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might be a better description, though they are somewhat different from ordinary isocurves. I am not sure if
Clifford parallels can exist in a 2-sphere, I think they may need at least a 3-sphere or higher. The illustrations I recall once seeing were more like spirals around an axial line, but I cannot
285:(where an isocurve to a line is a conic) can be understood as elliptic. This is very different from the analytic approach via quaternions, about which I know even less. I created this article at least in part in the hope that others would answer some of these questions. — Cheers,
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Thank you, I may try to add some of that to the article. As an aside, the description in the
Clifford torus article that it is an example of Euclidean geometry appears to be wrong. The Euclidean plane is equivalent to
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I wish I knew. Whether a line "is", or appears, metrically straight or curved can depend on its projection into the observer's space. The fact that these lines "are in fact curves" makes me wonder whether
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recall the context in which these spirals were "lines". My own interest in elliptic geometries comes from the broader axiomatic treatment, and especially the sense in which certain manifestations of
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where the versor lives. Parallel to which line? To the line through 1. Picturing the
Clifford parallelism and other elliptic relations is challenging since the versors form a
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Right, the
Clifford parallel occurs in the 3-sphere. An animation at
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