Art And Mathematics:Escher And Tessellations
On first thought, mathematics and art seem to be totally opposite fields of study with absolutely no connections. However, after careful consideration, the great degree of relation between these two subjects is amazing. Mathematics is the central ingredient in many artworks. Through the exploration of many artists and their works, common mathematical themes can be discovered. For instance, the art of tessellations, or tilings, relies on geometry. M.C. Escher used his knowledge of geometry, and mathematics in general, to create his tessellations, some of his most well admired works.
It is well known that in the past, Renaissance artists received their training in an atmosphere of artists and mathematicians studying and learning together (Emmer 2). People also suggest that the art of the future will depend on new technologies, computer graphics in particular (Emmer 1). There are many mathematical advantages to using computer graphics. They can help to visualize phenomena and to understand how to solve new problems (Emmer 2). “The use of ‘visual computers’ gives rise to new challenges for mathematicians. At the same time, computer graphics might in the future be the unifying language between art and science” (Emmer 3).
However, one must remember that art is by no means the same as mathematics. “It employs virtually none of the resources implicit in the term pure mathematics.” Many people object that art has nothing to do with mathematics; that mathematics is unemotional and injurious to art, which is purely a matter of feeling. In The Introduction to the Visual Mind: Art and Mathematics, Max Bill refutes this argument by stati...
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...d Mathematics. Ed. Michele Emmer. Cambridge: MIT Press. 5-9.
Emmer, Michele. “Intoduction to the Visual Mind:Art and Mathematics.” The Visual Mind: Art and Mathematics. Ed. Michele Emmer. Cambridge: MIT Press. 1-3.
Escher, M.C. Escher on Escher- Exploring the Infinite. New York: Harry N. Abrams, Inc., 1986.whattess.html.
“Math Forum: What is a Tessellation?” Available Online.http://forum.swarthmore.edu/sum95/suzanne/whattess.html.Accessed 10/5/99.
“Maurits Cornelius Escher.” Available Online. http://www-groups.dcs.st-and.ac.uk/~history/Mathematicians/Escher.html. Accessed 10/16/99.
”M.C. Escher- Interlocking Shapes and Tessellations.” Available Online. http://www.znet.com/~wchow/escher.htm. Accessed 10/7/99.
Schattschneider, Doris. “The Fascination of Tiling.” The Visual Mind: Art and Mathematics. Ed. Michele Emmer. Cambridge: MIT Press. 157-164.
One of the most well-known urban legends told is the story of Bigfoot. Much of the research has shown that there are several names assigned to the mammoth ape. According to Napier (1973), Bigfoot would be the creature found mostly in Northwest America, Sasquatch would be a creature named in British Colombia, the 49th parallel in the north-west states of America and Northern California, and the Abominable Snowman, or the Yeti would be the creature named in the Himalayas. Of course, “Wild Man” and “Savage” have also been names used to identify the creature. There’s been thousands of sightings across the world, but there have also been many misidentifications where those who think they have seen Bigfoot have really just seen an ordinary animal or person. Arment (2006) states an individual’s perception may color the eyewitness account. Such misidentifications include: hermits, fugitives, refugees, bears, gorillas, and simply people making up stories or rumors. In addition to sightings, there have been photos, videos, movies, and TV shows that strongly indicates the possibility of the existence of this creature. Though there is much evidence from sightings, myths, and recordings that Bigfoot exists, there is also much proof that it could all be a hoax. Incorrect sightings have led skeptics to argue over the existence of this being stating Bigfoot is really just a fable. So one has to ask oneself, does Bigfoot really exist or is it just another urban legend?
Though most works of art have some underlying, deeper meaning attached to them, our first impression of their significance comes through our initial visual interpretation. When we first view a painting or a statue or other piece of art, we notice first the visual details – its size, its medium, its color, and its condition, for example – before we begin to ponder its greater significance. Indeed, these visual clues are just as important as any other interpretation or meaning of a work, for they allow us to understand just what that deeper meaning is. The expression on a statue’s face tells us the emotion and message that the artist is trying to convey. Its color, too, can provide clues: darker or lighter colors can play a role in how we judge a piece of art. The type of lines used in a piece can send different messages. A sculpture, for example, may have been carved with hard, rough lines or it may have been carved with smoother, more flowing lines that portray a kind of gentleness.
Bigfoot is often considered to be the most argued about hoax. The man-like ape creature catches our attention when brought up in conversation and sparks a fierce debate whether or not the creature is real or just a man cleverly disguised in an ape-like costume. In 1967, Roger Patterson and Robert Gimlin filmed what they believe to be was the real Bigfoot. Unfortunately, this doesn’t provide a strong foundation for a new scientific discovery, the film that Patterson and Gimlin shot doesn’t seem to be very convincing. While Patterson and Gimlin swear the footage is authentic, there are many reasons as to why the footage is not as convincing as it seems. The reasons why the footage isn’t convincing is because of the enormous height of the creature, the unconvincing costume, and the hernia that is claimed to be shown in the footage analysis.
