Log in

Relevant bibliographies by topics / Geometry, Non-Euclidean. Parallels (Geometry) / Journal articles

To see the other types of publications on this topic, follow the link: Geometry, Non-Euclidean. Parallels (Geometry).

Journal articles on the topic 'Geometry, Non-Euclidean. Parallels (Geometry)'

Author: Grafiati

Published: 4 June 2021

Last updated: 13 February 2022

Create a spot-on reference in APA, MLA, Chicago, Harvard, and other styles

Select a source type:

Consult the top 50 journal articles for your research on the topic 'Geometry, Non-Euclidean. Parallels (Geometry).'

Next to every source in the list of references, there is an 'Add to bibliography' button. Press on it, and we will generate automatically the bibliographic reference to the chosen work in the citation style you need: APA, MLA, Harvard, Chicago, Vancouver, etc.

You can also download the full text of the academic publication as pdf and read online its abstract whenever available in the metadata.

Browse journal articles on a wide variety of disciplines and organise your bibliography correctly.

1

BEESON, MICHAEL, PIERRE BOUTRY, and JULIEN NARBOUX. "HERBRAND’S THEOREM AND NON-EUCLIDEAN GEOMETRY." Bulletin of Symbolic Logic 21, no. 2 (2015): 111–22. http://dx.doi.org/10.1017/bsl.2015.6.

Full text

Abstract:

AbstractWe use Herbrand’s theorem to give a new proof that Euclid’s parallel axiom is not derivable from the other axioms of first-order Euclidean geometry. Previous proofs involve constructing models of non-Euclidean geometry. This proof uses a very old and basic theorem of logic together with some simple properties of ruler-and-compass constructions to give a short, simple, and intuitively appealing proof.

APA, Harvard, Vancouver, ISO, and other styles

2

BEESON, MICHAEL. "CONSTRUCTIVE GEOMETRY AND THE PARALLEL POSTULATE." Bulletin of Symbolic Logic 22, no. 1 (2016): 1–104. http://dx.doi.org/10.1017/bsl.2015.41.

Full text

Abstract:

AbstractEuclidean geometry, as presented by Euclid, consists of straightedge-and-compass constructions and rigorous reasoning about the results of those constructions. We show that Euclidean geometry can be developed using only intuitionistic logic. This involves finding “uniform” constructions where normally a case distinction is used. For example, in finding a perpendicular to line L through point p, one usually uses two different constructions, “erecting” a perpendicular when p is on L, and “dropping” a perpendicular when p is not on L, but in constructive geometry, it must be done without

APA, Harvard, Vancouver, ISO, and other styles

3

Budiarto, Mega Teguh, and Rini Setyaningsih. "KONFLIK KOGNITIF MAHASISWA DALAM MEMAHAMI KONSEP GEOMETRI HIPERBOLIK DAN ELLIPTIK." JUPITEK: Jurnal Pendidikan Matematika 2, no. 2 (2020): 69–76. http://dx.doi.org/10.30598/jupitekvol2iss2pp69-76.

Full text

Abstract:

Using schemes of Euclid's geometrical concepts in long-term memory to understand hyperbolic geometry and elliptic geometry concepts with assimilation and accommodation allows for cognitive conflict. This study aims to reduce the occurrence of cognitive conflict by understanding the mathematical content of the three of Euclidean geometries, hyperbolic and elliptic. The research was conduct used descriptive exploratory. The results indicate that Euclid's geometry representation is still used in representing hyperbolic and elliptic geometry so that cognitive conflict occurs. Cognitive conflicts t

APA, Harvard, Vancouver, ISO, and other styles

4

Dursun, Uğur. "Null 2-type submanifolds of the Euclidean space E5 with non-parallel mean curvature vector." Journal of Geometry 86, no. 1-2 (2007): 73–80. http://dx.doi.org/10.1007/s00022-006-1817-3.

Full text

APA, Harvard, Vancouver, ISO, and other styles

5

Tsyrenova, V. B. "Lines on the surface in the quasi-hiperbolic space 11^S1/3." Differential Geometry of Manifolds of Figures, no. 51 (2020): 123–34. http://dx.doi.org/10.5922/0321-4796-2020-51-14.

