Reading+2

Reading Log 2 - Math on Display. Visualizations of mathematics create remarkable artwork **
 * Good Job... 7pts


 * Pre-Reading **


 * Read the title and write a list of ten words you think you might find in the text. **


 * 1. ****Mathematics. **
 * 2. ****Display. **
 * 3. ****Create. **
 * 4. ****Artwork. **
 * 5. ****Art. **
 * 6. ****See. **
 * 7. ****<span style="color: black; font-family: 'Arial','sans-serif'; font-size: 12pt;">Screen. **
 * <span style="color: black; font-family: 'Palatino Linotype','serif'; font-size: 12pt;">8. ****<span style="color: black; font-family: 'Arial','sans-serif'; font-size: 12pt;">Exhibition. **
 * <span style="color: black; font-family: 'Palatino Linotype','serif'; font-size: 12pt;">9. ****<span style="color: black; font-family: 'Arial','sans-serif'; font-size: 12pt;">Beauty. **
 * <span style="color: black; font-family: 'Palatino Linotype','serif'; font-size: 12pt;">10. ****<span style="color: black; font-family: 'Arial','sans-serif'; font-size: 12pt;">Work. **


 * <span style="color: black; font-family: 'Palatino Linotype','serif'; font-size: 13pt;">What do you know about the link between artwork and mathematics? Mention some examples. **

<span style="color: black; font-family: 'Trebuchet MS','sans-serif'; font-size: 13.5pt;"> [|**http://www.sciencenews.org/view/generic/id/9383/title/Math_on_Display**]
 * <span style="color: black; font-family: 'Palatino Linotype','serif'; font-size: 13pt; line-height: 115%;">I know about the link between artwork and mathematics are things related to the proportion as the picture Vitruvian Man made by Da Vinci, the Greek Parthenon, the Pyramid of Cheops and others that I can’t remember now. **
 * <span style="color: black; font-family: 'Trebuchet MS','sans-serif'; font-size: 13.5pt;">During Reading and After Reading **
 * <span style="color: black; font-family: 'Palatino Linotype','serif'; font-size: 12pt;">1. Please click on the following link to read the article. **


 * <span style="color: black; font-family: 'Palatino Linotype','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="color: black; font-family: 'Arial','sans-serif'; font-size: 12pt;">1. Beauty. **
 * <span style="color: black; font-family: 'Arial','sans-serif'; font-size: 12pt;">2. Display. **
 * <span style="color: black; font-family: 'Arial','sans-serif'; font-size: 12pt;">3. Exhibition. **
 * <span style="color: black; font-family: 'Arial','sans-serif'; font-size: 12pt;">4. Mathematics. **
 * <span style="color: black; font-family: 'Arial','sans-serif'; font-size: 12pt;">5. Art. **
 * <span style="color: black; font-family: 'Arial','sans-serif'; font-size: 12pt;">6. Create. **

<span style="color: black; font-family: 'Arial','sans-serif'; font-size: 10pt;"> __<span style="color: black; font-family: 'Arial','sans-serif'; font-size: 10pt;">That __<span style="color: black; font-family: 'Arial','sans-serif'; font-size: 10pt;"> refers to a simpler sort of beauty.
 * <span style="color: black; font-family: 'Palatino Linotype','serif'; font-size: 12pt;">3. Please write what the following referents ****<span style="color: #c60606; font-family: 'Palatino Linotype','serif'; font-size: 12pt;">(in bold letters) ****<span style="color: black; font-family: 'Palatino Linotype','serif'; font-size: 12pt;"> refer to in the text: **
 * <span style="font-family: 'Trebuchet MS','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','sans-serif'; font-size: 12pt;">that **<span style="font-family: 'Trebuchet MS','sans-serif'; font-size: 12pt;"> is perhaps easier to appreciate <span style="font-family: 'Trebuchet MS','sans-serif'; font-size: 10pt;">...

__<span style="color: black; font-family: 'Trebuchet MS','sans-serif'; font-size: 12pt;">Where __<span style="color: black; font-family: 'Trebuchet MS','sans-serif'; font-size: 12pt;"> refer to an exhibition of mathematical art. <span style="color: black; font-family: 'Arial','sans-serif'; font-size: 10pt;">
 * <span style="font-family: 'Trebuchet MS','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: #c60606; font-family: 'Trebuchet MS','sans-serif'; font-size: 12pt;">where **<span style="font-family: 'Trebuchet MS','sans-serif'; font-size: 12pt;"> more than 40 artists showed their creations.
 * <span style="font-family: 'Trebuchet MS','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','sans-serif'; font-size: 12pt;">it **<span style="font-family: 'Trebuchet MS','sans-serif'; font-size: 12pt;"> to a different spot. Field repeats **<span style="color: #c60606; font-family: 'Trebuchet MS','sans-serif'; font-size: 12pt;">this process **<span style="font-family: 'Trebuchet MS','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 **<span style="color: #c60606; font-family: 'Trebuchet MS','sans-serif'; font-size: 12pt;">it ****<span style="font-family: 'Trebuchet MS','sans-serif'; font-size: 12pt;">. **

