Results 331 to 340 of about 1,591,753 (376)
Some of the next articles are maybe not open access.
2021
Four-dimensional theories match Virtual Reality because here time and space are configured through mutable lines. Since the discovery of non-Euclidean geometry, linearity has been submitted to a profound crisis. Mathematicians showed that there are not one but several geometries.
openaire +2 more sources
Four-dimensional theories match Virtual Reality because here time and space are configured through mutable lines. Since the discovery of non-Euclidean geometry, linearity has been submitted to a profound crisis. Mathematicians showed that there are not one but several geometries.
openaire +2 more sources
Euclidean Geometry and Physical Space
The Mathematical Intelligencer, 2006It takes a good deal of historical imagination to picture the kinds of debates that accompanied the slow process, which ultimately led to the acceptance of non-Euclidean geometries little more than a century ago. The difficulty stems mainly from our tendency to think of geometry as a branch of pure mathematics rather than as a science with deep ...
openaire +2 more sources
Euclidean and Hyperbolic Geometry [PDF]
, 2012 X designates again an arbitrary real inner product space containing two linearly independent elements. As throughout the whole book, we do not exclude the case that there exists an infinite and linearly independent subset of X.
openaire +1 more source
1984
It is unlikely that Euclid ever held his five postulates to be self-evident. Mathematicians sharing the Aristotelian conviction that only manifest truths may be admitted without proof in geometry usually did not find the fifth postulate quite so obvious as the other four.
openaire +2 more sources
It is unlikely that Euclid ever held his five postulates to be self-evident. Mathematicians sharing the Aristotelian conviction that only manifest truths may be admitted without proof in geometry usually did not find the fifth postulate quite so obvious as the other four.
openaire +2 more sources
Euclidean Geometry, Generalities
2003In this chapter, all the vector spaces are defined over the field R of real numbers. The spaces under consideration all have finite dimension.
openaire +2 more sources
2020
One of the new frontiers in geometry opened up by calculus was the study of curvature. The concept of curvature is particularly interesting for surfaces, because it can be defined intrinsically. The intrinsic curvature, or Gaussian curvature as it is known, is unaltered by bending the surface, so it can be defined without reference to the surrounding ...
openaire +2 more sources
One of the new frontiers in geometry opened up by calculus was the study of curvature. The concept of curvature is particularly interesting for surfaces, because it can be defined intrinsically. The intrinsic curvature, or Gaussian curvature as it is known, is unaltered by bending the surface, so it can be defined without reference to the surrounding ...
openaire +2 more sources
Programmable interactions and emergent geometry in an array of atom clouds
Nature, 2021Avikar Periwal +2 more
exaly
Euclidean Geometry-Based Spatially Coupled LDPC Codes for Storage
IEEE Journal on Selected Areas in Communications, 2016Yixuan Xie +3 more
semanticscholar +1 more source