By Howard Iseri
A Smarandache Geometry (1969) is a geometrical area (i.e., one with issues, traces) such that a few "axiom" is fake in not less than alternative ways, or is fake and likewise occasionally real. Such axiom is expounded to be Smarandachely denied (or S-denied for short). In Smarandache geometry, the reason is to review non-uniformity, so we require it in a truly basic means.
A manifold that helps a such geometry is termed Smarandache manifold (or s-manifold for short). As a distinct case, during this e-book Dr. Howard Iseri reports the s-manifold shaped by way of any selection of (equilateral) triangular disks joined jointly such that every part is the id of 1 aspect each one from unique disks and every vertex is the id of 1 vertex each one of 5, six, or seven specified disks.
Thus, as a selected case, Euclidean, Lobacevsky-Bolyai-Gauss, and Riemann geometries should be united altogether, within the related house, via convinced Smarandache geometries. those final geometries will be partly Euclidean and in part Non-Euclidean.
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