영어에서 Euclidean space 을 사용하는 예와 한국어로 번역
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Euclidean space.
It's a definition really of Euclidean space.
In Euclidean space.
Examples in the three-dimensional Euclidean space R3.
For high-dimensional Euclidean space they were investigating the minimal varieties of the family of submanifolds.
A Klein bottle cannot be constructed in Euclidean space.
The spacetime gradient, like the gradient in a Euclidean space, is defined such that the directional derivative relationship is satisfied.
You all have a sense of what a flat space is, Euclidean space is.
While a Euclidean space has only spacelike dimensions, a Minkowski space also has one timelike dimension.
In theoretical physics, Minkowski space is often compared to Euclidean space.
He worked on conjugate functions in multidimensional euclidean space and the theory of functions of a complex variable.
In theoretical physics, Minkowski space is often contrasted with Euclidean space.
The Wente torus, the first known example of an immersed torus in Euclidean space with constant mean curvature, was found by Henry Wente in 1985 via analytic methods.
It's a bit like this: imagine that we would only ever encountered Euclidean space.
The Fourier transform can also be generalized to functions of several variables on Euclidean space, sending a function of 3-dimensional space to a function of 3-dimensional momentum(or a function of space and time to a function of 4-momentum).
For example, the Klein bottle is a surface that cannot be embedded in three-dimensional Euclidean space.
The Leech lattice Λ24 is the unique lattice in 24-dimensional Euclidean space, E24, with the following list of properties.
In Geometry, this 3D coordinate system defines what is more formally known as Euclidean space.
In geometry, curvilinear coordinates are a coordinate system for Euclidean space in which the coordinate lines may be curved.
However he continued to work on topological ideas, in particular embedding complexes in Euclidean space.
In particular he proved theorems about the embedding of an n-dimensional differentiable manifold in Euclidean space and he discovered characteristic classes at the same time as Stiefel.
Earlier, Hopf had conjectured that the round sphere was the only compact and immersed constant mean curvature surface in Euclidean space.
In this article, the concept of rigidity of smooth surfaces in the three dimensional Euclidean space which naturally arises in elementary geometry is introduced, and the natural process of the development of rigidity theory for compact surfaces and its generalizations are investigated.
In 1965 this result had been extended by de Giorgi and others to n-dimensional Euclidean spaces with n 8.
Riemann 's view… is that, having'in intellectu' a more general notion of space(in fact a notion of non-Euclidean space), we learn by experience that space(the physical space of our experience) is,if not exactly, at least to the highest degree of approximation, Euclidean space.
Together with Henry Whitehead and Christopher Zeeman he published Imbedding of manifolds in euclidean space in 1961.
He is remembered for Helly's theorem, published in 1923, which states that if there are given n convex subsets of a d-dimensional euclidean space with n d +1 and if each collection of d+ 1 of the subsets has a point in common then there is a common point of the n subsets.
But inflation is preferred over any alternative, which must explain why a big bang universe leaves the universe so flat- that is, Euclidean space.
But suppose the physical space of our experience to be thus only approximately Euclidean space, what is the consequence which follows?
Pearson's original paperwas entitled"On Lines and Planes of Closest Fit to Systems of Points in Space"-"in space" implies physical Euclidean space where such concerns do not arise.