Full text

Abstract:

Quasi-hyperbolic spaces are projective spaces with decaying absolute. This work is a continuation of the author's work [7], in which surfaces in one of these spaces are examined by methods of external forms and a moving frame. The semi-Chebyshev and Chebyshev networks of lines on the surface in quasi-hyperbolic space are considered. In this paper we use the definition of parallel transfer adopted in [6]. By analogy with Euclidean geometry, the semi-Chebyshev network of lines on the surface is the network in which the tangents to the lines of one family are carried parallel along the lines

APA, Harvard, Vancouver, ISO, and other styles

6

Sokolov, Kirill. "Aleksandr Drevin, Nadezhda Udal'tsova: An Exhibition That Never Was." Leonardo 35, no. 3 (2002): 263–69. http://dx.doi.org/10.1162/002409402760105253.

Full text

Abstract:

This juxtaposition of autobiographical statements written in 1933 by Aleksandr Drevin and Nadezhda Udal'tsova, together with an introduction to their artistic careers and a select chronology designed to place them in the context of their times, is intended to show how early twentieth-century Russian art evolved in parallel to Western thought and artistic practice, taking into account contemporary developments in non-Euclidean geometry, physics, mathematics, the laws of perspective and the awareness of the impossibility of “realistically” representing spatial forms on a flat surface, which, at

APA, Harvard, Vancouver, ISO, and other styles

7

Yashnikov, V. P., and H. J. Bunge. "Geometrical Foundations of Texture Analysis. Geodesic Curves and Motions in the group Space of Three-Dimensional Rotations." Textures and Microstructures 30, no. 1-2 (1997): 1–42. http://dx.doi.org/10.1155/tsm.30.1.

Full text

Abstract:

Principal concepts and selected results relating to the inner geometry of the three-dimensional rotation group SO(3) are presented in a form which is appropriate for further applications to various problems of texture analysis. Starting from the basic concepts of regular and piecewise regular curves in the group space SO(3) we consider the functional of the angular length and introduce further geodesic curves. It is shown that the geodesics can be fully characterized, in the group-theoretical terms, as cosets of all possible one-parametric subgroups in the space SO(3). Two kinds of parallelism

APA, Harvard, Vancouver, ISO, and other styles

8

Planat, M., and M. Saniga. "On the Pauli graphs on N-qudits." Quantum Information and Computation 8, no. 1&2 (2008): 127–46. http://dx.doi.org/10.26421/qic8.1-2-9.

Full text

Abstract:

A comprehensive graph theoretical and finite geometrical study of the commutation relations between the generalized Pauli operators of $N$-qudits is performed in which vertices/points correspond to the operators and edges/lines join commuting pairs of them. As per two-qubits, all basic properties and partitionings of the corresponding {\it Pauli graph} are embodied in the geometry of the generalized quadrangle of order two. Here, one identifies the operators with the points of the quadrangle and groups of maximally commuting subsets of the operators with the lines of the quadrangle. The three

APA, Harvard, Vancouver, ISO, and other styles

9

Barsht, Konstantin. "Тема самоубийства и неевклидово пространство в творчестве Федора Достоевского". Slavica Wratislaviensia 167 (21 грудня 2018): 133–46. http://dx.doi.org/10.19195/0137-1150.167.11.

Full text

Abstract:

The theme of suicide and the non-Euclidean spacein the works of Fyodor DostoevskyThe article proposes a hypothesis about the relation between the ethical imperative, inscribed in those Fyodor Dostoyevsky’s heroes-philosophers, who are seeking answers to the “eternal question” about the meaning and purpose of life, and their attempts to overcome Homo Sapiens limitations with the suicide and non-Euclidean geometry, which Dostoevsky met in the 1870s in the Hermann Helmholtz’s works. In the writer’s works was formulated an existential idea, exceeding the boundaries of possibilities, the width of m

APA, Harvard, Vancouver, ISO, and other styles

10

Gardiner, Tony, and H. S. M. Coxeter. "Non-Euclidean Geometry." Mathematical Gazette 86, no. 506 (2002): 364. http://dx.doi.org/10.2307/3621907.

