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Geometry |
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Authors: Hiroshi Okumura, Saburou Saitoh
In this paper, we will discuss Euclidean geometry from the viewpoint of the division by zero calculus with typical examples. Where is the point at infinity? It seems that the point is vague in Euclidean geometry in a sense. Certainly we can see the point at infinity with the classical Riemann sphere. However, by the division by zero and division by zero calculus, we found that the Riemann sphere is not suitable, but D\"aumler's horn torus model is suitable that shows the coincidence of the zero point and the point at infinity. Therefore, Euclidean geometry is extended globally to the point at infinity. This will give a great revolution of Euclidean geometry. The impacts are wide and therefore, we will show their essence with several typical examples.
Comments: 14 Pages.
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[v1] 2020-10-28 21:39:06
Unique-IP document downloads: 571 times
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