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Free research papers and essays on topics related to: geometry

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• Fractal Geometry - 589 words
Fractal Geometry Fractal Geometry Fractal geometry is a branch of mathematics having to do with fractals. Fractals are geometric figures, just like rectangles, circles and squares, but fractals have special properties that those figures do not have. In geometry two figures are similar if their corresponding angles are congruent in measure. Fractals are self-similar meaning that at every level the fractal image repeats itself. An example of self-similarity would be a triangle made up of triangles that are the same shape or are similar to the whole. Another important property of fractals is fractional dimensions. While in Euclidean geometry figures are either zero dimensional points, one dimen ...
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• Fractal Geometry - 545 words
Fractal Geometry Fractal geometry is a fascinating concept of dimension and shape. After being assigned this project I was recalled to the cookie jar that is on top of the fridge that I sought after as a child. The cookie jar features an image of a chef reaching into a cookie jar that featured the same repeating image of a chef. This particular ceramic piece of art was my first thought about the concept of infinity. The pioneering genius of fractal geometry, Benoit Mandelbrot, was a highly visual thinker who earned good grades through his outstanding visual representations. He stated "Clouds are not spheres, mountains are not cones, coastlines are not circles, bark is not smooth, nor does li ...
Related: fractal geometry, geometry, yard, dimensional
• Geometry In Nature - 217 words
GEOMETRY IN NATURE SPHERES: A Sphere is an object shaped so that all points on its surface are the same distance from a center point. Number 1: THE EARTH The Earth is a sphere due to its shape. The earth is shaped this way to assist in axis rotation plus the shape is needed to keep the earth in its orbit around the sun. Number 2/Number 3: FRUIT Fruit is shaped like a sphere to ensure overall ripening of the fruit. Number 4: BUBBLES Bubbles can be found in ponds from air rising from the bottom. They are spherical in shape to help in moving freely. Number 5: PEARLS Pearls are spherical because the sand accumulates equally around the grain of sand. SYMMETRY: Symmetry is exact matching of parts ...
Related: geometry, mechanism, enhance
• Math Report Fractal Geometry Fractal Geometry Is Not Just A Chapter Of Mathematics, But One That Helps Everyman To See The Sa - 1,309 words
Math Report Fractal Geometry Fractal Geometry is not just a chapter of mathematics, but one that helps everyman to see the same old world differently". - Benoit Mandelbrot The world of mathematics usually tends to be thought of as abstract. Complex and imaginary numbers, real numbers, logarithms, functions, some tangible and others imperceivable. But these abstract numbers, simply symbols that conjure an image, a quantity, in our mind, and complex equations, take on a new meaning with fractals - a concrete one. Fractals go from being very simple equations on a piece of paper to colorful, extraordinary images, and most of all, offer an explanation to things. The importance of fractal geometry ...
Related: everyman, fractal geometry, geometry, math, computer program
• Rene Descartes Analytic Geometry - 1,137 words
Rene' Descartes Analytic Geometry Analytic geometry was brought fourth by the famous French mathematician Rene' Descartes in 1637. Descartes did not start his studying and working with geometry until after he had retired out of the army and settled down. If not for Descartes great discovery then Sir Isaac Newton might not have ever invented the concept of calculus. Descartes concept let to calculus and Newton and G.W. Leibniz would not be know as well as they are today if it were not for the famous mathematician Rene' Descartes. Analytic geometry is a, branch of geometry in which points are represented with respect to a coordinate system, such as Cartesian coordinates, and in which the appro ...
Related: analytic, descartes, geometry, projective geometry, rene, rene descartes
• A Failing Education - 523 words
A Failing Education I am a high school student, but I do know things. I know if I know something or not. After knowing someone for awhile, I know if they know anything or not. In school, I know that not knowing anything does not mean anything. I know I can pass a class without knowing anything about that subject. If you want to know why I know, look at some of my classes. I know I passed electronics. I also know that I know nothing about electronics. I really do not know geometry well, but I know I passed. I know that if you wanted to know about computer science I could not tell you a thing. Yet, I know I passed the class. Talk to me in Spanish and I would not know what you were saying, but ...
Related: failing, computer science, high school, electronics, letting
• A Philosopher Of Nature - 1,482 words
A Philosopher Of Nature A PHILOSOPHER OF NATURE December 1, 1998 Paper # 2 Intro to Philosophy Fifty years ago the single greatest philosopher walked upon this earth. How can I be so dauntless as to refer to one man as The Greatest philosopher? The answer is simple. All philosophers ask questions. Few of these questions will produce earth-shattering revelations and even fewer will change the world. Out of the handful of philosophers who have made a difference in the world I can think of only one who has, by use of an amazing mind and knowledge of complex mathematics, changed the world forever. Albert Einstein was born in Ulm Germany on March 14, 1879, and spent his youth in Munich, where his ...
