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Video 1: Dr. Quantum - Double slit experiment Before watching 1. You are about to watch a video called "Dr. Quantum - Double slit experiment". What do you think it will be about? I think the video will be on the use of two slits to be divided into two particles or molecules. 2. Go to a dictionary and copy the definition of "slit". Is it a noun , a verb? Is it is both? Mention all definitions. Please acknowledge the source. It is both. slit vb slits, slitting, slit (tr) 1. to make a straight long incision in; split open 2. to cut into strips lengthwise 3. to sever n 1. a long narrow cut 2. a long narrow opening Source: www.thefreedictionary.com/slit 3. Mention five words you think you will find in the video Slit, experiment, double, particle and pattern During watching and after watching 1. Are there any of the words you mentioned in the previous question in the video? Yes, all the words mentioned previously was told in the video 2. What's the experiment about? Describe it. The experiment consisted in using particles that pass through a grid marked a pattern, moving the particles or molecules of two grids are two patterns were the same. By repeating the experiment with one slit but in water and waves are formed, as in the previous case form a pattern, and using two slit see how they form a series of patterns according to the intensity of the interference waves. a.What does he need to do the experiment? In the experiment, he verify as matter is made up of little electrons that be divided form a pattern of interference, thus the particles need a board with one slit and with two slit, black water and a platform for the patterns formed onservar. b.How many steps does it have? The experiment has 4 steps c.What happens in each step? 1. First passes through the board with a slit with a pattern forming particles 2. Second particle passes through two slit forming two patterns. 3. Third with the board that has one slip immersed in the water and the waves create a pattern. 4. Finally, with the board that have two slit in water , waves are created with a pattern of interference d. What is the third element Dr. Quantum uses? The board with one slit in water 3. What happens with balls and one slit? And with two slits? The balls with one slit create one pattern and with two slits two patterns 4. What about waves? With the waves creates an interference pattern 5. What happens with electrons Created as a wave a interference pattern 6. What explanation does Dr. Quantum give? The electrones are divided touching the slit and pass through it for interference to be reattached after the pattern forms as the waves. Reading log 1 - Using Mathematical Models to Study the Dispersion of Exotic Marine Species Before Reading *Read the tilte and list 10 words you think you might find in the text. Species, sea, creatures, animals, survival, habitat, climate, equations, numbers and formulas. *How can you use math applied to biology. Mention one thing you can think of. The statistics are roughly the discipline that is responsible for the collection, analysis, presentation and interpretation of field data or experimental. By its very nature, statistics are inextricably linked to the empirical experience and its application to natural science can not transcend this limit. Because of this, the statistic is an assistant biology as an easy presentation and data collection and allows, under suitable assumptions, inferences about the variables involved. An example of this is to find the dynamics would cause changes in the magnitude of the population of certain species. *What do you know about jelly fish? What kind of fish is it? If you don't know, find out, cut and paste an image of this fish. Please acknowledge the source. Jellyfish are marine organisms belonging to the phylum Cnidaria and the Coelenterata, are pelagic, gelatinous body, shaped like a bell hanging a tubular handle, with the mouth at its lower end, sometimes for lengthy tentacles loaded with stinging cells called cnidocitos. Source: http://es.wikipedia.org/wiki/jellyfish_(animal) *What is dispersion? If you don't know, find out, please acknowledge the source. dis·perse (d-spûrs) v. dis·persed, dis·pers·ing, dis·pers·es v.tr. 1. a. To drive off or scatter in different directions b. To strew or distribute widely: 2. To cause to vanish or disappear. See Synonyms at scatter. 3. To disseminate (knowledge, for example). 4. To separate (light) into spectral rays. 5. To distribute (particles) evenly throughout a medium. v.intr. 1. To separate and move in different directions; scatter: The crowd dispersed once the concert ended. 2. To break up and vanish; dissipate Source: http://www.thefreedictionary.com/dispersed While Reading and After Reading 2. Try to locate the words you though you were going to find in the text (question 1 before reading) List the words you found Species, sea, creatures, animals, climate and formulas. 