Reading+2

Reading Log 2 - Math on Display. Visualizations of mathematics create remarkable artwork __ · Read the title and write a list of ten words you think you might find in the text. I guess I’ll find words as creation, geometry, patterns, colors, design, curves, plane figures, artists, and ratio. · What do you know about the link between artwork and mathematics? Mention some examples. I know about some applications of math to the visual art-designing process as considering golden ratio and repeating patterns of colors and geometrical figures.
 * Great Job Francis... 7pts **__
 * Pre-Reading **

· Please click on the following link to read the article. [] · While reading, please locate the words you listed in the pre-reading and write a list of the ones you found in the text I found creation, design, colors, patterns. · Please write what the following referents (in bold letters) refer to in the text:
 * During Reading and After Reading **

ü Mathematicians often rhapsodize about the austere elegance of a well-wrought proof. But math also has a simpler sort of beauty ** that ** is perhaps easier to appreciate...  That refers to the beauty of math simpler that the elegance of proofs. ü 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. Where refer to the exhibition of mathematical art in San Diego. ü 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 ** to a different spot. Field repeats ** this process ** 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 ****. ** First it refers to the selected point the dynamical system can move. This process refers to the instruction of picking a point and moving it on the plane according to an simple equation. Second it refers to the pixel Professor Field colored. ü 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 ** can create some beautiful images. Such complex behavior refers to the behavior of a point through a dynamical system. ü 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 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 **. His refers to Bosch inspiration. That refers to the problem Bosch picked that seems to be trivial. It refers to the selected loop of string. Itself refers to the same string. One inside refers to the region of the paper “contained in” the loop of string. One outside refers or the region of the paper surrounding the loop. ü 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 ** may not be obvious whether a particular point lies inside or outside the loop. Topologists, the type of mathematicians ** who ** study such things have managed to construct many strange, "pathological" mathematical objects with very surprising properties, so they know from experience that ** you ** shouldn't assume a proof is unnecessary in cases like **this one**. Who refers to a specific type of mathematicians being defined: topologists. You refers to anyone that receive this information; this one refers to the case in which might be very difficult describe point inside or outside the loop.

** After reading the text, please answer the following questions in your own words: ** · What is a mathematical dynamical System? Is any rule that determines the movement of a point in a plane.

· 2. Why does the image "Coral Star" get more and more complex? It gets more and more complex closer to the center because the functions associated to it is discontinuous at the origin.

· 3. Find a definition of the following words that fits in the text, please acknowledge the source: //__ Loop: __// anything with a round or oval shape (formed by a curve that is closed and does not intersect itself) (taken from [])

//__ Crinckly: __// wrinkled; crinkled. Crinkle: To form wrinkles or ripples (taken from [] ) //__ String: __// a lightweight chord (taken from [])

· 4. Where did Robert Bosch take his inspiration from? Describe the source of his inspiration. He inspired his work of the problem of describing whether a point is or no inside of a loop, no matter if the loop is too wrinkled.

· 5. What happened with Fathauer's arrangement? Why? He “ found that it doesn't require fancy mathematics to stumble upon remarkable mathematical patterns”, because he discovered that repeating patterns of red and orange cubes he designed a pyramid that approximates at each face Sierpinski Triangle, one of the first fractals ever studied. · 6. How did Andrew Pike create the Sierpinski carpet? To create Sierpinski carpet you must follow this instructions: “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.” But pike stopped the process and created tiles with several numbers of repetitions of the process, assigning degradations of grays to each tile. Then he divided a photograph of Sierpinski into tiny squares and associated a gray shade to each square. Finally, he spread some shades of grays from a square to a nearby other, so the transition between them were not so rough.

· 7. Why did he choose that image? He chose that image because of the reference it made to it-self, kind of a honorific work.