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• A Valediction: Forbidding Mourning - 1,054 words
A Valediction: Forbidding Mourning A Valediction: Forbidding Mourning Although the subject matter of A Valediction: Forbidding Mourning could be applied to any couple pending separation, John Donne wrote his poem for his wife on the eve of his departure for France in 1611.In the poem, the speaker pleads with his lady to accept his departure. The speaker defines and celebrates a love that transcends the physical and can therefore endure and even grow through separation. In arguing against mourning and emotional upheaval, Donne uses a series of bold and unexpected comparisons for the love between the speaker and his lady. Donne makes his first surprising analogy in the first stanza when he com ...
Related: mourning, john donne, subject matter, ordinary people, refer
• A Valediction: Forbidding Mourning - 1,305 words
A Valediction: Forbidding Mourning Intro to Poetry Oct 10 2000 Interpretation of A Valediction: Forbidding Mourning Although that it may seem that the meaning of A Valediction: Forbidding Mourning could be applied to any couple awaiting separation, according to Izaak Walton, a seventeenth-century biographer, John Donne wrote his poem for his wife, Anne Donne, right before his departure for France in 1611 (Damrosch 238). However, even though the poem is not written to an audience, many of us can learn from what Donne is trying to convey to his wife. In the poem, Donne pleads with his lady to accept his departure. He defines and celebrates a love that transcends the physical realm and expresse ...
Related: mourning, middle ages, true meaning, john donne, greek
• Aggressiveness Brain Success - 1,125 words
Aggressiveness + Brain = Success Aggressiveness + Brain = Success Nowadays, the women in Asia are receiving more and more reputations than before. In China the most successful and welcomed TV anchormen are the men and women half to half and the female anchormen have much more chance to take part in some TV series show than their male colleagues; even the national woman soccer team of China, after they acquired the second prize in the World Cup last year, their brilliant glory erased our male soccer players incompetence. Women, especially the Asian women, are no longer those whom only had to stay at home taking care of her husband and children, making dinners and cleaning the houses to spend ...
Related: aggressiveness, brain, real thing, more important, wisdom
• Albert Einstein - 1,590 words
Albert Einstein Albert Einstein Einstein was born on March 14, 1879, in Ulm Germany. He lived there with his parents, Herman and Pauline. After a year in Ulm, due to the failure of his father's electrical and engineering workshop, the Einstein family moved to Munich (the capital of Bavaria), where after a year in residence there, Einstein's mother had Maja, Einstein's sister. Despite the fact that he was Jewish, from age five until age ten, Einstein attended a Catholic School near his home. But, at age 10, Einstein was transferred to the Luitpold Gymnasium, where Latin, Greek, History, and Geography were pounded into childrens' heads. His parents wanted him to finish school, get his diploma ...
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• Albert Einstein - 749 words
Albert Einstein Albert Einstein was one of a few scientists that change the way we look at the world Today. He was born in 1879 and die on 1955. In that time he made many theories on how the world works. Einstein got married twice once to a class mate and once his cousin. Einstein also like music and he played the violin. Albert Einstein is on of few scientist who had changed the way the world works today. Albert Einstein was born in Ulm Germany on March 14 1879. He died in Princeton on April 18 1955 at the age of 76. Albert Einstein did not like his school in Germany. His best subject in school were mathematics and science. At The age of 12 he taught himself Euclidean geometry. Later when h ...
Related: albert, albert einstein, einstein, theory of relativity, world today
• Albert Einsteinman Of Vision - 1,905 words
Albert Einstein-Man Of Vision Albert Einstein: Man of Vision Albert Einstein, perhaps the greatest mind ever to have walked the face of the earth, was born on March 14, 1879 in Ulm, Germany. As a boy, he hated school, and felt that the regimented and repetitive nature of schooling in Germany at that time had any promise of helping his future. He did not do well in school, mainly because he did not care to learn what was being taught to him. While he seemed to be a bright child, his schoolwork did not interest him, but at the same time the simple compass that his father owned fascinated him. Albert constantly harassed his father and his Uncle Jake with questions concerning how the compass wor ...
