Reading+log+2

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

Art, Geometry, Figures, Ratios, Measures, Program, Mathematics, Golden, Numbers, Fibonnaci. ==== What do you know about the link between artwork and mathematics? Mention some examples. ==== Historically, Mathematics and artworks have been related, because all in the visible world has geometry. If we would want to make a representation of a object from nature, using mathematics we can achieve the perfection. Also, the sense of harmony and perfection is given by what is mathematically correct. For example, Greeks used mathematical proportions to make their artworks because, for them, that represented the geometric harmony.

=== 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 ====

Art, Program, Mathematics, Numbers. 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** **(A sort of beauty) ** is perhaps easier to appreciate ...
 * That beauty was richly on display at an exhibition of mathematical art at the Joint Mathematics Meeting in San Diego in January, **<span style="background-color: #ffffff; color: #c60606; font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 16px;">where **<span style="background-color: #ffffff; font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 12pt; line-height: 1.5;">**(At the Joint Mathematics Meeting in San Diego)** 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: #c60606; font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 12pt;">**it** <span style="background-color: #ffffff; font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 12pt;">**(A** **<span style="background-color: #ffffff; font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 16px;">ny point on a piece of paper) **<span style="font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 12pt;">to a different spot. Field repeats ** this process ** **<span style="font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 12pt;">(take any point on a piece of paper and moves it to a different spot) ** <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 12pt;">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 (A** <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 16px; line-height: 1.5;"> **pixel)**.
 * <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: #c60606; 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;"> **(the result of the dynamic process)** can create some beautiful images.
 * <span style="background-color: #ffffff; font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 12pt;">Robert Bosch, a mathematics professor at Oberlin College in Ohio, took ** his ** **(The inspirarion of the professor)** inspiration from an old, seemingly trivial problem ** that ** <span style="background-color: #ffffff; font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 16px;">**(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 ** 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: #c60606; font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 12pt;">**itself** **<span style="font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 16px;">(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, <span style="color: #c60606; font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 12pt;">**one inside** <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 12pt;"> **(A region of the paper)** the loop and ** one outside ** **<span style="font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 16px;">(The other region of the paper) **<span style="font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 12pt; line-height: 1.5;">.
 * <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: #c60606; 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: #c60606; font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 12pt;">**who** <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: #c60606; font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 12pt;">**you** <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 12pt;"> shouldn't assume a proof is unnecessary in cases like **<span style="color: #ff0000; font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 12pt;">this one **<span style="background-color: #ffffff; 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="background-color: #ffffff; font-family: 'Palatino Linotype','Book Antiqua',Palatino,serif; font-size: 14px;">1. What is a mathematical dynamical System? <span style="background-color: #ffffff; 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="background-color: #ffffff; 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="background-color: #ffffff; font-family: 'Palatino Linotype','Book Antiqua',Palatino,serif; font-size: 14px;">Loop, crinckly, string <span style="background-color: #ffffff; font-family: 'Palatino Linotype','Book Antiqua',Palatino,serif; font-size: 14px;">4. Where did Robert Bosch take his inspiration from? Describe the source of his inspiration. <span style="background-color: #ffffff; font-family: 'Palatino Linotype','Book Antiqua',Palatino,serif; font-size: 14px;">5. What happened with Fathauer's arrangement? Why? <span style="background-color: #ffffff; font-family: 'Palatino Linotype','Book Antiqua',Palatino,serif; font-size: 14px;">6. How did Andrew Pike create the Sierpinski carpet? <span style="background-color: #ffffff; font-family: 'Palatino Linotype','Book Antiqua',Palatino,serif; font-size: 14px;">7. Why did he choose that image?