Reading+2

Good job 6pts Reading Log 2 - Math on Display. Visualizations of mathematics create remarkable artwork Pre-Reading  Read the title and write a list of ten words you think you might find in the text.

 arts, mathematics , application, display, geometry, Greece, artists, image, numbers, F ibonacci

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

art and math are closely related. Many artists use many math concepts such as proportions, geometric relationships, etc ... for example the Vitruvian Man (Da Vinci). 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

 arts, mathematics, display, artists, image, numbers, 3. Please write what the following referents **(in bold letters)**  refer to in the text:

That refers to the simpler sort of beauty where refers to an exhibition of mathematical art at the Joint Mathematics Meeting in San Diego
 * Mathematicians often rhapsodize about the austere elegance of a well-wrought proof. But math also has a simpler sort of beauty **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="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="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 at point that it takes this process refers to <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 12pt;">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.

it refers to the pixel.

<span style="font-family: 'Trebuchet MS',Helvetica,sans-serif; line-height: 24px;">such complex behavior refers to at dynamical systems
 * <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="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 **.

His refers to Robert Bosch that refers to seemingly trivial problem it refers to a loop of string itself refers to the string one inside refers to region of the page. one outside refers to region of the page

it refers to the line who is refers to the Topologists you refers to lector. this one refers to experience that we shouldn't assume a proof is unnecessary.
 * <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="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: 14px;">1. What is a mathematical dynamical System? dynamical system is just any rule that determines how a point moves around a plane.

2.Why does the image "Coral Star" get more and more complex?

the image of "coral Galaxies" is becoming more complex as we approach the center, because the equation is discontinuous at the origin.

3. Find a definition of the following words that fits in the text, please acknowledge the source: Loop, crinckly, string

LOOP: the curved shape made when something long and thin, such as a piece of string, bends until one part of it nearly touches or crosses another part of it http://dictionary.cambridge.org/dictionary/british/loop_1?q=loop

CRINKLY: to become covered in many small lines and folds, or to cause something to do this http://dictionary.cambridge.org/dictionary/british/crinkle

STRING: (a piece of) strong thin rope which is made by twisting very thin threads together and which is used for fastening and tying thing http://dictionary.cambridge.org/dictionary/british/string_1?q=string

4. Where did Robert Bosch take his inspiration from? Describe the source of his inspiration. __t__ook 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 paper.

5. What happened with Fathauer's arrangement? Why? __ fathauer trabajado con cubos de colores. Se dio cuenta de que algo especialocurrió. Más sorprendente aún, se encontró con que las caras de la pirámide formó el triángulo de Sierpinski, uno de los primeros fractales jamás estudiado. ??? __

6. How did Andrew Pike create the Sierpinski carpet? STEPS: " To 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. D ived after Sierpinski photography by attaching a small gray square to each squareand was spreading shades of gray to the nearest square.

7. Why did he choose that image? He chose the image because it WAS sierponski self -referential. In addition the image was appropriate to use the technique of self- similar fractals.