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The History of Projective Geometry - Essay Example

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Name of the of the Concerned Professor Subject 2 May 2011 The History of Projective Geometry Introduction Projective geometry is the aspects of mathematical studies that had to do with the study of relationships existing between geometric figures and the mappings or images that are brought into existence as a result of the projection of these geometric figures on some other surface…
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Download file to see previous pages In the everyday life, one often does come across varied aspects of projective geometry. For example a motion picture being displayed on a screen is an example of projection. The shadows brought into existence by opaque objects are one other example of projective geometry. Projective geometry evolved and developed into a formal constituent of mathematical studies over a long period of time. History The history of projective geometry is an apt example of the confluence and collaboration between science and art. Projective geometry, to begin with had its origins in the studies in optics carried on by the Arab mathematicians like Alhazen (Boyer et al., 143). During the Renaissance, when the Western Europe developed a more look outside approach to varied aspects of life including mathematics and art, the discoveries and studies of Arab mathematicians that had by that time reached Europe through trade routes greatly influenced the Western world (Boyer et al., 145). The one big flaw in the Western art that had been created till now was that it was more or less flat in its presentation and style. However, soon, several early Renaissance artists after being influenced and inspired by the essentially Arab studies in optics, started to develop techniques of visual depiction that endowed their works of art with a three dimensional depth and perspective (Encyclopedia Britannica: Online) . The creations of Renaissance art had a significant impact on the contemporary and future mathematicians. The projective geometry evinced nascent reverberations in the architectural drawings of Leon Battista (1404-1472) and Filippo Brunelledchi (1377-1446). In fact, it was these two individuals who laid down the foundation of the method of perspective drawing (Encyclopedia Britannica: Online). The primary approach of this method was to connect the eyes of the painter to various points on a landscape with the help of seemingly straight lines. The original drawing was created on the basis of tracing the intersection of these lines on a vertical plane. Obviously, this approach towards drawing was named projective geometry as it intended to project a real plane on a picture plain (Encyclopedia Britannica: Online). Further, Johannes Kepler (1571-1630) and Gerard Desargues (1591-1661) further expanded the scope and possibility of projective geometry by developing the concept of ‘point of infinity’ (Boyer et al., 221). In that context, it would not be wrong to say that the works and studies of Gaspard Monge at some time during the end of the 18th century played a central and pivotal role in the future development and study of projective geometry (Boyer et al., 221). Still it was Jean-Victor Poncelet (1788-1867) who is attributed to be the father of modern projective geometry (.Encyclopedia Britannica: Online) Jean-Victor Poncelet was a renowned French engineer and mathematician who are credited with the honor of systematically and formally reviving projective geometry in the 19th century. Some mathematicians go even as far ahead to claim that his work Traite des proprietes projectives des figures was actually the first credible, authentic and well researched work on projective geometry after what was published by Gerard Desargues in the 17th century (.Encyclopedia Britannica: Online )To begin with it were the French mathematicians Blaise Pascal (1623-1662) and ...Download file to see next pagesRead More
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