| Papers [1-15] of 24 :: [Page 1 of 2] | | Go to page : 1 2 —> | Search results on "KINEMATIC GEOMETRY": |
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Kinematic Geometry, 2002.
An examination of Horace Barlow's paper on ?Exploitation of Regularities in the Environment by the Brain?.
1,465 words (approx. 5.9 pages), 10 sources, MLA, $ 48.95
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Abstract
This paper explores the general perceptions of Horace Barlow, reflected in his paper ?The Exploitation of Regularities in the Environment by the Brain?, pertaining to the role of evolutionary internalized regularities, especially as they occur in theories of vision. The focus lies principally on issues relevant to the ecological validity of Shepard's kinematic geometry constraint in ordinary motion perception perspective. This paper also establishes the thought for two individual sets of assertions; perception of apparent motion modeled as kinematic geometry theory and internalization of the like.
From the Paper
"The limitations of kinematic geometry proposed in Barlow?s paper have been recognized, however kinematic geometry being a model for perception of apparent motion in my opinion is an idea that can expand into new dimensions. However internalization of kinematic geometry does project reservations about being a possibility. As indicated by Barlow, internalized principle of object observation gives way to the perception of apparent motion. The human brain?s support for a percept is purged from an external stimulus. Conforming to the putative universals are the preferred perceptual solutions. "
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Origins and Significance of Hyperbolic Geometry, 2008.
An analysis of the origins and importance of hyperbolic (non-Euclidean) geometry.
1,279 words (approx. 5.1 pages), 6 sources, MLA, $ 43.95
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Abstract
This paper examines the origins and significance of hyperbolic geometry. Specifically,it briefly discusses the men who conceived of it, as well as how hyperbolic geometry differs from Euclidean geometry. Finally, and most importantly, the paper looks at the significance of hyperbolic geometry when it comes to exploring the universe around us.
From the Paper
"Delving deeper, the contemporary significance of non-Euclidean geometry grows more and more unavoidable - even to those disinclined to give it its "due". For one thing, it is well-known that hyperbolic geometry has shed some light on the immersion and curvature of spaces. More importantly, Einstein's theory of relativity is, at least in part, indebted to non-Euclidean geometry - though it is admittedly not clear from the available literature the precise extent to which hyperbolic geometry made his revolutionary findings vis-a-vis relativity possible. In any event, this writer - drawing upon course work completed in previous introductory classes that dealt with geometry and its relationship to modern cosmology - would be remiss if he did not also point out the fact that the "empty" regions in outer space where no matter exists can really only be described adequately using a hyperbolic model. In effect, understanding the Hubble Constant involves understanding and appreciating non-Euclidean, hyperbolic geometry."
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Technology and Geometry, 2002.
A look at the way teaching geometry is affected by technology.
2,400 words (approx. 9.6 pages), 10 sources, $ 89.95
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Abstract
This ten-page undergraduate level paper that discusses the effects of technology on teaching geometry. It will reflect the current trends in mathematics education from grades six to twelve and will point out the concerns of teaching geometry with the help of technology.
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Modern Geometry, 2000.
A brief history of modern geometry.
1,300 words (approx. 5.2 pages), 4 sources, $ 43.95
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Abstract
This paper gives a summary of the history of modern geometry, from ancient Greece to the present, including a discussion of the significance of Euclid?s first five postulates, emphasizing the fifth (Parallel Postulate) and how it relates to the Hyperbolic Geometry.
From the Paper
"Many great philosophers and mathematicians worked on the study of geometry. Euclid was perhaps the most famous of these. Almost nothing is known about his life, but his famous work ,?Elements? (ca. 300 BCE) remains one of the most widely read and copied texts to this day. He gathered all of the geometrical knowledge of his time and arranged it in a logical format. (36, Levine) What distinguishes ?Elements? from other works is the use of proof throughout. As far as is known, Euclid was the first person to attempt such a task. He used the Axiomatic Method to prove the correctness of the statements put forth in ?Elements?"
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Hyperbolic Geometry, 2007.
An examination on using M.C. Escher' "Circle Limit III" to instruct students in hyperbolic geometry.
