out the middle square. Then draw a tic-tac-toe pattern on each remaining square and knock out the middle squares of those. Continuing forever will create the Sierpinski carpet **"**

7. Why did he choose that image? Andrew Pike says: "We chose the image of Sierpinski because it was self-referential". "Seems appropiate for a technique using self-similar fractals".