Full text

APA, Harvard, Vancouver, ISO, and other styles

11

Diemente, Damon. "Algebra in the Service of Geometry: Can Euler's Line Be Parallel to a Side of a Triangle?" Mathematics Teacher 93, no. 5 (2000): 428–31. http://dx.doi.org/10.5951/mt.93.5.0428.

Full text

Abstract:

This investigation of Euler's line has become a regular and valued unit in my honors–geometry syllabus. It originated with an intelligent question from a curious student. Its geometric foundation comprises sophisticated Euclidean triangle geometry. Its solution requires plentiful but not excessively complicated algebra. It culminates in the discovery of a conic locus that can be verified by construction on a computer screen.

APA, Harvard, Vancouver, ISO, and other styles

12

Stewart, Ian. "Geometry: Non-euclidean kaleidoscopes." Nature 323, no. 6084 (1986): 114. http://dx.doi.org/10.1038/323114a0.

Full text

APA, Harvard, Vancouver, ISO, and other styles

13

SQUIRES, T. M. "A furtive stare at an intra-cellular flow." Journal of Fluid Mechanics 642 (December 23, 2009): 1–4. http://dx.doi.org/10.1017/s0022112009992990.

Full text

Abstract:

Rarely do intra-cellular flows amount to much: cells are small, and so are their Reynolds numbers. The extraordinarily large cells of the Characean algae provide a fascinating counter-example, as their geometry precludes the standard methods of distributing food and waste. van de Meent et al. (J. Fluid Mech., 2010, this issue, vol. 642, pp. 5–14) present nuclear magnetic resonance (NMR) velocimetry measurements of the fluid flow within individual living cells, which agree quantitatively with their fluid mechanical model and confirm a long-standing hypothesis. In addition to biomimetic parallel

APA, Harvard, Vancouver, ISO, and other styles

14

Bellot, F., and Eugene E. Krause. "Taxicab Geometry: An Adventure in Non-Euclidean Geometry." Mathematical Gazette 72, no. 461 (1988): 255. http://dx.doi.org/10.2307/3618288.

Full text

APA, Harvard, Vancouver, ISO, and other styles

15

Barreto, Mylane dos Santos, and Salvador Tavares. "From the myth of Euclidean Geometry to the teaching of Non-Euclidean Geometry." Revista Vértices 9, no. 1 (2007): 73–81. http://dx.doi.org/10.5935/1809-2667.20070007.

Full text

APA, Harvard, Vancouver, ISO, and other styles

16

Darke, Ian P., and Patrick J. Ryan. "Euclidean and Non-Euclidean Geometry: An Analytic Approach." Mathematical Gazette 71, no. 458 (1987): 349. http://dx.doi.org/10.2307/3617111.

Full text

APA, Harvard, Vancouver, ISO, and other styles

17

Sunada, T. "Euclidean versus Non-Euclidean Aspects in Spectral Geometry." Progress of Theoretical Physics Supplement 116 (May 16, 2013): 235–50. http://dx.doi.org/10.1143/ptp.116.235.

Full text

APA, Harvard, Vancouver, ISO, and other styles

18

Sunada, Toshikazu. "Euclidean versus Non-Euclidean Aspects in Spectral Geometry." Progress of Theoretical Physics Supplement 116 (1994): 235–50. http://dx.doi.org/10.1143/ptps.116.235.

Full text

APA, Harvard, Vancouver, ISO, and other styles

19

Popov, A. "Non-Euclidean geometry and differential equations." Banach Center Publications 33, no. 1 (1996): 297–308. http://dx.doi.org/10.4064/-33-1-297-308.

Full text

APA, Harvard, Vancouver, ISO, and other styles

20

Storer, W. O., and B. A. Rosenfeld. "The History of Non-Euclidean Geometry." Mathematical Gazette 74, no. 468 (1990): 203. http://dx.doi.org/10.2307/3619413.

Full text

APA, Harvard, Vancouver, ISO, and other styles

21

Hansen, Vagn Lundsgaard. "The dawn of non‐Euclidean geometry." International Journal of Mathematical Education in Science and Technology 28, no. 1 (1997): 3–23. http://dx.doi.org/10.1080/0020739970280102.

