Reading+2

Good
===**Pre-Reading Approximations, Symmetry, Apply, Functions, Square, Shape, Representation, Calculus, Geometry, Models. Sometimes the symmetry or the patterns some artwork has can be predicted by mathematic models, Someone in my class mention the symmetry that exist in the compositions of Chaikowski. **===

**During Reading and After Reading **

 *  Mathematicians often rhapsodize about the austere elegance of a well-wrought proof. But math also has a simpler sort of beauty **that (the simpler beauty of math)** 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, ** where (the exhibition in San Diego) ** more than 40 artists showed their creations.
 * 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 (the point)** to a different spot. Field repeats **this process (the use of the equation)** 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 (the pixel) .**
 * 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 (the equations)** can create some beautiful images.
 * Robert Bosch, a mathematics professor at Oberlin College in Ohio, took ** his (Robert Bosch) **inspiration from an old, seemingly trivial problem ** that (the problem) ** hides some deep mathematics. Take a loop of string and throw ** it (the loop) **down on a piece of papaer. It can form any shape you like as long as the string never touches or crosses **itself (the string)** . A theorem states that the loop will divide the page into two regions, **one inside(The region)** the loop and ** one outside (the region) **.
 * 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(the theorem)** may not be obvious whether a particular point lies inside or outside the loop. Topologists, the type of mathematicians **who(topologist)** study such things have managed to construct many strange, "pathological" mathematical objects with very surprising properties, so they know from experience that **you(everyone)** shouldn't assume a proof is unnecessary in cases like **this one**.

===**After reading the text, please answer the following questions **in your own words:===

1. What is a mathematical dynamical System?  __Its__ **IT'S ** a rule that determines how a point moves around a given plane..

2. Why does the image "Coral Star" get more and more complex? Because the equation is discontinuous in the middle.

3. Find a definition of the following words that fits in the text, please acknowledge the source: Loop: A length of line, thread, ribbon, or other thin material that is curved or doubled over making an opening. Crinkly : <span style="font-family: Arial,helvetica,sans-serif; font-size: 13px; line-height: normal;">To form wrinkles or ripples. <span style="font-family: 'Palatino Linotype','Book Antiqua',Palatino,serif; font-size: 14px; line-height: 19px;">String: <span style="font-family: Arial,helvetica,sans-serif; font-size: 13px; line-height: normal;">Something configured as a long, thin line

All three definition where taken from www.thefreedictionary.com. (profe por alguna razón los párrafos se pegan cuando le doy edit, no eh podido arreglarlo ) **<span style="color: #f95dbe; font-family: Tahoma,Geneva,sans-serif;">Okys... El wiki está un poco necio. Me lo debes... **

====<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; line-height: 19px;">4. Where did Robert Bosch take his inspiration from? Describe the source of his inspiration. <span style="font-family: Verdana,Arial,sans-serif; font-size: 12px; line-height: 16px;">From an old, seemingly trivial problem that hides some deep mathematics. Take a loop of string and throw it down on a piece of paper. 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. 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;">T o 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? <span style="font-family: Verdana,Arial,sans-serif; font-size: 12px; line-height: 16px;">he chose the image of Sierpinski because it was self-referential. ====