Reading+2


 * 3.5pts =( too late, plus I'm __very upset__ 'cause you plagiarize the written paper**

**Pre-Reading **
====Read the title and write a list of ten words you think you might find in the text. picture, fantasy, paint, lines, dimension, light, color, visual, formula, square ==== ====What do you know about the link between artwork and mathematics? Mention some examples. the dimension of the object in the paint for a balance, the same for the angle of light and shadows, etc. ====

**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 colors, aquare, visual. ====

 the sort of beauty
 *  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 ...

  the joint mathematics meeting
 * 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.

  **- the point - move the points to a different spot - the shade field colors**
 * <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 12pt;">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 .**

<span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;"> <span style="font-family: arial,helvetica,sans-serif; font-size: 13px; font-weight: normal;"> <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;"> **the complex behavior?**
 * <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 such complex behavior **can create some beautiful images.**

<span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;"><span style="font-family: arial,helvetica,sans-serif; font-size: 13px;"> <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;"> **- Robert bosh - old, seemingly trivial problem -a loop of string - a loop of string - one region - another region**
 * <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 **.**

<span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;"><span style="font-family: arial,helvetica,sans-serif; font-size: 13px;"> <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;"> **- imagine how it could do anything else -topologist - my self? - the loop of string**
 * <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, 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**.**

is the description of the movement of a point 2. Why does the image "Coral Star" get more and more complex? the center, this because the equation of movement are not define at 0 3. Find a definition of the following words that fits in the text, please acknowledge the source: Loop: bucle crinckly: arrugado, con pliegues string: cadena 4. Where did Robert Bosch take his inspiration from? Describe the source of his inspiration. trivial problems that have mathematics hides very deep like <span style="font-family: Verdana,Arial,sans-serif; font-size: 12px; line-height: 16px;">Take a loop of string and throw it down on a piece of paper. 5. What happened with Fathauer's arrangement? Why? <span style="font-family: Verdana,Arial,sans-serif; font-size: 12px; line-height: 16px;">The shape was approximating a pyramid, with triangular holes punched out. 6. How did Andrew Pike create the Sierpinski carpet? <span style="font-family: Verdana,Arial,sans-serif; font-size: 12px; line-height: 16px;">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. created tiles with different numbers of iterations of the process. Some of the tiles started white, with the knocked-out squares black, and some of them started black, with the knocked-out squares white. 7. Why did he choose that image? <span style="font-family: Verdana,Arial,sans-serif; font-size: 12px; line-height: 16px;">This gave him squares that approximated many gradations of gray. **
 * <span style="font-family: 'Palatino Linotype','Book Antiqua',Palatino,serif; font-size: 14px;">1. What is a mathematical dynamical System?