Full text

APA, Harvard, Vancouver, ISO, and other styles

22

Blum, Zoltan, Sven Lidin, and Ronnie Thomasson. "Zeolites: Coneyers of non-euclidean geometry." Journal of Solid State Chemistry 74, no. 2 (1988): 353–55. http://dx.doi.org/10.1016/0022-4596(88)90365-9.

Full text

APA, Harvard, Vancouver, ISO, and other styles

23

Kasimov, Nurlybek, Eric Dymkoski, Giuliano De Stefano, and Oleg V. Vasilyev. "Galilean-Invariant Characteristic-Based Volume Penalization Method for Supersonic Flows with Moving Boundaries." Fluids 6, no. 8 (2021): 293. http://dx.doi.org/10.3390/fluids6080293.

Full text

Abstract:

This work extends the characteristic-based volume penalization method, originally developed and demonstrated for compressible subsonic viscous flows in (J. Comput. Phys. 262, 2014), to a hyperbolic system of partial differential equations involving complex domains with moving boundaries. The proposed methodology is shown to be Galilean-invariant and can be used to impose either homogeneous or inhomogeneous Dirichlet, Neumann, and Robin type boundary conditions on immersed boundaries. Both integrated and non-integrated variables can be treated in a systematic manner that parallels the prescript

APA, Harvard, Vancouver, ISO, and other styles

24

Suter, Beth. "Non-Euclidean Geometry Before Breakfast, and: Inheritance." Colorado Review 45, no. 2 (2018): 151–52. http://dx.doi.org/10.1353/col.2018.0070.

Full text

APA, Harvard, Vancouver, ISO, and other styles

25

Leichtweiss, Kurt. "Polar Curves in the Non-euclidean Geometry." Results in Mathematics 52, no. 1-2 (2008): 143–60. http://dx.doi.org/10.1007/s00025-007-0247-3.

Full text

APA, Harvard, Vancouver, ISO, and other styles

26

Dollet, B., A. Scagliarini, and M. Sbragaglia. "Two-dimensional plastic flow of foams and emulsions in a channel: experiments and lattice Boltzmann simulations." Journal of Fluid Mechanics 766 (February 9, 2015): 556–89. http://dx.doi.org/10.1017/jfm.2015.28.

Full text

Abstract:

AbstractIn order to understand the flow profiles of complex fluids, a crucial issue concerns the emergence of spatial correlations among plastic rearrangements exhibiting cooperativity flow behaviour at the macroscopic level. In this paper, the rate of plastic events in a Poiseuille flow is experimentally measured on a confined foam in a Hele-Shaw geometry. The correlation with independently measured velocity profiles is quantified by looking at the relationship between the localisation length of the velocity profiles and the localisation length of the spatial distribution of plastic events. T

APA, Harvard, Vancouver, ISO, and other styles

27

GUILFOYLE, BRENDAN, WILHELM KLINGENBERG, and SIDDHARTHA SEN. "THE CASIMIR EFFECT BETWEEN NON-PARALLEL PLATES BY GEOMETRIC OPTICS." Reviews in Mathematical Physics 17, no. 08 (2005): 859–80. http://dx.doi.org/10.1142/s0129055x05002431.

Full text

Abstract:

The first two authors have developed a technique which uses the complex geometry of the space of oriented affine lines in ℝ3 to describe the reflection of rays off a surface. This can be viewed as a parametric approach to geometric optics which has many possible applications. Recently, Jaffe and Scardicchio have developed a geometric optics approximation to the Casimir effect and the main purpose of this paper is to show that the quantities involved can be easily computed by this complex formalism. To illustrate this, we determine explicitly and in closed form the geometric optics approximatio

APA, Harvard, Vancouver, ISO, and other styles

28

Wanas, M. I., Samah A. Ammar, and Shymaa A. Refaey. "Teleparallel gravity with non-vanishing curvature." Canadian Journal of Physics 96, no. 12 (2018): 1373–83. http://dx.doi.org/10.1139/cjp-2017-0997.

