why this theorem was never discovered in NonEuclidean geometry #407 Correcting Math
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From: Archimedes Plutonium on 8 Feb 2010 15:09 Archimedes Plutonium wrote: (snipped) > > New Theorem: Given a NonEuclidean Geometry, that the lines in that > geometry, > that 10% or less of a particular line of that NonEuclidean Geometry is > matched by the > same arc in the Reverse NonEuclidean Geometry. Example, tractrix in > Hyperbolic > geometry line, if given 10% or less of that line is matched by an arc > of a great-circle > of the reverse-geometry of Elliptic. > The reason why the above theorem was never discovered until now is obvious, why. It is because we all look at geometry from the standpoint of Euclidean. Our minds are totally Euclidean devoted and only in rare cases do we venture off our platform of framing NonEuclidean geometry correctly. We learn and instinctively know that it matters not "how small we have a Euclidean straight line segment" for if we chose to extend that tiny segment, we all know that it just becomes a bigger line-segment, a bigger straight line. So that when we venture into NonEuclidean geometry, we hold out those very same expectations that if you have a tiny line segment of a great-circle and extend it, it can only become a larger great-circle line segment. And if we have a tiny tractrix line segment and extend it out further, that our Euclidean beliefs and delusions can only think and imagine that the extension of that tiny tractrix segment can only be a larger tractrix segment. So it is the Euclidean delusion of a straight line that we were never able to realize that in NonEuclidean geometry, that given a 10% of smaller line segment, and when extended can have an infinite variety of "different curved arcs". Archimedes Plutonium www.iw.net/~a_plutonium whole entire Universe is just one big atom where dots of the electron-dot-cloud are galaxies |