Reading+2

What do you know about the link between artwork and mathematics? Mention some examples.
====--> The relation between the art and the mathematics is bidirectional since thanks to several ancient works of art, there were created several theorems that they speak about the triangles, internal and external angles, sum of angles, rotation, traslation and symmetry, etc. And in addition thanks to the mathematics many works of art have been created since they use regular figures (polygons) which are distorted and form irregular figures, beside using the angles, the symmetries, etc. It is to say the art complements to the mathematics and viceversa. Some examples of this are the tessellations, the golden reason, fractals, etc.====

[]
====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 ====

3. Please write what the following referents **(in bold letters)** refer to in the text:
= = --> That refers to another simpler sort of beauty. --> Where refers to an exhibition of mathematical art at the Joint Mathematics Meeting in San Diego. --> It refers to a piece. --> This process refers to field uses an equation that takes any point on a piece of paper and moves **it** to a different spot. --> It refers to a pixel. --> Such complex behavior refers to dynamical systems. --> His refers to Robert Bosch, a mathematics professor at Oberlin College in Ohio. --> That refers to seemingly trivial problem. --> it refers to a loop of string. --> Itself refers to the string. --> One inside refers to the inside region of the page. --> One outside refers to the outside region of the page. --> It refers to a line. --> Who refers to the topologists. --> You refers to the lector that no are a topologist. --> This one refers to the experience that we shouldn't assume a proof is unnecessary.
 *  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, **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** shouldn't assume a proof is unnecessary in cases like ** this one. **

1. What is a mathematical dynamical System? --> A mathematical dynamic system is any rule that it determines like moves a point about a plane. For this system there is used an equation that takes a point on a leaf of paper and moves it to another point, this process repeats itself infinite times and guards the track of every obtained point.

2. Why does the image "Coral Star" get more and more complex? --> The image "Coral Star" is more complex since thanks to the mathematical dynamical system, they can produce complex behaviors from simple equations which is reflected in the above mentioned image when on having been more near the center, it becomes more complex in view of the spectator. This owes technically to that in the origin the equation is discontinuous.

3. Find a definition of the following words that fits in the text, please acknowledge the source: Loop, crinckly, string --> Loop means in mathematical terms: 1. Loop (algebra) a quasigroup with an identity element. 2. L oop (graph theory), an edge that begins and ends on the sam.e vertex 3. Loop (topology), a path that starts and ends at the same point. --> Crinckly means cutting so the result is corrugated (forms regular waves). --> String means generally, a thin, flexible piece of rope or twine which is used to tie, bind, or hang other objects.

Source: [|www.wikipedia.com]

4. Where did Robert Bosch take his inspiration from? Describe the source of his inspiration. --> Robert inspired in solving the problem that some deep mathematics conceal. This inspiration was taken of mathematical old men. For it it took a loop of string and threw it down on a leaf of paper, wherefrom there arose a theorem that he says that the bow will divide the above mentioned leaf in two regions, one inside and one outside.

5. What happened with Fathauer's arrangement? Why? --> Fathauer on the other hand, found his inspiration in the puzzles since for him these were not needing that they stumble on the notable mathematical model. For it it played with several squares that they were arranging a model, then this repeated several times with buckets of different colors. In addition Fathauer said that " After a few iterations, I noticed that something special was happening with that arrangement". Process: he started with a red cube and placed five half-sized orange cubes on its exposed faces. Then he put five smaller yellow cubes on the faces of each of those, and five even smaller greenish cubes on the faces of those, and so on. The shape was approximating a pyramid, with triangular holes punched out. Even more remarkably, he found that the faces of the pyramid formed the Sierpinski Triangle, one of the earliest fractals ever studied.

6. How did Andrew Pike create the Sierpinski carpet? --> Andrew Pike inspired by the artistic creations of Waclaw Sierpinski. To create the carpet which name is the surname of the artist from which his inspiration arose, it took a square, tic - tac-toe divided it in a model and extracted the square of the way; then he draw a model on every remaining square and it made the average squares amazed of these. The repetition of the above mentioned process created the carpet. Then it created one created a program in the computer that divided Sierpinski's photography in tiny squares, did an average of the shades of gray color in the picture across every individual square, and selected the blue roller Sierpinski that was the most nearby in to protect of the Sun. But since simply it could not do the smallest blue rollers, because the printers can produce the points that are only so tiny. Then he used a so called technology " being nervous ". He calculated the mistake - the difference between to protect of the Sun of the photography and to protect of the Sun of the blue roller the most similar Sierpinski - and extended it between other nearby blue rollers. This with efficiency softened the image, removing the awkward transitions between blue rollers.

7. Why did he choose that image? --> He chose the image of Sierpinski because it was autoreferential it is to say that it uses a technology with autosimilar fractals.