Full text

Abstract:

Guided by the rules of Einstein’s geometrization philosophy, a pure geometric field theory is constructed. The Lagrangian used to derive the field equations of the theory is a curvature scalar of a version of absolute parallelism (AP) geometry known in the literature as the parameterized absolute parallelism (PAP) geometry. The linear connection of this version has simultaneously non-vanishing curvature and torsion. Analysis of the theory obtained shows clearly that it is a pure gravity theory. The theory is a teleparallel one, since the building blocks of both PAP and AP geometries are the sa

APA, Harvard, Vancouver, ISO, and other styles

29

Deprez, Johan. "Semi-parallel surfaces in Euclidean space." Journal of Geometry 25, no. 2 (1985): 192–200. http://dx.doi.org/10.1007/bf01220480.

Full text

APA, Harvard, Vancouver, ISO, and other styles

30

Afgoustidis, Alexandre. "Orientation Maps in V1 and Non-Euclidean Geometry." Journal of Mathematical Neuroscience 5, no. 1 (2015): 12. http://dx.doi.org/10.1186/s13408-015-0024-7.

Full text

APA, Harvard, Vancouver, ISO, and other styles

31

Bruss, I. R., and G. M. Grason. "Non-Euclidean geometry of twisted filament bundle packing." Proceedings of the National Academy of Sciences 109, no. 27 (2012): 10781–86. http://dx.doi.org/10.1073/pnas.1205606109.

Full text

APA, Harvard, Vancouver, ISO, and other styles

32

Griffin, Nicholas. "Non-Euclidean geometry: Still some problems for Kant." Studies in History and Philosophy of Science Part A 22, no. 4 (1991): 661–63. http://dx.doi.org/10.1016/0039-3681(91)90038-t.

Full text

APA, Harvard, Vancouver, ISO, and other styles

33

Szalay, Istvan, and B. Szalay. "Introduction into the Extra Geometry of the Three–Dimensional Space I." European Journal of Engineering Research and Science 5, no. 5 (2020): 538–44. http://dx.doi.org/10.24018/ejers.2020.5.5.1856.

Full text

Abstract:

Using the theory of exploded numbers by the axiom–systems of real numbers and euclidean geometry, we introduce a geometry in the three–dimensional space which is different from the euclidean-, Bolyai – Lobachevsky- and spherical geometries. In this part the concept of extra-line and extra parallelism are detailed.

APA, Harvard, Vancouver, ISO, and other styles

34

Bellone, T., F. Fiermonte, and L. Mussio. "THE COMMON EVOLUTION OF GEOMETRY AND ARCHITECTURE FROM A GEODETIC POINT OF VIEW." ISPRS - International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences XLII-5/W1 (May 16, 2017): 623–30. http://dx.doi.org/10.5194/isprs-archives-xlii-5-w1-623-2017.

Full text

Abstract:

Throughout history the link between geometry and architecture has been strong and while architects have used mathematics to construct their buildings, geometry has always been the essential tool allowing them to choose spatial shapes which are aesthetically appropriate. Sometimes it is geometry which drives architectural choices, but at other times it is architectural innovation which facilitates the emergence of new ideas in geometry. <br><br> Among the best known types of geometry (Euclidean, projective, analytical, Topology, descriptive, fractal,…) those most frequently employed

APA, Harvard, Vancouver, ISO, and other styles

35

Posamentier, Alfred S. "Delving Deeper: Trisecting the Circle: A Case for Euclidean Geometry." Mathematics Teacher 99, no. 6 (2006): 414–18. http://dx.doi.org/10.5951/mt.99.6.0414.

Full text

Abstract:

As an undergraduate mathematics major, a prospective teacher usually takes at least one geometry course. Typically, these courses focus on non–Euclidean geometry (sometimes presented as Modern Geometry), or vectors, transformations, or topology. Instead, we at the City College of New York offer a course on more advanced Euclidean geometry in which prospective teachers investigate a plethora of geometric theorems (or relationships) that enrich their understanding of Euclidean geometry and, consequently, their teaching of it.

APA, Harvard, Vancouver, ISO, and other styles

36

Song, Xiao Zhuang, Ming Liang Lu, and Tao Qin. "The Use of Projective Geometry on the Mechanism System Motion and Stability of the Special Problems in Judgement." Advanced Materials Research 482-484 (February 2012): 1041–44. http://dx.doi.org/10.4028/www.scientific.net/amr.482-484.1041.

