Abstract
The idea of a 4-web grid from the fourth dimension was developed in the previous chapter. Such a grid may be moved into human view with its structure preserved. While living in the fourth dimension, however, a 4-web grid may be used to capture those points where the grid meets a hyper-sphere (3-sphere). Then these captured hyper-sphere points may be moved into human view using the technique for moving the grid into human view. The result? A partial picture of a 3-sphere.
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Notes
- 1.
When the mustache is viewed as “spread angel wings” in Figure 7.2 one can also “see” (with some effort) two pairs of “folded angel wings”: One pair on each side of the vertical central axis — in the right side of Figure 7.2 look at the boundary areas at the level where the “skull” suddenly becomes much wider. The “right-side pair” of “folded wings” appears to be at 45∘ relative to the vertical, and likewise for the “left-side pair”. In fact, all three of these pairs of “angel wings” appear as mustaches when viewed “straight on”. The movies within the supplemental Blu-ray Disc clearly expose the “3-fold symmetry” of these “angel wings”, which is induced by the 3-fold symmetry of the 4-web cell.
- 2.
The review quoted in this section is part of the review in §13. Section 13 also contains the details of the original reference (Encyclopædia Britannica).
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Lipscomb, S.L. (2014). The Partial Picture. In: Art Meets Mathematics in the Fourth Dimension. Springer, Cham. https://doi.org/10.1007/978-3-319-06254-9_7
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DOI: https://doi.org/10.1007/978-3-319-06254-9_7
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