2,279 words (approx. 9.1 pages), 6 sources, MLA, $ 70.95
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Abstract
The paper examines how, though not always apparent, there are a number of significant connections between mathematics and art. The purpose of this paper is to demonstrate how the fundamental similarity between math and art can be exploited as a means to teach difficult mathematical concepts to students. To show how this could happen, a particularly complex--if intellectually intriguing--mathematical concept is explored: the concept of distance in hyperbolic geometry, specifically in a Poincare disk.
Outline:
Introduction
Context: What Is Hyperbolic Geometry?
Context: Who Is M.C. Escher?
Developing an Appropriate Class Project
Conclusions
Works Cited
From the Paper
"Since mathematics education produces singular anxiety for many students, this confluence with art presents significant possibilities for the imaginative educator (Granger 10). It is possible that we could, as educators, use art as a physical and visual means of explaining complex mathematical concepts in other than abstract terms. Over reliance on complex equations and difficult language can and will stymie many students. By endeavoring to ground mathematical theory in artistic reality, students can leans mathematical lessons in the process of seeing how math and art aren't really all that dissimilar."
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Teaching Geometry, 2002.
A study of the manipulative method of teaching geometry.
2,150 words (approx. 8.6 pages), 18 sources, $ 80.95
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Abstract
A paper that states that the use of math manipulative to teach math concepts in geometry increases the student's ability to grasp skills and concepts.
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Plane Projective Geometry, 1996.
Technical analysis of mathematical process involved in producing Reuleaux triangle from equilateral triangle.
2,250 words (approx. 9.0 pages), 4 sources, $ 79.95
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From the Paper
"The Reuleaux triangle is derived from an equilateral triangle. It is produced by replacing each side of the equilateral triangle with the arc of a circle. These two-dimensional triangles can be used to create somatocharts. Three-numeral somatotype data can additionally be plotted within a standard rectangular coordinate axis system. Geometric figures may be analyzed according to their component parts. Perhaps the most basic components of the Reuleaux triangle consist of those points which comprise it. The position of a point in a plane can be given by means of two numbers. For example, x, y can be the distances of a point, P, from two given perpendicular lines. Given this information, the position of P can be determined when the values of both x and y..."
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A Rolling Sphere and the Kinematics of Constant Acceleration, 2000.
A detailed outline of a scientific experiment designed to show that the kinematics of constant acceleration are valid when applied to a rolling sphere.
1,280 words (approx. 5.1 pages), 0 sources, $ 43.95
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Abstract
This experiment investigates the relationship of the horizontal displacement of a metal sphere, descending from an inclined plane falling through a vertical distance. With the speed of a metal sphere V0x, and the height of the ramp y, we can find the horizontal distance squared X?.
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Biomechanics and Kinematics of the Jete?, 2002.
This paper explores the body mechanics involved in all phases of the ballet leap, called the Jete?.
1,825 words (approx. 7.3 pages), 4 sources, MLA, $ 58.95
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Abstract
The paper describes kinesthesiology as a branch of physics dedicated to the physics involved in movement. It shows that several scientists of note contributed to this field including Aristotle, who applied geometry to the acts of walking, running and jumping. The paper describes that as a dancer moves across the stage force is transferred from one element to another. This paper explores the body mechanics involved in all phases of the ballet leap, called the jete?.
Table of contents
Introduction
Phases of the Jete?
Analysis of the Muscles Involved
Analysis of the Injuries Prone to the Movement
From the Paper
"The landing phase of the leap is by far the most dangerous. If the body is not positioned properly to absorb the impact, injuries could be extensive, particularly if they cause a fall. Every part of the body is at risk in a fall situation. Injuries could be more severe involving broken bones, especially in the ankle and foot of the leading leg. If a fall is involved bruising could result."
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Euclid's Fifth Postulate, 2002.
A paper which discusses the philosophical and logical problems contained in Euclid's 'Fifth Postulate' on planar geometry.
