Wire Boundary

2018-01-01 - 18:57 | News | Tags: , |

Sphere in three dimensions – a ball, "ordinary" sphere. But here's the curious thing: Wire can break down a sheet of paper cut and cube cut it. And yet it turns out that one-dimensional surface, line, separated by a surface of zero measure – a point. A two-dimensional plane is divided into two-dimensional line and three-dimensional cube – two-dimensional plane. In other words, the boundary of "fault" of the body is some other body, which is measured by one below. What then is the boundary of four-dimensional sphere? Reasoning by analogy, we can remotely imagine the four-sphere. If you project a globe onto a plane, the projections of its two halves will overlap one another, and New York will be somewhere in the middle of Siberia. Projecting the globe, we are missing one it through the other hemisphere, and connect their projections, circles, just over the boundary of the circle (like the squares on the tops).

The projection of the hypersphere – two balls in the last one through the other and connected only on exterior surfaces. Of course, imagine all this is not easy, but nothing mystical is not here. Thus, the introduction took place. One would like to ask "chetyrehmertsam" traditional question: "How is it?" But hypercube silent all its eighty items, and we can only once again resort to the tried and tested approach – run up to spring: time necessary to investigate the properties of the fourth dimension – while the second retreat. I'll give you an excerpt from the book "Geometric rhapsody": Imagine a kind of fairy-tale country of the two-dimensional – "Ploskatiyu", whose inhabitants live in a flat world, and ourselves too two-dimensional.