: not assuming or in accordance with all the postulates of Euclid's Elements non-euclidean geometry Word History First Known Use 1872, in the meaning defined above Time Traveler The first known use of non-euclidean was in 1872 See more words from the same year ...
. A straight line divides a plane in which it lies into two congruent parts—;this, of course, has no real meaning, since we are dealing with infinite areas, but such is the argument—;and two rays from a point enclose an (infinite) area which is less than half the whole plane. ...
For mathematics educators and other who need to understand the meaning of geometry. 展开 被引量: 36 年份: 2005 收藏 引用 批量引用 报错 分享 全部来源 免费下载 求助全文 catalog.lib.kyushu-u.ac.jp ulb.tu-darmstadt.de (全网免费下载) tocs.ulb.tu-darmstadt.de (全网免费下载) metmini.ru (...
In conclusion any local physical change or physical process is reflected in all the universe by the change of its geometry, This is the deepest meaning of the entanglement in Quantum mechanics and quantum computing. We stress the connection between metric and information as measure of change. ...
non-Euclidean geometry refutes Kant's theory, such a view fails to take into account themeaningof the term "synthetic," which is that a synthetic proposition can be denied without contradiction.Leonard Nelsonrealized that Kant's theory implies apredictionof non-Euclidean geometry, not a denial ...
In this paper, using the classical methods of differential geometry, we define invariants of non-developable ruled surfaces in Euclidean 3-space, called structure functions, and show kinematics meaning of these invariants. We also generalize the notion of the angle of pitch of a closed ruled surfa...
Very generally speaking, statistical data analysis builds on descriptors reflecting data distributions. In a linear context, well studied nonparametric descriptors are means and PCs (principal components, the eigenorientations of covariance matrices). In
The term “expansive” has a different meaning in dynamical systems theory. For a compact infinite metric space [Math Processing Error]X, a continuous surjection [Math Processing Error]f:X→X is called positively expansive if there is a constant [Math Processing Error]e>0 such that if [Math...
With the development of non-Euclidean geometries in the nineteenth century, the concern arose as to whether these alternatives constituted a refutation of Kant's theory of geometry. Partly the concerns were related to Kant's argument that geometric judgments were synthetic judgments, meaning that the...
This article first explores the meaning that attaches to the flexibility in the choice of technology and defines the concept of equity in the distribution of income. It then proceeds to demonstrate how the ability to explore the limits of technological flexibility, both in its static and dynamic ...