Xander du Plooy
Mrs. Virginia Campo
Geometry Honors
20 April 2014
The One-Sided Object
Why did the chicken cross the Möbius Strip? Well, of course, to get to the same side! Wait, what? Born in 1790, Augustus Ferdinand Möbius would grow up to become a great astronomer and mathematician. Not only this, but his name would be remembered throughout geometry and science as the man who discovered what is known as the Möbius Strip. He discovered the Möbius Strip in September of 1858 and later wrote an article on it in 1865. Although Möbius received the credit, the first person to actually discover both this strange, three-dimensional figure and have the opportunity to publish his findings was Johan Benedict Listing. Listing found it in July of 1858, and established this revelation to the public in 1861. Even so, the base knowledge of this strip have records that date back to ancient times where the mention of something of similar description was made in an Alexandrian manuscript. The Möbius strip or Möbius band is a surface with only one side and contains only one boundary elemental property. The Möbius strip has the mathematical property of being non-orientable. It can additionally be realized as a ruled surface.
Furthermore, the Möbius Strip composes of various mathematical properties. If a strip of paper is taken and it's ends taped together, it would most likely end up being a belt. It would be a loop with both an inside surface and an outside surface. But what if you took that same strip of paper and gave it a half twist before taping the ends together? The result would be this fascinating geometric complexity, which is known as the Möbius Strip. If a Möbius Strip is cut length-wise (all the way around) it will end up with a loop ...
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...of half-twists is cut in half along its length, it will result in two linked strips, each with the same number of twists as the original.
Möbius Strips have been put to use by engineers. Found throughout science and mathematics, the Möbius Strip is used create advances in industrial production and other fields, as well as, solve problems relating to such. For example, some conveyor belts are made with a half twist so that the wear and tear on the belt is equal on both sides. The belt itself only wears out half as fast. In a similar fashion, continuous loop recording tapes are made in this way in order to double the recording surface using the same amount of tape. As one can see, the Möbius Strip is an outstanding mathematical and geometrical discovery with an array of complex properties. So again, why did the chicken cross the Möbius Strip? To get to the same side.
We put a rectangular piece of cardboard vertically in the middle of an empty rectangular box. One side of the box was filled up with damp soil, and the other side was filled with dry soil. We filled the soil up to the level of the rectangular piece of cardboard, so that the cardboard wall would not deter the sowbug from crossing. We gathered 4 sowbugs, and placed them in a petri dish. We placed the sowbugs one by one on the border between both soils. Each of us tracked one sowbug, and diagrammed the movement. Every minute we would make a mark of where the sowbug had travelled. We continued this process for five minutes. We took the sowbugs out of the chamber, and placed them back in the petri dish. We repeated the experiment under the same conditions. Because we were short on time, we kept the same sowbugs for the second experiment
According to Roland Shearer (1992) the release of non-Euclidean geometries at the end of the 19th Century copied the announcement of art movements occurring at that time, which included Cubism, Constructivism, Orphism, De Stijl, Futurism, Suprematism and Kinetic art. Most of the artists who were involved in these beginnings of Modern art were directly working with the new ideas from non-Euclidean geometry or were at least exposed to it – artists such as Picasso, Braque, Malevich, Mondrian and Duchamp. To explain human-created geometries (Euclidean, non-Euclidean), it is a representation of human-made objects and technology (Shearer
The "Yellow Wallpaper" by Charlotte Gilman is a great story about the repression of women in the late 1800's but is still representative of issues faced by women today. She writes from her own personal experiences and conveys a message that sometimes in a male dominated society women suffer from the relentless power that some men implement over women.
Women in the 19th century were expected to fulfill their duties as wives and mothers. They were to be content with their lifestyle and ask of nothing more. Women were doomed to live in a male dominant world. Women who dared to enter this masculine realm were associated with prostitutes, the lowest level of society. In the story, The Yellow Wallpaper, John seems deemed as the evil physician with a sick wife whom he dominates. Truthfully, he is simply the product of society. The narrator has a desire to have more in her life than just her husband and her child, but this was not the social norm. Also, the love she had for writing and creativity did not make her the ideal wife for this era. The major theme throughout this story is the domestic trap women faced from their husbands in the 19th century.
After analyzing Charlotte Perkins Gilman's, "The Yellow Wallpaper", from a feminist perspective it is undoubtedly shown to challenge patriarchal ideals through the stories heavy amounts of symbolism. The story revolves around the thoughts of a woman suffering from hysteria who ultimately loses her sanity due to her interactions with the isolated environment and husband, John. The story does a clear job at showing the oppressions of women in the late nineteenth century through the narrator's conversations with John, the ideas she has written down and in her head, the room in which she is caged in and finally the reflection of the Gilman's life in this story.