__<span style="color: black; font-family: 'Arial','sans-serif'; font-size: 10pt;">It __<span style="color: black; font-family: 'Arial','sans-serif'; font-size: 10pt;"> refers to any point on a piece of paper. __<span style="color: black; font-family: 'Arial','sans-serif'; font-size: 10pt;">This process __<span style="color: black; font-family: 'Arial','sans-serif'; font-size: 10pt;">refer to the process of to move any point on a piece of paper to a different spot. __<span style="color: black; font-family: 'Arial','sans-serif'; font-size: 10pt;">It __<span style="color: black; font-family: 'Arial','sans-serif'; font-size: 10pt;">refers to a pixel. __<span style="color: black; font-family: 'Arial','sans-serif'; font-size: 10pt;">Such complex behavior __<span style="color: black; font-family: 'Arial','sans-serif'; font-size: 10pt;"> refers to behavior produced by very simple equations.
 * <span style="font-family: 'Trebuchet MS','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','sans-serif'; font-size: 12pt;">such complex behavior **<span style="font-family: 'Trebuchet MS','sans-serif'; font-size: 12pt;"> can create some beautiful images.


 * <span style="font-family: 'Trebuchet MS','sans-serif'; font-size: 12pt;">Robert Bosch, a mathematics professor at Oberlin College in Ohio, took **<span style="color: #c60606; font-family: 'Trebuchet MS','sans-serif'; font-size: 12pt;">his **<span style="font-family: 'Trebuchet MS','sans-serif'; font-size: 12pt;"> inspiration from an old, seemingly trivial problem **<span style="color: #c60606; font-family: 'Trebuchet MS','sans-serif'; font-size: 12pt;">that **<span style="font-family: 'Trebuchet MS','sans-serif'; font-size: 12pt;"> hides some deep mathematics. Take a loop of string and throw **<span style="color: #c60606; font-family: 'Trebuchet MS','sans-serif'; font-size: 12pt;">it **<span style="font-family: 'Trebuchet MS','sans-serif'; font-size: 12pt;"> 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','sans-serif'; font-size: 12pt;">itself **<span style="font-family: 'Trebuchet MS','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','sans-serif'; font-size: 12pt;">one inside **<span style="font-family: 'Trebuchet MS','sans-serif'; font-size: 12pt;"> the loop and **<span style="color: #c60606; font-family: 'Trebuchet MS','sans-serif'; font-size: 12pt;">one outside **<span style="font-family: 'Trebuchet MS','sans-serif'; font-size: 12pt;">.

__<span style="color: black; font-family: 'Arial','sans-serif'; font-size: 10pt;">His __<span style="color: black; font-family: 'Arial','sans-serif'; font-size: 10pt;"> refer to Robert Bosch. __<span style="color: black; font-family: 'Arial','sans-serif'; font-size: 10pt;">That __<span style="color: black; font-family: 'Arial','sans-serif'; font-size: 10pt;"> refers to an old, seemingly trivial problem. __<span style="color: black; font-family: 'Arial','sans-serif'; font-size: 10pt;">It __<span style="color: black; font-family: 'Arial','sans-serif'; font-size: 10pt;"> refers to a loop of string. __<span style="color: black; font-family: 'Arial','sans-serif'; font-size: 10pt;">Itself __<span style="color: black; font-family: 'Arial','sans-serif'; font-size: 10pt;"> refer to the string. __<span style="color: black; font-family: 'Arial','sans-serif'; font-size: 10pt;">One inside __<span style="color: black; font-family: 'Arial','sans-serif'; font-size: 10pt;"> refer to one of the two regions. __<span style="color: black; font-family: 'Arial','sans-serif'; font-size: 10pt;">One outside __<span style="color: black; font-family: 'Arial','sans-serif'; font-size: 10pt;"> refer to the other region.


 * <span style="font-family: 'Trebuchet MS','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','sans-serif'; font-size: 12pt;">it ** <span style="font-family: 'Trebuchet MS','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','sans-serif'; font-size: 12pt;">who **<span style="font-family: 'Trebuchet MS','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','sans-serif'; font-size: 12pt;">you **<span style="font-family: 'Trebuchet MS','sans-serif'; font-size: 12pt;"> shouldn't assume a proof is unnecessary in cases like **this one**.

