Reading+2


 * Wow ** [[image:paintor_2.jpg width="140" height="134"]]

1. Read the title and write a list of ten words you think you might find in the text.
-Artist -Art -Numbers -Mathematics -Colors -Image -Paint -Shape -Abstract -Properties

2. What do you know about the link between artwork and mathematics? Mention some examples.
====I don´t really know much about it but i believe the link between both is that in artwork we can use forms like circles, ==== ==== triangles, squares,... which are figures that have their own math properties and are use to enunciate math theorems. ====

***During Reading and After Reading**

====1. While reading, please locate the words you listed in the pre-reading and write a list of the ones you found in the ====

text.
-Art -Artist -Image -Colors -Numbers -Mathematics -Shape -Properties

==== 2. 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 the simpler sort of beauty-//


 * 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 //. -Where refers to the exhibition of mathematical art at the Joint Meeting in San Diego-//


 * 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 <span style="color: #000000; font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 12pt;">**it** //-It refers to the point-// <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 12pt;">to a different spot. Field repeats <span style="color: #000000; font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 12pt;">**this process** //-This process refers to use an equation that takes any point on a piece of paper and moves it//<span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;">// - // 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 <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;">** it. <span style="font-family: arial,helvetica,sans-serif; font-size: 13px; font-weight: normal; line-height: 19px;">//-It refers to the pixels-// **
 * <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 12pt;">The reason mathematicians are so fascinated by dynamical systems is that very simple equations can produce very complicated behavior. Field has found that <span style="color: #000000; font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 12pt;">**such complex behavior** <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 12pt;"> can create some beautiful images. //-Such complex behavior refers to very simple equations that can produce very complicated behavior-//


 * <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 12pt;">Robert Bosch, a mathematics professor at Oberlin College in Ohio, took **his** //-His refers to somethig of his property, something that belong him-// <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 12pt;">inspiration from an old, seemingly trivial problem **that**  //-That refers to the trivial problem-// <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 12pt;">hides some deep mathematics. Take a loop of string and throw **it**  //-It refers to the loop-// <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 12pt;">down on a piece of papaer. It can form any shape you like as long as the string never touches or crosses <span style="color: #000000; font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 12pt;">**itself** //-Itself refers to the string-// <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 12pt;">. A theorem states that the loop will divide the page into two regions, **one inside** //-One inside refers to one of the regions that is divide by the loop-//<span style="font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 12pt;"> the loop and **one outside.**  //-One outside refers to the other region that is divide by the loop-//


 * <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 12pt;">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, <span style="color: #000000; font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 12pt;">**it** <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 12pt;">may not be obvious whether a particular point lies inside or outside the loop. Topologists, the type of mathematicians <span style="color: #000000; font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 12pt;">**who** //-Who refers to topologists-// <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 12pt;">study such things have managed to construct many strange, "pathological" mathematical objects with very surprising properties, so they know from experience that <span style="color: #000000; font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 12pt;">**you** //-You refers to the reader-//<span style="font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 12pt;"> shouldn't assume a proof is unnecessary in cases like **this one** //-This one refers to the case where we dont know if something is too much obvious-//

===<span style="color: #43f5f9; font-family: 'Palatino Linotype','Book Antiqua',Palatino,serif; font-size: 16px; line-height: 24px;">*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: 14px; line-height: 21px;">1. What is a mathematical dynamical System? <span style="font-family: 'Palatino Linotype','Book Antiqua',Palatino,serif; line-height: 21px;">A hematical dynamical system is any rule that determines how apoint moves in a plane, with the use of an equation that <span style="font-family: 'Palatino Linotype','Book Antiqua',Palatino,serif; line-height: 21px;">takes any point from a piece of paper and moves it to a completely different spot.

<span style="font-family: 'Palatino Linotype','Book Antiqua',Palatino,serif; font-size: 14px;">2. Why does the image "Coral Star" get more and more complex? <span style="font-family: 'Palatino Linotype','Book Antiqua',Palatino,serif; font-size: 14px; line-height: 21px;">Because the equation is discontinuous at the origin.

<span style="font-family: 'Palatino Linotype','Book Antiqua',Palatino,serif; font-size: 14px;">3. Find a definition of the following words that fits in the text, please acknowledge the source: <span style="font-family: 'Palatino Linotype','Book Antiqua',Palatino,serif; font-size: 14px;">Loop, crinkly, string

//-Loop:// the curved shape made when something long and thin, such as a piece of string, bends until one part of it nearly touches or crosses another part of it.

//-Crinkly:// to become covered in many small lines and folds, or to cause something to do this

//-String:// (a piece of) strong thin rope which is made by twisting very thin threads together and which is used for fastening and tying things

__The three definitions are taken from **[]**__

<span style="font-family: 'Palatino Linotype','Book Antiqua',Palatino,serif; font-size: 14px;">4. Where did Robert Bosch take his in spiration from? Describe the source of his inspiration. he took his inspiration from an old, seemingly trivial problem that hides some deep math. When you take a loop of string and throw it down on a piece of paper it form any shape as long as the string never touches or crosses itself.

<span style="font-family: 'Palatino Linotype','Book Antiqua',Palatino,serif; font-size: 14px;">5. What happened with Fathauer's arrangement? Why? Fathauer realized that something amazing was happening with his arrangement, this was that the shape was approximating a pyramid, with triangular holes punched out. In fact, he noticed that the faces of the pyramid were forming one of the earliest fractals, the Sierpinski triangle. <span style="font-family: 'Palatino Linotype','Book Antiqua',Palatino,serif; font-size: 14px;">6. How did Andrew Pike create the Sierpinski carpet? he took a square and divide it in a tic-tac-toe pattern and took out the middle square, after that he draw a tic-tac-toe pattern on each remaining square and knock out the middle squares of those, he repeated the process over and over again and thats how he create the Sierpinski carpet.

<span style="font-family: 'Palatino Linotype','Book Antiqua',Palatino,serif; font-size: 14px;">7. Why did he choose that image? He said that he choosed the image of Sierpinski because it was self-referential. It seems appropriate for a technique using self-similar fractals.