Vi Hart founded a research group, eleVR, and he led a group that created a virtual landscape that looked like a group of rooms that were endlessly repeated. This virtual landscape follows a non-Euclidean geometric rule called hyperbolic geometry (also known as H space). It operates in a different way from the normal world, which follows the so-called Euclidean geometry. In this virtual reality world, if you go forward, the floor will fall and hit your feet, and the distance is not what it looks like, because the lines and angles are not like in the ordinary world.
"In H space, when you move your head a little, it's normal, but if you move more, it's different," study co-author Henry Segerman, an assistant professor of mathematics at Oklahoma State University, told Life Science. This is because "there are many people approaching you" in H space, that is to say, the space between two points is smaller in some directions than in Euclidean space, and the unit of distance in Euclidean space is the same length. [5 reasons why we may live in a multiverse]
The research results have been applied in academic field and video game industry. However, the driving force of this project is more art than science: "Mathematics and art are not so far away," Hart said. Whether it is mathematics or art, we can talk about a completely fictional world.
Most of the geometry used in daily life is the geometry of plane space, or Euclid geometry, because the Greek mathematician Euclid wrote down many of its principles. For example, people on earth expect that parallel lines will never intersect. If you add up the internal angles of a triangle, it will become 180 degrees. This also means that if you go forward 10 feet, go right, walk the same distance, and repeat this process three times, you will return to the same point.
Non-Euclidean geometry is not like this. The internal angle of the triangle inscribed on the spherical surface (spherical geometric space) exceeds 180 degrees, while the internal angle of the triangle drawn on the saddle surface (hyperbolic geometric space) can be smaller. Because the surface of the earth is spherical, spherical geometry is used in navigation. Hyperbolic geometry is more prominent in cosmology.
"Hyperbolic space is more like a pringle chip," Segerman said.
In this way, it will be very strange to explore the non-Euclidean world through virtual reality. Segerman said that in order for scientists to turn this weird field into a virtual reality space, they must contain at least some Euclidean features, even if only to make users less confused. [1 1 the most beautiful mathematical equation]
This project is not designed for immediate use. The resulting virtual reality landscape can become an interesting video game world, and even be used to teach students how to navigate in such a space. In addition, in these types of spaces, you can see some data with a large number of "branch trees" (which are usually difficult to visualize).
It is also very useful in mathematics. Sometimes, entering this world is more direct than reading or calculating, "Segerman said. For many people, it is much easier to experience a non-Euclidean space personally than to try to analyze it on paper, because people interact through their senses, just like in the ordinary world.
For example, Jeff Weeks, another researcher cited in the paper, has made flight simulators that can work in these spaces.