__<span style="color: black; font-family: 'Arial','sans-serif'; font-size: 10pt;">It __<span style="color: black; font-family: 'Arial','sans-serif'; font-size: 10pt;"> refers to a line. __<span style="color: black; font-family: 'Arial','sans-serif'; font-size: 10pt;">Who __<span style="color: black; font-family: 'Arial','sans-serif'; font-size: 10pt;"> refer to the Topologists. __<span style="color: black; font-family: 'Arial','sans-serif'; font-size: 10pt;">You __<span style="color: black; font-family: 'Arial','sans-serif'; font-size: 10pt;"> refer to the persons that are reading this article. __<span style="color: black; font-family: 'Arial','sans-serif'; font-size: 10pt;">This one __<span style="color: black; font-family: 'Arial','sans-serif'; font-size: 10pt;"> refer to mathematical objects with very surprising properties.


 * <span style="color: black; font-family: 'Palatino Linotype','serif'; font-size: 15pt;">After reading the text, please answer the following questions ****<span style="color: black; font-family: 'Palatino Linotype','serif'; font-size: 15pt;">in your own words: **

<span style="color: black; font-family: 'Palatino Linotype','serif';">1. What is a mathematical dynamical System?

A mathematical dynamical System is any rule that determines how a point moves around a plane.

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

Coral Star gets more and more complex when is closer to the center, because it 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 <span style="font-family: 'Palatino Linotype','serif';">

__<span style="font-family: 'Palatino Linotype','serif';">Loop: __ <span style="font-family: 'Palatino Linotype','serif';">Source: [] __<span style="font-family: 'Palatino Linotype','serif';">Crinckly: __ //<span style="color: black; font-family: 'Arial','sans-serif'; font-size: 10pt; line-height: 115%;">v.intr. // //<span style="color: black; font-family: 'Arial','sans-serif'; font-size: 10pt;">v.tr. //<span style="color: black; font-family: 'Arial','sans-serif'; font-size: 10pt;"> To cause to crinkle. //<span style="color: black; font-family: 'Arial','sans-serif'; font-size: 10pt;">n. //<span style="color: black; font-family: 'Arial','sans-serif'; font-size: 10pt;"> A wrinkle, ripple, or fold. Source: <span style="font-family: 'Arial','sans-serif'; font-size: 10pt;">[] <span style="color: black; font-family: 'Arial','sans-serif'; font-size: 10pt;">
 * <span style="color: black; font-family: 'Arial','sans-serif'; font-size: 10pt;">1. a. **<span style="color: black; font-family: 'Arial','sans-serif'; font-size: 10pt;">A length of line, thread, ribbon, or other thin material that is curved or doubled over making an opening.
 * <span style="color: black; font-family: 'Arial','sans-serif'; font-size: 10pt;">b. **<span style="color: black; font-family: 'Arial','sans-serif'; font-size: 10pt;">The opening formed by such a doubled line.
 * <span style="color: black; font-family: 'Arial','sans-serif'; font-size: 10pt;">2. **<span style="color: black; font-family: 'Arial','sans-serif'; font-size: 10pt;">Something having a shape, order, or path of motion that is circular or curved over on itself.
 * <span style="color: black; font-family: 'Arial','sans-serif'; font-size: 10pt;">1. **<span style="color: black; font-family: 'Arial','sans-serif'; font-size: 10pt;">To form wrinkles or ripples.
 * <span style="color: black; font-family: 'Arial','sans-serif'; font-size: 10pt;">2. **<span style="color: black; font-family: 'Arial','sans-serif'; font-size: 10pt;">To make a soft crackling sound; rustle.

__<span style="color: black; font-family: 'Arial','sans-serif'; font-size: 10pt;">String: __ Source: <span style="font-family: 'Arial','sans-serif'; font-size: 10pt;">[] <span style="color: black; font-family: 'Palatino Linotype','serif';">
 * <span style="color: black; font-family: 'Arial','sans-serif'; font-size: 10pt;">1. **<span style="color: black; font-family: 'Arial','sans-serif'; font-size: 10pt;">A cord usually made of fiber, used for fastening, tying, or lacing.
 * <span style="color: black; font-family: 'Arial','sans-serif'; font-size: 10pt;">2. **<span style="color: black; font-family: 'Arial','sans-serif'; font-size: 10pt;">Something configured as a long, thin line: //<span style="color: #226699; font-family: 'Arial','sans-serif'; font-size: 10pt;">limp strings of hair. //<span style="color: black; font-family: 'Arial','sans-serif'; font-size: 10pt;">

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

Robert Bosch took inspiration from an old problem that consists in to throw a loop of string to a piece of paper and to see if the loop divide the paper into two regions, one inside and the other outside.

5. What happened with Fathauer's arrangement? Why?

He saw that the shape was approximate to a pyramid and he found that their faces formed the Sierpinski Triangle, which is one of the first and most important fractal studied.

6. How did Andrew Pike create the Sierpinski carpet?

Andrew Pike took a square and divided it into a pattern of tic tac toe and took out the middle square and then he did the same with all the remaining squares infinitely.

7. Why did he choose that image?

He chooses that image because it was his auto-referential.