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• Albrecht Durer - 1,562 words
Albrecht Durer Albrecht Durer was born in Nurembourg in May 21, 1471. His father, Albrecht Durer was a goldsmith, he had come from Germany to Nurembourg in 1455 and married Barbara Holper. Barbara's father was Albrecht's master. Albrecht was his father's third son. He was named Albrecht because of a family tradition which he has been the third representative so far. Albrecht had three brothers named Laszlo, Albrecht, and Ajtos. Albrecht was apprenticed to his father at the age of 13. His father introduced him to the working with metal and the use of tools with laid the ground work for his skill of engraving. He also learned painting from his father at the age of 13. He preferred to draw and ...
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• Analysis Of A Drawing For Art His Class - 1,321 words
Analysis Of A Drawing For Art His Class Analysis of 'Chance Meeting' by Martin Lewis 'Chance Meeting' is a dry point etching print by Martin Lewis and was created in the early 1930's. The subjects are two figures, male and female, who have happened upon each other in the setting of a public sidewalk at the entrance of a storefront. It may be a dichotomy in terms to call the piece, Idealized Urban Realism, though Lewis' work does harmonize well with the Urban Realist movement surfacing in this period with artists such as Edward Hopper. It also has a very idealized and stylistic quality not unlike the work of artists like Roy Liechtenstein in a much later time period. At a glance, 'Chance Meet ...
Related: drawing, urban america, young woman, edward hopper, symbolism
• Anaximander - 725 words
Anaximander With his discoveries, Anaxamander of Miletus attempted to bring the realm of the unreal to the world where common man could conceive it. As successor and pupil of Thales of Miletus, Anaxamander worked on the fields of geometry, natural science, and astrology. The culmination of his life attempted to define the indefinite or undetermined. He was the first to discover and apply the theory of the unlimited. For a philosopher of this time period, he had many radical ideas. Anaxamander believed many different things about the position of the Earth. He also published a book, On Nature, which revealed his theories about the evolution of Earth and man. Under the tutelage of Thales, Anaxa ...
Related: natural science, cambridge university, university press, socratic, apply
• Ancient Egyptian Mathematics - 1,010 words
Ancient Egyptian Mathematics Ancient Egyptian Mathematics The use of organized mathematics in Egypt has been dated back to the third millennium BC. Egyptian mathematics was dominated by arithmetic, with an emphasis on measurement and calculation in geometry. With their vast knowledge of geometry, they were able to correctly calculate the areas of triangles, rectangles, and trapezoids and the volumes of figures such as bricks, cylinders, and pyramids. They were also able to build the Great Pyramid with extreme accuracy. Early surveyors found that the maximum error in fixing the length of the sides was only 0.63 of an inch, or less than 1/14000 of the total length. They also found that the err ...
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• Archimedes - 894 words
Archimedes Archimedes is considered one of the three greatest mathematicians of all time along with Newton and Gauss. In his own time, he was known as the wise one, the master and the great geometer and his works and inventions brought him fame that lasts to this very day. He was one of the last great Greek mathematicians. Born in 287 B.C., in Syracuse, a Greek seaport colony in Sicily, Archimedes was the son of Phidias, an astronomer. Except for his studies at Euclid's school in Alexandria, he spent his entire life in his birthplace. Archimedes proved to be a master at mathematics and spent most of his time contemplating new problems to solve, becoming at times so involved in his work that ...
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• Archimedes - 727 words
Archimedes Archimedes was born in 287bc in Syracuse, Sicily. He was then killed in 212bc during the capture of Syracuse, second Punic War. Archimedes was working on one of his diagrams when a Roman soldier approached him and asked him to come with him. (As the soldier was told to capture him alive.)Archimedes refused to leave his drawing and the impatient soldier killed him on the spot. It was a tragic end to who maybe the greatest founder of geometry and calculus. He simply just had great enjoyment out of making new properties and find answers. Archimedes is famous for many things, but most so for this discovery. Archimedes proved that the volume of a sphere is two-thirds the volume of a ci ...
Related: archimedes, second punic, punic war, cylinder, syracuse
• Archimedes Of Syracuse - 362 words
Archimedes Of Syracuse Archimedes of Syracuse (ca. 287-ca. 212 BC) Greek mathematician who flourished in Sicily. He is generally considered to be the greatest mathematician of ancient times. Most of the facts about his life come from a biography about the Roman soldier Marcellus written by the Roman biographer Plutarch. Archimedes performed numerous geometric proofs using the rigid geometric formalism outlined by Euclid (Greek geometer who wrote the Elements, the world's most definitive text on geometry.), excelling especially at computing areas and volumes using the METHOD OF EXHAUSTION(a integral-like limiting process to compute the area and volume of 2-D lamina and 3-D solids.). 2-D Lamin ...
Related: archimedes, syracuse, ancient times, correct answer, displaced
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