Results 11 to 20 of about 1,591,753 (376)
Non-Euclidean geometry in nature [PDF]
, 2017 I describe the manifestation of the non-Euclidean geometry in the behavior of collective observables of some complex physical systems. Specifically, I consider the formation of equilibrium shapes of plants and statistics of sparse random graphs.
Nechaev, Sergei
core +2 more sources
On the Geometry of No-Boundary Instantons in Loop Quantum Cosmology
Universe, 2019 We study the geometry of Euclidean instantons in loop quantum cosmology (LQC) such as those relevant for the no-boundary proposal. Confining ourselves to the simplest case of a cosmological constant in minisuperspace cosmologies, we analyze solutions of ...
Suddhasattwa Brahma, Dong-han Yeom
doaj +3 more sources
Euclidean N=2 Supergravity [PDF]
, 2012 Euclidean special geometry has recently been investigated in the context of Euclidean supersymmetric theories with vector multiplets. In the rigid case, the scalar manifold is described by affine special para-Kahler geometry while the target geometries of Euclidean vector multiplets coupled to supergravity are given by projective special para-Kahler ...
Andrianopoli +25 more
arxiv +4 more sources
Nature, 1943 THE philosopher Kant declared that Euclidean geometry was inherent in the human mind and expressed the truth about space. We now recognize that non-Euclidean geometry is equally valid as an abstract system, and that one particular form (due to Riemann) has more claim than Euclidean geometry to represent the properties of physical space.
H. T. H. Piaggio
openalex +3 more sources
From Euclidean Geometry to Knots and Nets [PDF]
Synthese, 2017 This document is the Accepted Manuscript of an article accepted for publication in Synthese. Under embargo until 19 September 2018. The final publication is available at Springer via https://doi.org/10.1007/s11229-017-1558-x.This paper assumes the ...
A Pelc +36 more
core +3 more sources
Statics and kinematics of frameworks in Euclidean and non-Euclidean geometry [PDF]
arXiv, 2017 This is a survey article on the infinitesimal rigidity of frameworks in Euclidean, hyperbolic, and spherical geometry. We discuss the equivalence of the static and kinematic formulations of the infinitesimal rigidity, the projective interpretation of statics (representing forces as bivectors), and the infinitesimal Pogorelov maps that establish ...
Ivan Izmestiev
arxiv +3 more sources
Geometric Algebras for Euclidean Geometry [PDF]
, 2016 The discussion of how to apply geometric algebra to euclidean $n$-space has been clouded by a number of conceptual misunderstandings which we first identify and resolve, based on a thorough review of crucial but largely forgotten themes from $19^{th ...
Gunn, Charles G.
core +2 more sources
Visual outdoor space perception [PDF]
Scientific ReportsVisual space perception has been a topic of sustained research since the nineteenth century. Much of this research into the geometry of visual space, however, required observers to make judgments about spatial relationships between isolated points in ...
J. Farley Norman +6 more
doaj +2 more sources
Experience of Euclidean geometry sculpts the development and dynamics of rodent hippocampal sequential cell assemblies [PDF]
Nature CommunicationsEuclidean space is the fabric of the world we live in. Whether and how geometric experience shapes our spatial-temporal representations of the world remained unknown.
Usman Farooq, George Dragoi
doaj +2 more sources
Mathematical Gazette, 1901 Non-Euclidean geometry began as an inquiry into a possible weakness in Euclid’s Elements and became the source of the ideas that there are geometries of spaces other than the one imagined in elementary geometry and that many mathematical theories, not ...
Tony Gardiner
openaire +5 more sources