tessellations. This brings me to my research question: how does Maurits Cornelis Escher’s Regular Division of the Plane with Birds relate to the tiling view of the torus? Tessellations and the torus are related to mathematics in the areas of geometry, topology, and the geometry of space. “A regular tiling of polygons (in two dimensions), polyhedras (three dimensions), or polytopes (n dimensions) is called a tessellation.” (Weisstein, Eric W.). Tessellations, or regular divisions of the plane, cover the
Around the date 1763, a problem arose in Königsberg, Germany (Diestel). This problem began with a few curious citizens but soon spread to scientists and other intellects, and eventually became known as the Königsberg Bridge Problem. The town of Königsberg was cut into four separate land masses by the river Pregel (Green). At the time, Königsberg was a large trading city, valuable because of its position on the river. The prosperity of the city allowed the people to build seven bridges so citizens
Mr. McCoy’s testimony revealed that his first issue is regarding the custodial parent (CP), Sabrina Durant Hawthorne. He stated the CP has not had his daughter, Daisha Durant, since she was three years old. He stated he mailed the court order that stated that the child support was to stop to the DHR. He stated he received a garnishment from his bank account and did not understand why. He stated that he called Child Support and was told that he owed the CP $3,000.00; he did not understand why
Mesh, Bus, Ring and Star Topologies Mesh A mesh topology typically refers to a Wide Area Network where there are multiple paths connecting multiple sites. A router is used to search multiple paths and determine the best path for the data. Routes are determined by least cost, time of day and performance. A three or four site mesh network is relatively easy to create, whereas it is impractical to set up a mesh network of 100 sites or nodes. Mesh networks are used in Wide Area Networks (WANs) where
Sutherland’s Differential Association Born August 13, 1883 in Gibbon, Nebraska, Edwin H. Sutherland grew up and studied in Ottawa, Kansas, and Grand Island, Nebraska. After receiving his B.A degree from Grand Island College in 1904, he taught Latin, Greek, History, and shorthand for two years at Sioux Falls College in South Dakota. In 1906 he left Sioux Falls College and entered graduate school at the University of Chicago from which he received his doctorate. (Gaylord, 1988:7-12) While attending
of the ancient city of Königsberg posed a famous and almost problematic challenge a few centuries ago. But this isn’t just about the math problem; it’s also a story about a famous Swiss mathematician named Leonhard Euler who founded the study of topology and graph theory by solving this problem. The effects of this problem have lasted centuries, and have helped develop several parts of our understanding of mathematics. We don’t hear too much about Euler, but he is one of the most important and influential
in 4-dimensional space. Brouwer was a Dutch mathematician who founded mathematical intuitionism, which is a doctrine that views the nature of mathematics as mental constructions governed by self-evident laws, and whose work completely transformed topology which is the study of the most basic properties of geometric surfaces and configurations. The life of Brouwer is easily summarized. His upbringing was entirely uneventful. Luitzen Egbertus Jan Brouwer was born on February 27, 1881 in Overschie, Amsterdam
With economic decline in full effect, the city of Anderson is on track to become a ghost town. Anderson is located in Northern California, 150 miles north of Sacramento, and a 10-minute drive to Redding. The primary source of the problem is in Anderson’s Downtown which is defined as I-5 to 273 and North Street to Balls Ferry (See Reference 1). Nearby attractions include the Sacramento River, Turtle Bay Exploration Park, and the Mt Shasta Mall (Things Web). However, all the main attractions are found
Leonhard Euler A world relying so heavily on technology was not something that anyone hundreds of years ago could have predicted. In today’s modern society, computers can be seen practically everywhere. Computers can be programmed to do an unimaginable list of things, making them one of the most useful technologies. However, the people that use them seem to forget that the backbone of computers and technology is math. Mathematics is one of the core subjects that are associated with computing, and
The Thames barrier is a barrier system that consists of 2 different types of gates: falling radial gates and rising sector gates. The falling radial gates are held in position over the river and are non-navigable. The Rising sector gates rest on the river beds allowing the traffic to pass over them in the open position. The gates are rotated by hydraulic cylinders and the whole barrier takes approximately one and a half hours to close, usually taking place after low tide. The barrier creates a solid
