Reading+2

Read the title and write a list of ten words you think you might find in the text.
Mathematics, display, visualization, artwork, desing, art, application, see, geometry, combination.

What do you know about the link between artwork and mathematics? Mention some examples.
I don’t know about it. But I know that geometry plus paper is art. For example: the origami.

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
Mathematics, display, art, see.

3. Please write what the following referents ** (in bold letters) ** __ refer to __ in the text:
· 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 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. · 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. **    · 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. · __ 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 ** itself ** ** * ****. ** A theorem states that the loop will divide the page into two __regions(of the page)__ __, __ ** one inside ** ** * ** the loop and ** one outside ** ** * **. · 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 ** ** *(the reader) ** 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? A mathematical dynamical system is a rule. It says what behavior should have a point around a plane. 2. Why does the image "Coral Star" get more and more complex?

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

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

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

6. How did Andrew Pike create the Sierpinski carpet? Why did he choose that image?