Reading+2




**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 ...
 * <span style="font-family: 'Trebuchet MS', Helvetica, sans-serif; font-size: 12pt;">That beauty was richly on display at an exhibition of mathematical art at the Joint Mathematics Meeting in San Diego in January, **<span style="color: rgb(198, 6, 6);">where ** more than 40 artists showed their creations.
 * <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 <span style="color: rgb(198, 6, 6);">**it** to a different spot. Field repeats <span style="color: rgb(198, 6, 6);">**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 **<span style="color: rgb(198, 6, 6);">it .**
 * <span style="font-family: 'Trebuchet MS', Helvetica, sans-serif;"> 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: rgb(198, 6, 6);">**such complex behavior** can create some beautiful images.
 * <span style="font-family: 'Trebuchet MS', Helvetica, sans-serif;"> Robert Bosch, a mathematics professor at Oberlin College in Ohio, took **<span style="color: rgb(198, 6, 6);">his ** inspiration from an old, seemingly trivial problem **<span style="color: rgb(198, 6, 6);">that ** hides some deep mathematics. Take a loop of string and throw **<span style="color: rgb(198, 6, 6);">it ** 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: rgb(198, 6, 6);">**itself** . A theorem states that the loop will divide the page into two regions,<span style="color: rgb(198, 6, 6);">**one inside** the loop and **<span style="color: rgb(198, 6, 6);">one outside **.
 * <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: rgb(198, 6, 6);">**it** may not be obvious whether a particular point lies inside or outside the loop. Topologists, the type of mathematicians <span style="color: rgb(198, 6, 6);">**who** 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: rgb(198, 6, 6);">**you** shouldn't assume a proof is unnecessary in cases like **this one**.

===**<span style="font-family: 'Trebuchet MS', Helvetica, sans-serif; font-size: 12pt;"> <span style="font-family: 'Palatino Linotype', 'Book Antiqua', Palatino, serif; font-size: 16px;">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: 15px;">
<span style="font-family: 'Palatino Linotype', 'Book Antiqua', Palatino, serif; font-size: 14px;">1. What is a mathematical dynamical System? 2. Why does the image "Coral Star" get more and more complex? 3. Find a definition of the following words that fits in the text, please acknowledge the source: Loop, crinckly, string 4. Where did Robert Bosch take his inspiration from? Describe the source of his inspiration. 5. What happened with Fathauer's arrangement? Why? 6. How did Andrew Pike create the Sierpinski carpet? 7. Why did he choose that image?