In the past, humanity has always pursued the mysteries of science and sought to explain the nature of the universe. In this ongoing exploration, an ancient hypothesis has recently captured widespread attention – the existence of four-dimensional space.
How a German Mathematician Proved the Existence of Four-Dimensional Space
The German mathematician Ulrich Hirschfeld has demonstrated the existence of four-dimensional space, and his proof has drawn significant attention within the mathematical community. In this article, we will delve into his research methods and the key findings he has achieved.
In his research, Ulrich Hirschfeld utilized concepts and tools related to linked structures and linear algebra. For the first time, he defined a special type of four-dimensional space that includes Euclidean space with additional coordinates.
In this space, Ulrich Hirschfeld introduced supplementary coordinates to allow for a rigorous mathematical description and study of this space. He conducted an in-depth analysis of the properties of points and lines within this space, leading to several important conclusions about four-dimensional space. (Image: Zhihu).
Ulrich Hirschfeld proposed a critical concept known as manifold. In geometry, a manifold refers to a space that has a locally Euclidean structure. By applying the concept of manifolds to four-dimensional space, Hirschfeld was able to carry out more detailed and precise studies of this domain.
He proved that four-dimensional space is a differentiable manifold, and through reasoning and mathematical proof, he deduced important characteristics and properties of this space.
In further research, Hirschfeld demonstrated that four-dimensional space possesses several properties that are fundamentally different from those of three-dimensional space. He discovered that within four-dimensional space, there are peculiar geometric structures such as hypercubes and rotating objects. These structures cannot exist in three-dimensional space, but they can be described and analyzed using rigorous mathematical methods in four-dimensional space.
Four-dimensional space possesses several properties that are fundamentally different from three-dimensional space. (Illustration: Zhihu).
Beyond geometric structures, Hirschfeld also investigated vector fields and their properties in four-dimensional space. He found that there are certain very special vector fields in four-dimensional space that are entirely unimaginable in three-dimensional space. Through the analysis of these vector fields, Hirschfeld provided deeper insights into the structure and characteristics of four-dimensional space.
Hirschfeld’s research is not only theoretical. He also verified his theoretical results through simulations and numerical experiments. Through these experiments, he reaffirmed the