Full text

Abstract:

In a principle of kinematics, when a rigid body is motion in a plane, and the fixed plane only the presence of a speed zero point -- the instantaneous center of velocity. In the mechanism of two rigid bodies be connected by two parallel connection links, why can the continuous relative translation? Where is the instantaneous center of velocity? ... ... The traditional Euclidean geometry theory can’t explain these phenomenon, must use projective geometry theory to solve. The actual motion of the mechanism is disproof in Euclidean geometry principle limitation. This paper introduces the required

APA, Harvard, Vancouver, ISO, and other styles

37

Sun, B. W., L. T. Jiang, H. Pan, and H. Zhu. "Realization on Fractal Interpolation of Non-Rule Geometry." Key Engineering Materials 392-394 (October 2008): 523–25. http://dx.doi.org/10.4028/www.scientific.net/kem.392-394.523.

Full text

Abstract:

The traditional geometric modeling is generally described by means of Euclidean geometry, and objects for the geometric modeling are usually artificial work-pieces with smooth and regular contour. However in real world, there are so many irregular geometric objects(such as cavernous body, geological body, rough surface body and so on) with extremely complicated structure that the constructing method based on Euclidean geometry equation has been already helpless, while the process constructing method based on fractal geometry can. Taking rough surface body as examples, in order to explore a met

APA, Harvard, Vancouver, ISO, and other styles

38

Shillor, Irith. "Gifted Mathematicians Constructing Their Own Geometries — Changes in Knowledge and Attitudes." Gifted Education International 12, no. 2 (1997): 102–5. http://dx.doi.org/10.1177/026142949701200210.

Full text

Abstract:

A previous paper (1) looked at how gifted mathematicians in primary school respond to the study of Non-Euclidean geometries. In this study children in the secondary school are asked to construct their own Non-Euclidean Geometries. Using Taxi-Cab Geometry (2) as the starting point, children are asked to focus on the non-Euclidean elements of this geometry, and consider the differences between Euclidean and Non-Euclidean geometries. They are then asked to construct their own geometry, and consider the non-Euclidean elements within it. Young children find this task quite complex, but slightly old

APA, Harvard, Vancouver, ISO, and other styles

39

Sitenko, Yurii, and Volodymyr Gorkavenko. "Non-Euclidean Geometry, Nontrivial Topology and Quantum Vacuum Effects." Universe 4, no. 2 (2018): 23. http://dx.doi.org/10.3390/universe4020023.

Full text

APA, Harvard, Vancouver, ISO, and other styles

40

Kisil, Vladimir V. "MoebInv: C++ libraries for manipulations in non-Euclidean geometry." SoftwareX 11 (January 2020): 100385. http://dx.doi.org/10.1016/j.softx.2019.100385.

Full text

APA, Harvard, Vancouver, ISO, and other styles

41

Leichtweiss, K. "Curves of constant width in the non-euclidean geometry." Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg 75, no. 1 (2005): 257–84. http://dx.doi.org/10.1007/bf02942046.

Full text

APA, Harvard, Vancouver, ISO, and other styles

42

Leichtweiss, Kurt. "Linear combinations of convex hypersurfaces in non-Euclidean geometry." Beiträge zur Algebra und Geometrie / Contributions to Algebra and Geometry 53, no. 1 (2011): 77–88. http://dx.doi.org/10.1007/s13366-011-0080-4.

Full text

APA, Harvard, Vancouver, ISO, and other styles

43

Noro, Shuta, Masahiko Okumura, Satoshi Hongo, et al. "Langevin simulations of protoplasmic streaming in non-Euclidean geometry." Journal of Physics: Conference Series 1730, no. 1 (2021): 012037. http://dx.doi.org/10.1088/1742-6596/1730/1/012037.

Full text

APA, Harvard, Vancouver, ISO, and other styles

44

Loiola, Carlos Augusto Gomes, and Chrsitine Sertã Costa. "AS CÔNICAS NA GEOMETRIA DO TÁXI." Ciência e Natura 37 (August 7, 2015): 179. http://dx.doi.org/10.5902/2179460x14596.