Gilman uses this story to show a woman 's struggle with her oppressive limitations. She begins her journal by marveling at the grandeur of the house and grounds her husband has taken for their summer vacation. She describes it in romantic terms as an aristocratic estate or even a haunted house and wonders how they were able to afford it, and why the house had been empty for so long. Her feeling that there is “something queer” about the situation leads her into a discussion of her illness and of her marriage. As the Fourth of July passes, the narrator reports that her family has just visited, leaving her more tired than ever. John threatens
Though most women in the 21st century obtain degrees and indulge in the workforce as opposed to being the stereotypical housewife, gender roles among men and women have not changed in the minds of the majority. It is still believed that there is more of an advantage to being a man than a woman. From physical to intellectual dominance, many men and women themselves buy into this facade that being a man is significantly more desirable. Not that women desire to be men, though that sometimes is the case, but women want the same perks and respect that you get being a man. Women do in fact have more power in the workforce, and more men can be found running their homes, yet there are still social expectations that guide the idea of what it means to be male or female.
In this paper I will present two differing views on the topic of the design argument. In particular, I will explain William Paley's view supporting the design argument and Bertrand Russell's view against the design argument. After a presentation of the differing views, I will then evaluate the arguments to show that William Paley has a stronger argument.
“The Yellow Wall Paper” is the story about a journey of a woman who is suffering from a nervous breakdown, descending into madness through her “rest cure” treatment. Basically, the woman is not allowed to read, write or to see her new-born baby. Charlotte Perkins Gilman captures the essence of this journey into madness by using the first person narration. The story plot’s is by taking the reader through the horrors of one woman’s neurosis to make strong statements about the oppression faced by women in their marriage roles. The narrator’s mental condition is characterized by her meeting with the wallpaper in her room. In addition to the story’s plot, the use of symbolism and irony throughout her story also show how males dominate during her time.
Richeson, David. Euler's Gem: The Polyhedron Formula and the Birth of Topology. 1st. ed. Princeton, New Jersey 08540: Princeton University Press, 2008. Print. .
The way Gilman describes the wallpaper tells of what the narrator's mind is thinking, 'and when you follow the lame uncertain curves for a little distance they suddenly commit suicide.';(Gillman 206) She doesn't think this on the conscious level but more on the unconscious level. When the narrator writes, '(The designs) destroy themselves in unheard of contradictions.';(Gillman 206) She is speaking of her state of mind subconsciously, the narrator is on the brink of losing her mind at this point. Gillman writes, 'There is a recurrent spot where the pattern lolls like a broken neck and two bulbous eyes stare at you upside down. '(Gillman 207) She was explaining how the wallpaper is like a 'watchdog'; or a guard of some type, watching her every move, naturally making her nervous.
Wall" appears on the surface to be simple and plain. However, a closer study will reveal
There are six diagonal lines. At one end there are circles on them giving the impression of three circular prongs. At the other end the same size lines have cross connecting lines consistent with two square prongs. These perceptions can violate our expectations for what is possible often to a delightful effect.
Euclidean Geometry is the study of plane and solid figures based on the axioms and theorems outlined by the Greek mathematician Euclid (c. 300 B.C.E.). It is this type of geometry that is widely taught in secondary schools. For much of modern history the word geometry was in fact synonymous with Euclidean geometry, as it was not until the late 19th century when mathematicians were attracted to the idea of non-Euclidean geometries. Euclid’s geometry embodies the most typical expression of general mathematical thinking. Rather than simply memorizing basic algorithms to solve equations by rote, it demands true insight into the subject, cleaver ideas for applying theorems in special situations, an ability to generalize from known facts, and an
Abstract: There are many Analyst who would agree that the novel Moby-Dick by Herman Melville, the whale is just half of what the novel is really talking about. They would also agree that Melville employs some sort of spiritual read by simply by providing scriptures and rephrasing verses from the Bible into the text. But what is it really about? What made Melville come up with this idea style of writing Moby-Dick? Other analyst who also asked themselves this questions, probably looked deeper into the novel doing tons of research figured out a possible solution. The solution that Melville was influenced by Shakespeare novel ‘Hamlet’ this has been established because of the allusions Melville makes to Hamlet are countless. Moby-Dick may be a contemporary version of Hamlet. This paper will illustrate how the characters of Moby-Dick counterparts with the characters in Hamlet, expanding the reason why the character in one works with the other.