3. Find what the following referents in bold letters refer to in the text: Mathematical models can be used to simulate the spreading of exotic marine species. Marine environments around the world are being threatened by exotic species of moon jellyfish being dispersed by international shipping and trade, according to research by staff at the School of Mathematics and Statistics, UNSW. Using genetic data and computer simulations of ocean currents and water temperatures, researchers from the School of Mathematics and Statistics, UNSW and the University of California, Davis, have revealed that the jellyfish could not have migrated naturally. The species of Jellyfish studied are known as Aurelia (Fig. 1) and these are found over much of the world’s temperate oceans. By simulating the movement of the jellyfish (shown in Fig. 2) over a 7,000-year period the study provides strong evidence that the world-wide dispersal post-dates European global shipping and trade, which began almost 500 years ago. To investigate the limits of natural dispersion of species of the moon jellyfish over multi century time scales, the researchers developed a global Lagrangian model incorporating representative life-history characteristics of the moon jellyfish. The researchers used both the known lifecycle of the moon jellyfish and climate and ocean current information to create a mathematical model of their dispersion over time. Each experiment was based on the virtual release of 20 000 lavae from known moon jellyfish zones of occurrence (see red coastal zones of Fig. 2). The model can be summarised by: In the formula xt is the moon jellyfish location at time of t, U is the current speed, Δt is time, Rn is a normal distributed random number, and Kh is a lateral mixing rate and Cmix is tidal mixing near the coast. The model is then integrated and the results can be shown on a global map of dispersal (Fig. 2 below). During the model integration, biological processes such as temperature limits, mortality, re-settlement and spawning are included to take account of the life cycle of the jellyfish. The red areas show virtual release points off the coast of Australia, around Japan, United States and Europe. Unnatural migration occurs via ballast water from international shipping and because of international trade of marine species. About 3,000 species of marine organisms are believed to travel the world in ships' ballast water on a daily basis. Ships take in water for stability before a voyage and, despite preventative measures such as mid-ocean exchange/ flushing, this 'foreign' water and its contents can find its way into bays and harbours at the ships destination. The computer model could answer similar questions about the migration and introduction of any suspected non-native marine creatures, according to its developers Professor Matthew England and Alex Sen Gupta. "Up until now our knowledge of natural and human-assisted dispersal of species has been insufficient to confidently track and predict the spread of non-indigenous marine species," Now we have a tool that can include data on currents, geography and the biology of an organism to help separate natural dispersal from that which happens through shipping and trade," says Professor England. 4. What is happening with the fish? The jellyfish are migrating from their natural hábitat 5. What explanation scientists had given? Unnatural migration occurs through ballast water from international shipping and international trade in marine species. 6. What did mathematicians find out? What does the formula explain? About 3,000 species of marine organisms are believed to travel the world in ships' ballast water on a daily basis. Ships take in water for stability before a voyage and, despite preventative measures such as mid-ocean exchange/ flushing, this 'foreign' water and its contents can find its way into bays and harbours at the ships destination and that produce the unnatural migration. Video 2: The Elegant Universe Einstein's - Relativity Before watching What is gravity? Gravity, is a natural phenomenon by which physical bodies attract with aforce proportional to their masses. Who discovered it? Isaac Newton How does the Einstein’s Relativity Theory relate with gravity? The general theory of relativity and general relativity is a theory of gravitational field and the reference systems in general and she describes the acceleration and gravity as different aspects of the same reality Mention five words you might find in the video Gravity, relativity, Einstein, mass and Newton During watching and after watching 2. Which of the words in the question above did you find in the video? Yes, all the words mentioned previously was told in the video 3. What was the embarrassing secret Newton was holding about gravity? He had no idea how gravity acctually works 4. The narrator presents some examples in the video. What happens in the first one? What happens to the sun and planets? Explain A cosmic catastrophe, where according to Newton's theory the sun vaporizes and desappears, the planets fly out of their orbits careening of into space, but Einstein showed that this is incorrect because the speed of light the planets would come out of its orbit before this reached them. 5. What happens in the second one? What happens to the sun and planets? Explain A cosmic catastrophe, where the sun desappears and according to Einstein , the gravitational disturbance that results will form a wave that travels across the spatial fabric, these ripples of gravity travel at exactly the speed of light. 6. Why was Newton’s idea of gravity incorrect for Einstein? Because if the sun and disappear desytuyera, seguen Newton would come out of orbit planets, made it impossible for Einstein since the speed of light the planets would come out of its orbit before this reached them. 7. What is the final definition of gravity given in the video? It is warps and curves in the fabric of space and time 8. What’s the name Einstein gave to it? General Relativity 9. What’s the difference between Newton’s gravity and Einstein’s gravity? Newton considered the graveda a force acting at once, Einstein denied this by saying that nothing can go faster than the speed of light. Then he said that gravity is nothing but the deformation of space-time fabric caused by the planets or other bodies. 