Full text

Abstract:

http://dx.doi.org/10.5902/2179460X14596This paper aims to present conics when defined in a non-Euclidean geometry: the Taxicab geometry. The choice of this geometry was due to the simplicity of its definitions enabling diverse applications in Basic Education. It differs from Euclidean geometry by its metric and presents interesting and surprising results that enable the development of a more critical and meaningful learning.

APA, Harvard, Vancouver, ISO, and other styles

45

Jovanovic, Radmila. "Three views on epistemological status of geometry." Theoria, Beograd 55, no. 4 (2012): 21–38. http://dx.doi.org/10.2298/theo1204021j.

Full text

Abstract:

The subject of this paper is the epistemological status of geometry. This problem appeared in the beginning of XIX century, after the birth of non-euclidean geometries. This scientific discovery had a big influence on philosophy of science. We will deal with different systems of geometry, interpreted by means of physics. We will discuss several positions regarding their epistemological status. The key question is about the nature of geometry as a science- is there one real geometry of our world and which one? Both euclidean and non-euclidean geometries can be seen as to be in accordance with o

APA, Harvard, Vancouver, ISO, and other styles

46

Coxeter, H. S. M., and Jan van de Craats. "Philon lines in non-Euclidean planes." Journal of Geometry 48, no. 1-2 (1993): 26–55. http://dx.doi.org/10.1007/bf01226799.

Full text

APA, Harvard, Vancouver, ISO, and other styles

47

van den Brink, Johan S., and Jos J. Koonen. "Inherent Geometry Correction for Diffusion EPI Using the Reference Echoes as Navigators." Concepts in Magnetic Resonance Part B 2019 (May 26, 2019): 1–8. http://dx.doi.org/10.1155/2019/4139726.

Full text

Abstract:

Diffusion-weighted EPI has become an indispensable tool in body MRI. Geometric distortions due to field inhomogeneities are more prominent at large field–of–view and require correction for comparison with T2W TSE. Several known correction methods require acquisition of additional lengthy scans, which are difficult to apply in body imaging. We implement and evaluate a geometry correction method based on the already available non phase-encoded EPI reference data used for Nyquist ghost removal. The method is shown to provide accurate and robust global geometry correction in the absence of strong,

APA, Harvard, Vancouver, ISO, and other styles

48

WANAS, M. I. "THE ACCELERATING EXPANSION OF THE UNIVERSE AND TORSION ENERGY." International Journal of Modern Physics A 22, no. 31 (2007): 5709–16. http://dx.doi.org/10.1142/s0217751x07038943.

Full text

Abstract:

In the present work, it is shown that the problem of the accelerating expansion of the Universe can be directly solved by applying Einstein geometrization philosophy in a wider geometry. The geometric structure used to fulfil the aim of the work is a version of Absolute Parallelism geometry in which curvature and torsion are simultaneously non vanishing objects. It is shown that, while the energy corresponding to the curvature of space- time gives rise to an attractive force, the energy corresponding to the torsion indicates the presence of a repulsive force. A fine tuning parameter can be adj

APA, Harvard, Vancouver, ISO, and other styles

49

Tamm, Martin. "Minimizing Curvature in Euclidean and Lorentz Geometry." Symmetry 13, no. 8 (2021): 1433. http://dx.doi.org/10.3390/sym13081433.

Full text

Abstract:

In this paper, an interesting symmetry in Euclidean geometry, which is broken in Lorentz geometry, is studied. As it turns out, attempting to minimize the integral of the square of the scalar curvature leads to completely different results in these two cases. The main concern in this paper is about metrics in R3, which are close to being invariant under rotation. If we add a time-axis and let the metric start to rotate with time, it turns out that, in the case of (locally) Euclidean geometry, the (four-dimensional) scalar curvature will increase with the speed of rotation as expected. However,

APA, Harvard, Vancouver, ISO, and other styles

50

Berrett, Joshua, Virginia Marquardt, and Linda Dalrymple Henderson. "The Fourth Dimension and Non-Euclidean Geometry in Modern Art." Technology and Culture 26, no. 4 (1985): 879. http://dx.doi.org/10.2307/3105651.

Full text

APA, Harvard, Vancouver, ISO, and other styles

We offer discounts on all premium plans for authors whose works are included in thematic literature selections. Contact us to get a unique promo code!