| 单词 | Euclidean space |
| 例句 | For example, in linear algebra one studies abstract vector spaces such as three-dimensional Euclidean space. Infinity Category Theory Offers a Bird’s-Eye View of Mathematics 2021-09-14T04:00:00Z In Euclidean space, staring at a point at infinity means that the lines of sight of the two eyes track parallel lines. Mathematicians create warped worlds in virtual reality 2017-03-20T04:00:00Z Angles are much more restricted in Euclidean space than in hyperbolic space. Everything Looks Better in the Hyperbolic Plane 2015-08-21T04:00:00Z The 'extrinsic' approach views them in 'Euclidean space', rather like plotting them against the familiar axes of graphs — for example a sphere is the surface of a three-dimensional ball. 'Beautiful mind' John Nash adds Abel Prize to his Nobel 2015-03-24T04:00:00Z A three-manifold is an object in which every point looks locally like three-dimensional Euclidean space. The Mathematical Legacy of William Thurston (1946-2012) 2012-08-24T03:15:00.177Z It has abandoned a Euclidean space with its axioms as a metaphysical presupposition, and it has abandoned an Aristotelian subsumptive logic for which definition is a necessary presupposition. Creative Intelligence Essays in the Pragmatic Attitude I take the position that the human mind apparently is able to conceptualise Euclidean space - and that this actually defines our concept of space. Definition & Reality in the General Theory of Political Economy G. Cantor, and others, which look on our Euclidean space of three dimensions as a special case of the unintuitable yet thinkable analytic concept of a space of n dimensions. History of Modern Philosophy From Nicolas of Cusa to the Present Time A few years before Nash, Nirenberg had proved a result for a special case of the same problem, showing that a class of two-dimensional surfaces can be embedded as convex bodies in three-dimensional Euclidean space. 'Beautiful mind' John Nash adds Abel Prize to his Nobel 2015-03-24T04:00:00Z Motion is thus quite different from what it is in Euclidean space. Man or Matter In a space of this kind there is no Here and There, as in Euclidean space, for the consciousness is always and immediately at one with the whole space. Man or Matter If we take a non-Euclidean geometry - such as a globe - then this still can be imagined to exist within Euclidean space. Definition & Reality in the General Theory of Political Economy In this way he arrived at a space-structure which possesses neither the three-dimensionality nor the rectilinear character of so-called Euclidean space - a space-picture which, though mathematically consistent, is incomprehensible by the human mind. Man or Matter By positing the point as the unit from which to start, and deriving our conception of the plane from the point, we constitute Euclidean space. Man or Matter |
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