1,622 words (approx. 6.5 pages), 3 sources, APA, $ 52.95
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Abstract
Euclid gave the world much of the information it has on planar geometry in his five postulates. The paper shows that while the first four are relatively easy to understand, the fifth one is very difficult in relation to the others. It is this fifth postulate that many people feel can never be proven. The paper discusses how there are those that say it is simply incorrect, those that say it's both true and false and others that say there is no possible way to prove it, and Euclid himself may have realized that the task was impossible. The author of the paper surmizes that if someday the fifth postulate is proven to be either true or false, and the decision is agreed upon, then it could change the way mathematics are done and the way geometry is looked at.
From the Paper
"Theoretically it would be possible for the lines to move toward one another so slowly, because of the low degree of angle, that they take a huge amount of space to come together at the end. But is it possible to have such a slight angle that the lines are almost parallel? They would be so close to parallel at that point that the impression that they are drawing closer together wouldn't be noticed unless they were looked at over miles at one time. That must be possible, but they still must meet somewhere in infinity.
Perhaps Euclid was right and the lines do meet somewhere, but the angles can be so minute that the lines go on almost to infinity, and we don't have the capabilities to calculate just how far that is yet. Perhaps Euclid is wrong and lines will go on into infinity still never touching, but only being a hair's width apart. Mathematicians may never know, since they haven't discovered any way to prove Euclid's fifth postulate by now."
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Fluid Mechanics, 1996.
Study of behavior of fluids. Fluid statics, kinematics, conservation of mass, momentum, energy, potential & viscous flow, more.
3,150 words (approx. 12.6 pages), 7 sources, $ 111.95
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From the Paper
"The engineering definitions, methods of analysis, and significance of many elements of the study of fluid mechanics are presented.
Definitions and Fluid Properties
Fluids can be either liquids or gases, and fluid mechanics "refers to the study of the behavior of fluids, either at rest or in motion." Nunn elaborates that there are "two main physical properties defining a fluid: density and viscosity." Nunn then subdivides fluid mechanics into three major categories of ideal fluid flow, in which density is constant and viscous effects are negligible; compressible flow, in which density varies from place to place throughout the fluid and viscosity effects are trivial or..."
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Friedrich Bernhard Riemann, 2001.
This paper looks at the life and works of Friedrich Bernhard Riemann.
4,000 words (approx. 16.0 pages), 6 sources, $ 108.95
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Abstract
This paper examines the life and the work of the 19th century German mathematician Friedrich Bernhard Riemann, whose ideas concerning geometry of space had a profound effect on the development of modern theoretical physics, including providing the foundation for the concepts and methods used later in relativity theory.
From the paper:
"An examination of the facts of Riemann?s family background would not have led one to suspect that he would have become the great mathematician that he would develoo into. He was the second of six children of a Lutheran pastor and it was this pastor/father who gave him his first formal education. Indeed, much of his early education was centered in his family, which was by all accounts both happy and deeply devout. He later attended the local high school, where he made quick and substantial progress in mathematics, soon moving beyond the ability of his teachers to educate him further (Laugwitz 38-41). He quickly mastered calculus and theory of numbers of Adrien-Marie Legendre. After graduating from the high school (or gymnasium), he studied at the universities of G?ttingen and Berlin from 1846-51. It was at this point in his education that he became interested in problems concerning the theory of prime numbers, elliptic functions, and geometry, theoretical interests that would guide much of his later work."
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Symmetry in Islamic Art, 2008.
This paper explains how geometric concepts can be taught based on the symmetry found in Islamic art.
2,537 words (approx. 10.1 pages), 13 sources, MLA, $ 76.95
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Abstract
The paper looks at the extensive use of geometric and symmetrical patterns in Islamic art. The paper provides a definition of geometry and looks at translations, rotations and reflections in Islamic art. The paper then examines the mathematics of symmetry and how symmetry, as manifested in Islamic art, can be utilized to teach geometry in the contemporary classroom.
