The way this works is: make an ordinary 3D trefoil knot, except open the closed curve in a boring part of the knot. Put the two new endpoints on an axis of rotation. Flatten the knot to 2D, encoding the third dimension with color. (This flattening isn't necessary, I suppose it was done to simplify things for the graphics program.) The idea is that objects with different color may appear to be intersecting but they really aren't because they are separate in the color dimension. Rotate the trefoil around the access of rotation, with each point in the string leaving a colored space-filling trace. The end result is a 2D embedded in 4D version of the trefoil knot.
It seems plausible that all 3D knots can be 4Dized this way. Question : are there 4D knots that can't be created this way? That is, is there a bijection between knots in 3D and those in 4D?
| # | Наименование новости | Тональность | Информативность | Дата публикации |
|---|---|---|---|---|
| 1 | 0 | 0 | 24-03-2026 | |
| 2 | 0 | 0 | 24-02-2026 | |
| 3 | 0 | 0 | 14-10-2026 | |
| 4 | Differentiating connections along a worldline | 0 | 10 | 22-03-2026 |
| 5 | 4 - Compute correspondence | 0 | 35 | 05-11-2019 |
| 6 | Катэ | 0 | 10 | 15-08-2026 |
| 7 | Knowledge Map | 0 | 10 | 13-10-2026 |
| 8 | 5 - Generate retargeted mesh | 0 | 30 | 05-11-2019 |
| 9 | Differentiation of the connections | 0 | 5 | 22-03-2026 |