Do hyperbolic and elliptic versions coexist with Euclidean Space-time?

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Speculation for helical mechanics in space-time.

These illustrations may demonstrate [not prove] how Euclidean space [anthropic perspective] may coexist with hyperbolic space of Gaussian curvature and elliptic space of Riemannian curvature. [The hyperbola is reciprocal to the ellipse in eccentricity - the R:1/R relationship?] Is it possible that one can alternately be nested within the other as planets in a solar system within a local bubble within a galaxy within a cluster?

1- Why Barred Spiral Galaxies have features in common with the logarithmic spiral -
Hermann Riecke and Alex Roxin in their ‘Rotating Convection in an Anisotropic System’ features images remarkably like Barred Spiral Galaxies. Published in Phys. Rev. E 65 (2002) 046219 and on-line at
http://www.esam.northwestern.edu/~riecke/research/Modrot/research_klias.htm

2 - Why the helix may be the geodesic of all mechanical [and electrical?] motion -
This Japanese website [author: iittoo?] in English has numerous elliptic and hyperbolic examples.
http://www1.kcn.ne.jp/~iittoo/index.html#chapters [Broken]

The most interesting may be the tractoid or pseudosphere - perhaps related to the structure of rotating spiral galaxies.
Figures 6, 6’ illustrate how the helix may be a geodesic for the moving tractoid.
Figure 16 is credited to Tore Nordstrand from Gallery of Curved Surfaces [French].
This may illustrate how a solar system or galaxy may retain the logarithmic spiral as they move through space-time.
http://www1.kcn.ne.jp/~iittoo/us20_pseu.htm [Broken]
 
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