My learner profile for this activity: Knowledgeable - Thinker
In this activity I demonstrated these IB attitudes: Commitment - Independence - Enthusiasm - Confidence After I finished this project I felt proud because: I had done very well in the math contest. Something I learned while completing this activity: Contests are fun! Something I could do next time to improve the quality of my work: Deepen my knowledge. My learner profile for this activity: Inquirer - Thinker - Communicator In this activity I demonstrated these IB attitudes: Curiosity - Creativity - Confidence After I finished this project I felt intrigued because: I really enjoyed learning about the endless possibilities with Möbius Strips. Something I learned while completing this activity: That math is connected to many different subjects and can be very complicated at times. Something I could do next time to improve the quality of my work: Things in a twistThe Möbius strip is a wonderful discovery. Not only in its simplistic form does it astound you, but the more you learn about it, the more it amazes you. The Möbius strip was discovered in 1858 by August Ferdinand Möbius, and since then, many different Möbius combinations have been made and theorized, some of which cannot even exist in our dimension! Although there are many different aspects of the Möbius strip, this report is mostly based on the relation between the Möbius strip and our universe. The Möbius strip is such interesting a shape that many people have wondered what would happen if we lived on a Möbius strip. A story by Clifford Pickover in his book The Möbius Strip makes the reader imagine that they are a character living in a town called New Devonshire. When they decide to take a bicycling trip farther than anyone has gone before, they discover curious things. After a few hours of bicycling, they get back to their town, only to find that they are a mirror image of themselves! They are now left-handed, their watches are backward and even their organs are all on the wrong side of their body. Of course, this story would only work if the people in this universe are "inside" the Möbius strip, not on top of it. You can do this experiment yourself by creating your own Möbius strip and drawing arrows that turn in a counterclockwise direction all along the strip. These arrows represent the watches in the story. When you come back to the beginning, the arrows will be backwards to the ones when you started! Unfortunately, a disease resembling the one mentioned in the story exists, where all of one's organs are on the other side of the body. It is called Situs inversus, and it is found in about one in a ten thousand people. Fortunately it is not fatal, although there is an increased risk of heart disease. Another interesting fact about the Möbius strip is the product of combining two Möbius strips together. This result is called the Klein bottle (see above), named after its discoverer, Felix Klein. The Klein bottle is a one-sided surface, and it doesn't have boundaries. On the other hand, the Möbius strip has a boundary, its single edge. Another product of the Möbius strip is the real projective plane, which is so complicated it cannot be made in our 3-D universe! The Möbius strip is also interlinked with many theories of the universe. Some of these theories state that the universe might turn back on itself like the 2-D surface on a 3-D sphere. This theory would be just moving everything up one dimension, and our 3-D universe would turn back on itself into a fourth dimensional sphere. This sphere is called a hypersphere. Other theories suggest that things could be flipped in a 4-D universe, as when something in a Möbius strip travels once around the strip. The Möbius strip is a very interesting mathematical object. Despite its mathematical origin, it can be found in many different non-mathematical places. One such example is the symbol for recycling! There is still much to learn about this amazing discovery, and it may help us better understand our universe! Bibliography"Real Projective Plane." Wikipedia. Wikimedia Foundation, 30 Sept. 2013. Web. 03 Oct. 2013. <http://en.wikipedia.org/wiki/Real_projective_plane>.
"Möbius Strip." Wikipedia. Wikimedia Foundation, 21 Sept. 2013. Web. 03 Oct. 2013. <http://en.wikipedia.org/wiki/Möbius_strip>. Devlin, Keith. "Devlin'sAngle." Commonconfusions. N.p., Oct. 2005. Web. 04 Oct. 2013. <http://www.maa.org/external_archive/devlin/devlin_10_05.html>. Clifford Pickover, (2006). The Möbius trip. 1st ed. New York: Thunder's Mouth Press. Burger, Edward, and Michael Starbird. "The Joy of Thinking: The Beauty and Power of Classical Mathematical Ideas." The Great Courses : Science and Mathematics. The Teaching Company, Chantilly. 01 June 2003. Lecture. |
AuthorD. K. Archives
June 2014
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