Robert, A. Wayne and Dale E. Varberg. Faces of Mathematics. New York: Harper & Row Publishers, Inc., 1978.
Today everybody goes back to the film that was taken by Roger Patterson and Bob Gimlin. It is the most famous evidence of the creature. The story is that the two men were riding horseback through the woods to Bluff Creek. When they got there they saw something crouching on the other side of the water. The creature got up two legs and started walking away, so Patterson hurried off his horse, got his camera and ran after it. In the video the creature looks like a woman and it did the Bigfoot look. They chased after it into the woods but lost it, when both of them got back to the Creek there were footprints. Both of them took plasters of the footprints. But throughout the years
Whether it is a book, piece of art or even something that we eat, most of the things that we see and perceive in our lives are generally distinguished by their form and content. Form and content have always been a discussion topic among great philosophers (such as Aristotle, Kant, Hegel), lovers of art and intellectuals. These two categories, seemingly different from one another, when fully elaborated, are actually interrelated ide...
Personal sightings or eyewitness accounts make up what seems to be the most numerous amounts of evidence that’s been brought to attention. Sightings are not justifiable to whether “ Squatch” is real no matter how many sightings are reported. The Pennsylvania Bigfoot Society stores archives of Bigfoot reports across Pennsylvania for almost the past century. Locally, in Erie County, there has suspected to be several eyewitness accounts of Bigfoot encounters. People often confuse a Sasquatch with a bear or some other unknown animal that they may seem to not make out clearly. “ Eyewitness testimony is notoriously unreliable”(Radford 2002). Sure some people would not believe a person ...
According to the American Heart Association / American Stroke Association’s About Stroke (2014) “stroke is the number four cause of death and the leading cause of adult disability in the United States” (para.1). On average, a stroke happens every 40 seconds in the United States (Impact of Stroke, para. 1) About 4% to 17% of all patients with stroke experience symptom onset while hospitalized (Cumbler, et al., 2014). This amounts to about 35,000-75,000 in-hospital strokes in the United States annually.
This module has enabled the author to understand the concept of vulnerability, risk and resilience in relation to stroke. Therefore, it will contribute to her professional development and lifelong learning (NES, 2012). Additionally, the author has gained evidence based knowledge of person-centred care, compassion and self-awareness; all of which can be used to inform future practice (Miller, 2008). Consequently, she will be able to provide the appropriate level of care that can make a difference to a person’s recovery.
Throughout the 150 year history of Bigfoot many concerns have raised, the most in number have been from Native Americans. The Karok Indians tell of an “upslope person” who lurks far up in the mountains (Gaffron, 22-24). Some medicine men have told stories of “snow-walkers” that haunt the Forrest depths (Short). The creatures North American habitat covers over 125,000 square miles of forest, contained in the states of Oregon, Washington, and California, constituting a large number of Native American tribes to encounter and frighten (Gaffron, 22). This phenomenon is not just a Native American one told by medicine men, and tribe leaders, Bigfoot plays an enormous role in the ancient folklore of such civilizations as, the Russians, Greeks, and Anglo-Saxons (Brunvand). These civilizations have been around for hundreds of years, and have been telling stories of Bigfoot long before any one; they hold the true key to Bigfoot’s history.
Stroke has been classified as the most disabling chronic disease, with deleterious consequences for individuals, families, and society1. Stroke impacts on all domains in the ICF. The body dimension (body functions and structures), the individual dimension (activity), and the social dimension (participation). All domains influence each other2.
the genius of the artist and the method of the scientist, I find many of
Durer's famous engraving, “Melencolia I” depicts an exasperated thinker sitting by what is best elucidated as a “truncated rhomboid” or a “rhombohedron with 72-degree face angles, which has been truncated so it can be inscribed in a sphere”. It has been the subject of more interpretation than most any other print.
Among the many theories of art that have emerged over time, the theory I will defend in this paper is the Neo-Wittgensteinian theory of Art. I will defend this view against the following (two) objections: a) The “open concept” idea of art is too expansive, and b) the “family resemblance” theory of artworks is also too expansive.
Unemployment is controversial topic, especially in the last few years. CNN reported that 91 million Americans are currently unemployed. That sounds like an astounding number; however, that number includes teenagers, stay at home mothers and caretakers. In the current economy, unemployment is high among teenagers as well, “Last month the employment –to-population ratio for teens was stuck at 25.8 percent – it’s worse than the Great Depression.” (Coy, 2014). It is important for teenagers to have an opportunity and obtain experience in order to be successful once they become adults. It is important to help teens move out the long-term unemployment statistics by having more job opportunities for that population. In addition, long term unemployment has a negative effect on the economy compared to short-term unemployment. Even though the United States has a high volume of unemployment, short term unemployment is minimum in comparison to Europe. Unemployment benefits offered in the US run out in six months while in Europe benefits continue indeterminately. Perhaps the US unemployment system is not so bad after all.