Reading+Log+2

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

1.- Mathematics 2.- Visualizations 3.- Art 4.- Figures 5.- Colors 6.- puzzle 7.- Geometry 8.- Simetry 9- Ecuation 10.- Artists

==== What do you know about the link between artwork and mathematics? Mention some examples. ====

=== During Reading and After Reading === ==== 1. Please click on the following link to read the article. ==== ==== [] ==== ==== <span style="font-family: 'Palatino Linotype','Book Antiqua',Palatino,serif; font-size: 12pt;">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 ====

<span style="background-color: #ffffff; font-family: 'Palatino Linotype','Book Antiqua',Palatino,serif; font-size: 12pt;">Mathematics, "visualization", art, colors, puzzle, artists.

<span style="background-color: #ffffff; font-family: 'Palatino Linotype','Book Antiqua',Palatino,serif; font-size: 12pt;">(Visualization is not in the text, is more in the sub-title.)

==== <span style="font-family: 'Palatino Linotype','Book Antiqua',Palatino,serif; font-size: 12pt;">3. Please write what the following referents <span style="color: #c60606; font-family: 'Palatino Linotype','Book Antiqua',Palatino,serif; font-size: 12pt;">**(in bold letters)** <span style="font-family: 'Palatino Linotype','Book Antiqua',Palatino,serif; font-size: 12pt;"> refer to in the text: ====


 * <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 12pt;">Mathematicians often rhapsodize about the austere elegance of a well-wrought proof. But math also has a simpler sort of beauty <span style="color: #c60606; font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 12pt;">**that** <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 12pt;"> is perhaps easier to appreciate <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;">...

<span style="background-color: #ffffff; font-family: 'Trebuchet MS',Helvetica,sans-serif;">"That" refers to the simpler sort of beauty
<span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;">
 * <span style="background-color: #ffffff; 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, ** where ** more than 40 artists showed their creations.

<span style="background-color: #ffffff; font-family: 'Trebuchet MS',Helvetica,sans-serif;">"Where" refers to an exhibition of mathematical art
<span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;">
 * <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="font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 12pt;"> to a different spot. Field repeats <span style="color: #c60606; font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 12pt;">**this process** <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 .**

"it" refers to the pixels
<span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;"> <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;">
 * <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;"> can create some beautiful images.

<span style="background-color: #ffffff; font-family: 'Trebuchet MS',Helvetica,sans-serif;">"Such complex behavior" refers to very simple equations that produce complicated behavior
<span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;">
 * <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 <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: 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;"> the loop and ** one outside **.

<span style="background-color: #ffffff; font-family: 'Trebuchet MS',Helvetica,sans-serif;">"One inside" and "one outside" refers to two regions that is divide by the loop
<span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;">
 * <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 **this one**.

<span style="background-color: #ffffff; font-family: 'Trebuchet MS',Helvetica,sans-serif;">"This one" refers to a case when we don't know if something were obviously
=== <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?

It's a rule, that determines how a point moves around the place where it is. (in a plane)
<span style="font-family: Impact,Charcoal,sans-serif;"> <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;">Because the equation is discontinuous at the origin.
<span style="font-family: Impact,Charcoal,sans-serif;"> <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

//-String:// Something configured as a long, thin line or a cord usually made of fiber, used for fastening, tying, or lacing
( [|http://www.thefreedictionary.com] )

<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.

==== He took his inspiration from an old, seemingly trivial problem that hides some deep math. A theorem states that the loop divides a page in two regions, this happen 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: Impact,Charcoal,sans-serif;"> <span style="background-color: #ffffff; font-family: 'Palatino Linotype','Book Antiqua',Palatino,serif; font-size: 14px;">5. What happened with Fathauer's arrangement? Why?

It became a fractal, like Sierpinski's carpet. Because it kept putting the same initial shape into the one thar was originaly made and the others that result form putting the shapes in them
<span style="font-family: Impact,Charcoal,sans-serif;"> <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;">It draw a squre and then put a tic-toe pattern, and take out the middle square, and he kept doing it repitedly ====

<span style="font-family: Impact,Charcoal,sans-serif;"> <span style="background-color: #ffffff; font-family: 'Palatino Linotype','Book Antiqua',Palatino,serif; font-size: 14px;">7. Why did he choose that image?