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How is geometry more then just shapes and theorems?

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February 21, 2008 10:09PM

Geometry (Greek γεωμετρία; geo = gaia or earth, metria = measure) is a part of mathematics concerned with questions of size, shape, and relative position of figures and with properties of space. Geometry is one of the oldest sciences. Initially a body of practical knowledge concerning lengths, areas, and volumes, in the third century B.C., geometry was put into an axiomatic form by Euclid, whose treatment - Euclidean geometry - set a standard for many centuries to follow. The field of astronomy, especially mapping the positions of the stars and planets on the celestial sphere, served as an important source of geometric problems during the next one and a half millennia. However, the real problem with geometry is that these shapes we speak about are not, in reality "geo" or of earth, but rather in our minds as mental gymnastics. That is why calculus was developed in an attempt to measure the curvatures that elude geometric forms' more linear factors. Essentially, the circle is considered classically as a geometric form and perhaps should be. But the problem remains that albeit a circle would be more relevant to physical life as of it curvature, the problem remains of its measured exactitude. Since we have pi radius squared as the area of circle, we find that "pi" is a fraction and therefore, not exact. Classical math tries to dodge this question regarding the inexactness of a circle claiming equations exist to measure it exactly, but even the Fibonacci sequence is a fraction at 1.625 (some argue 1.618, but do the math of the square root of 5 minus 1 divided by 2). Therefore, the exacting factor means nothing and we must move on from there. It is similar to Einstein's claim to fame because his deflection of light theory was .83 of second arch more than Newton's at .87 second. Who cares about these exiguous degrees when 2/3 of the world is starving? We spend 200 million dollars on the restoration of the Parthenon in the past thirty years equating an obvious misprioritization when our neighbors starve to death. How sad.