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. What do you know about the link between artwork and mathematics? Mention some examples. Art, paintings, painting, symmetry, mathematics, angles, body, vision, equations and numbers. There is a close relationship between mathematics and art, as to paint a picture for example requires the use of symmetry and proportion which are obtained by mathematical calculations. It is also known to use geometry and geometric figures in it, to create sculptures and so on. During Reading and After Reading 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 Art, symmetry, mathematics, vision, equations and numbers 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: It can be used to create objects that are just plain pretty—and fascinating to boot. That beauty was richly on display at an exhibition of mathematical art at the Joint Mathematics Meetings in San Diego in January, where more than 40 artists showed their creations. Michael Field, a mathematics professor at the University of Houston, finds artistic inspiration in his work on dynamical systems. 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. For example, the dynamical system he depicts in "Coral Star" does some peculiar things as it gets closer to the center (technically, the equation is discontinuous at the origin). So as you get closer and closer to the center, the image gets more and more complex. "Even apart from the center, the image has quite a lot of depth to it," Field says. "It's a feature of the way it's colored. I'm not so keen on bright primary colors. The shading makes it more interesting." This image has an unusual 35-fold symmetry, and Field created it as a present for his wife on their 35th anniversary. 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. 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. And this problem did turn out to be very difficult to solve: It took about 20 years after mathematicians began working on the problem to find a correct proof. Bosch created a simple string-loop on a page and colored the resulting region inside the loop red and the region outside black. From afar, the image looks like two interlaced loops—one red and one black—that form a Celtic knot. For more information about his method for creating the image, see "Artful Routes". Robert Fathauer, an artist with a mathematical puzzle business in Phoenix, Ariz., found that it doesn't require fancy mathematics to stumble upon remarkable mathematical patterns. He was playing around with various ways of arranging squares in repeating patterns. 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. "After a few iterations, I noticed that something special was happening with that arrangement," Fathauer says. 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. Andrew Pike took inspiration from a similar Sierpinski fractal in creating his art. The senior at Oberlin College started with a photograph of the Polish mathematician Waclaw Sierpinski and recreated a version of it with tiles made from the "Sierpinski carpet." 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. Pike stopped short of continuing forever and instead created tiles with different numbers of iterations of the process. Some of the tiles started white, with the knocked-out squares black, and some of them started black, with the knocked-out squares white. This gave him squares that approximated many gradations of gray. Then he created a computer program that divided the photograph of Sierpinski into tiny squares, averaged the shades of gray in the picture across each individual square, and selected the Sierpinski tile that was closest in shading. "But it didn't look good," Pike says. "The transitions were really rough." He couldn't simply make the tiles smaller, because printers can produce dots that are only so tiny. So he used a technique called "dithering." He calculated the error—the difference between the shading of the photograph and the shading of the most similar Sierpinski tile—and spread it between the other nearby tiles. This effectively softened the image, removing the awkward transitions between tiles. "We chose the image of Sierpinski because it was self-referential," Pike says. Seems appropriate for a technique using self-similar fractals. After reading the text, please answer the following questions in your own words: 1. What is a mathematical dynamical System? A mathematical dynamic system are all those rules that explain how a deerminado point or object moves around another in a plane. 2. Why does the image "Coral Star" get more and more complex? Because it is a dynamic mathematical system that often move toward the center (technically, the equation is discontinuous at the origin), creating depths and shadows. 3. Find a definition of the following words that fits in the text, please acknowledge the source: Loop: Something having a shape, order, or path of motion that is circular or curved over on itself. Crinkly: To form wrinkles or ripples String: A series of similar or related acts, events, or items arranged or falling in or as if in a line Source: http://www.thefreedictionary.com 4. Where did Robert Bosch take his inspiration from? Describe the source of his inspiration. 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 in 5. What happened with Fathauer's arrangement? Why? It formed the Sierpinski triangle, as juice with plazas organizations and how they obtained approximates a pyramid with triangular holes drilled. 6. How did Andrew Pike create the Sierpinski carpet? He 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. 7. Why did he choose that image? Because it was self-referential.

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