A Kantian Interpretation of Demonstrative Reference ABSTRACT: According to Kant, we refer to what is out there in the world by performing a demonstrative act, like pointing at an object with a finger. A Kantian mode of demonstrative reference is characterized by the existence of a real, 2-placed affective relation between an intuiting subject and the referent. Parsons suggests that Kantian intuition is both singular and immediate, and immediacy demands an object of intuition to be present, a condition
Forward This essay discusses an important view concerning the differential diagnosis of infantile autism. As you will see, the symptomology common to autistic infants mimics that of severely retarded children in the early months of life. In addition, the identification of autism as a "disease" in infants is impeded by the lack of biological evidence to support such a diagnosis. Autism has, in multiple studies, been related to a multitude of organic dysfunction’s. These include everything from
As a student of Saint Leo, it is our responsibility to uphold and utilize our core values. The core vale of “Excellence” states as follows, “All of us, individually and collectively, work hard to ensure that our students develop the character, learn the skills, and assimilate the knowledge essential to become morally responsible leaders” (Florida Catholic University). Using and creating opinions on data leaves one vulnerable to data fraud and other unethical qualms. In order to uphold the integrity
Bernard Tschumi was a one of the few architects that connected with the people and essential focused on the inhabitants. He did not care how you should inhabit it, but what you experience from it. These experiences essentially become stories of events that are eventually retold events. Tschumi argues that these events or in other words sequences that establish a memory of the proceeding frame or space. These sequences often tell a story or follow a scenario. The architecture itself becomes part of
Sutherland proposed his theory of Differential Association in his Principles of Criminology textbook. Differential Association theory states that criminal behavior is learned behavior. Sutherland along with Richard Cloward, and Lloyd Ohlin attempted to explain this phenomenon by emphasizing the role of learning. To become a criminal, a person must not only be inclined toward illegal activity, he or she must also learn how to commit criminal acts. Sutherland’s differential association theory contends that
Differential Reinforcement is defined to occur when behavior is reinforced by being either rewarded or punished while interacting with others (Siegel, 2003). With this said, the theory was developed as a way of labeling both positive, as well as negative aspects of individual action. This idea of reinforcement is a branch of the infamous Differential Association theory presented by Edwin H. Sutherland in 1939. Another commonly used term for this theory of reinforcement is called differential conditioning
Part one of Sutherland and Cressey’s differential association theory explains that criminal behavior is learned. Applying this to Nate and Sam involves explicating their childhood and how they were raised. From a young age both Nate and Sam were conditioned by their father, Big Willie to be aggressive, and that in life you have to take what you want (take home outline). Nate and Sam’s father unknowingly conditioned them in a harsh way that made them susceptible to becoming date rapists. As a result
A Mesh topology is a style of connecting computers in a network in a fashion where every link has a redundant path. A mesh topology is also known as a self healing network in that if a segment of the network fails for what ever reason then the data can still be transmitted across another linked path. This would include possibly hoping across a few extra network segments to reach the destination but it would be able to do it. This redundancy of course comes with a price for the extra pathing that
Tangents and Normals of Curves If you differentiate the equation of a curve, you will get a formula for the gradient of the curve. Before you learnt calculus, you would have found the gradient of a curve by drawing a tangent to the curve and measuring the gradient of this. This is because the gradient of a curve at a point is equal to the gradient of the tangent at that point. Example: Find the equation of the tangent to the curve y = x³ at the point (2, 8). dy = 3x² dx Gradient
The problem of small oscillations can be solved through the study of molecular vibrations which further, can be introduced by considering the elementary dynamical principles. The solution for the problem of small oscillations can be found out classically, as it is much easier to find its solution in classical mechanics than that in quantum mechanics. One of the most powerful tools to simplify the treatment of molecular vibrations is by use of symmetry coordinates. Symmetry coordinates are the linear