Abstract
The Pythagorean Theorem, combined with the analytic geometry of a right circular cone, has been used by H. Minkowski and subsequent investigators to establish the 4-dimensional spacetime continuum associated with A. Einstein's Special Theory of Relativity. Although the mathematics appears sound, the incorporation of a hyper-cone into the analytic geometry of a right triangle in Euclidean 3-space is in conflict with the rules of pure mathematics. A metric space of n dimensions is necessarily defined in terms of n independent coordinates, one for each dimension. Any coordinate that is a combination of the others for a given space is not independent so cannot be an independent dimension. Minkowski-Einstein spacetime contains a dimensional coordinate, via the speed of light, that is not independent. Consequently, Minkowski-Einstein spacetime does not exist.
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