4 ms·
Totally different thing, but reminds me of the Hopf Fibration, which you should really look up if you never have before.
by macawfish 8y ago
Totally different thing, but reminds me of the Hopf Fibration, which you should really look up if you never have before.
- alanbernstein 8y agoI'm not sure I'm grasping the significance of this, is there an article or video you'd recommend?
- macawfish 8y agoDefinitely this one! https://youtu.be/10sDqSUjXHc https://youtu.be/10sDqSUjXHc Think about how you could fill a 2D plane with infinite parallel lines, one for every single point on a real line. Imagine, for example, running vertical lines through every point on the x-axis, how this would fill the entire plane. The Hopf Fibration is similar. It's a way of filling all of the space on the surface of a 3-sphere (which locally feels like 3D Euclidean space) with interlocking circles. Each of these circles can be mapped a point on an ordinary sphere. Thinking of it in the other direction: for every point on the surface of an ordinary (2-)sphere, you can assign a circle on the surface of a 3-sphere. By taking into consideration all of the points on the 2-sphere, and all of the circles they represent, you can fill the entire surface of the 3-sphere with these interlocking circles!