Outline:
Introduction
Symmetry in Islamic art, Part I
Symmetry in Islamic Art, Part II
Symmetry in Islamic Art, Part III
From the Paper
"Many civilizations have long used artistic designs for a variety of purposes. For instance, some civilizations have used artistic designs for emblematic purposes, while some have used artistic designs for ornamental and/or architectural purposes; still others, perhaps unsurprisingly, have used artistic designs for spiritual symbolism. Another thing that is not at all a surprise is that artistic designs almost invariably utilize mathematical concepts. Specifically, within the Islamic art tradition, there has long been the extensive use of geometric and symmetrical patterns - so much so that it may be put forward that one of the defining features of Islamic art is its ability to incorporate mathematical concepts and ideas in ways that are rich, vibrant and aesthetically pleasing."
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ARCS Model of Motivation.
This paper discusses John Keller's ARCS motivation model, a very useful tool for creating learner-centered lessons.
2,910 words (approx. 11.6 pages), 7 sources, APA, $ 86.95
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Abstract
This paper explains that Keller's ARCS motivation model identifies the four characteristics, which are capitalized and form the acronyms for ARCS and are applied in a sequential manner: Attention (arouse and sustain interest), Relevance (connect lives, needs and interests of the student to the content), Confidence (create a positive expectation for student success) and Satisfaction (intrinsic and extrinsic reward for effort). The author points out that Keller breaks the four major ARCS characteristics into three sub-components: Attention into the sub-components of perceptual arousal, inquiry arousal and variability; Relevance into goal orientation, motive matching and familiarity; Confidence into the sub-components of learning requirements, success opportunities and personal responsibility and Satisfaction into intrinsic reinforcement, extrinsic rewards and equity. The paper applies this teaching method in a detailed lesson plan on using geometry to build a tower, to teaching swimming and states that the method can be used in business.
Table of Contents
Introduction
A Review of the Literature and Applications in the Classroom
Characteristics of the ARCS Model
Attention
Relevance
Confidence
Satisfaction
Table 1: Instructional Strategies for Stimulating Motivation as Suggested by the ARCS Model
The Application of ARCS to an Actual Lesson Plan
Attention
Relevance
Confidence
Satisfaction
The Application of ARCS outside the Classroom
Attention
Relevance
Confidence
Satisfaction
Summary
Appendix A: Using Geometry to Build a Tower
From the Paper
"In the lesson, confidence is first instilled in the learners by supplying them with a rubric that outlines the expectations for success in the project. The assignment begins with the relatively simple assignment of taking pictures or looking at pictures on the internet and then describing those structures in their notebooks. Next, the lesson encourages success by having the student build two simple geometric figures, a triangle and a square, and then add to the design of each to strengthen the figures. Once the students have built the simple geometric figures, the lesson challenges the students to build a three dimensional figure and then to build a tower. Each step adds new challenges and opportunities for success. The hands-on nature of the activity also provides the learner with a certain degree of control over the learning environment. This also serves to foster confidence in the learner."
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Analytical and Synthetic Cubism, 2004.
A discussion on the terms analytical Cubism and synthetic Cubism with reference to the work of Pablo Picasso and Georges Braque.
2,117 words (approx. 8.5 pages), 8 sources, MLA, $ 66.95
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Abstract
This paper explains that Cubism is the process of passage from a bar-baric dis-symmetry to an advanced abstract geometry. The paper then looks at how the the term analytical Cubism refers to Picasso and Braque's work of 1910 through early 1912 and how the term synthetic Cubism refers to their work of later 1912 through 1914. It also examines the objective contributions of Picasso and Braque to the development of modern art, particularly towards abstraction.
From the Paper
"By 1909, Picasso, working in close collaboration with Georges Braque, had invented Cubism, a kind of painting more sculptural than any before, since it presented simultaneously more than one view of the subject. Indeed, Picasso had definitely renounced the traditional chia roscuro - the technique of evoking three-dimensional form by reproducing the way that incident light plays across it, producing a sequence of highlights and shadows. Picasso apparently considered chiaroscuro a "dishonest" way of representing three-dimensional form; he therefore turned to faceting as a means of describing three-dimensional form without using conventional shading. After the dematerialization of form in Impressionism, and the flattening of form in Post-Impres sionism, this restoration of a sense of sculptural solidity (without a return to conventional real ism) was a major achievement. "
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