arc of tractrix and circle that are equal (proofs??) #405 Correcting Math
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From: Archimedes Plutonium on 8 Feb 2010 04:07 Now here is a related question that seemingly adds further support to the idea that a tractrix must contain an arc that matches a great-circle arc. Throughout this thread I kept harping on the idea that the sphere has the same radius as the pseudosphere (tractrix) , but let us for a moment relax that requirement. Suppose we gather all different radii spheres larger than the given tractrix. Are we to think, then, that none of those infinite set of larger spheres has no arcs which matches any of the infinite set of arcs in the tractrix? It seems somewhat paradoxical that no great circle arc of an infinite set of varying spheres would match any arc to the tractrix arcs. Of course, that is not a proof but a rather sketch of a commonsense argument in favor of a tractrix having a matching arc to a arc of a circle. Archimedes Plutonium www.iw.net/~a_plutonium whole entire Universe is just one big atom where dots of the electron-dot-cloud are galaxies |