scholarly journals The Third Dimention in a Landscape

Secreta Artis ◽  
2021 ◽  
pp. 74-82
Author(s):  
Daria Vladimirovna Fomicheva
Keyword(s):  
Land Surface ◽  
Dimensional Space ◽  
Three Dimensional ◽  
The Other ◽  
Landscape Painting ◽  
The Third ◽  
Soviet Art ◽  
Other Hand ◽  
Third Dimension ◽  
Three Dimensional Space

The present study examines the principles of conveying the third dimension in landscape painting. The author analyzes the recommendations provided in J. Littlejohns’ manual entitled “The Composition of a Landscape” [London, 1931]. J. Littlejohns describes four methods of showing depth in a landscape painting, each illustrated with pictorial composition schemes: 1) portrayal of long roads, which allows one to unveil the plasticity of the land surface; 2) creation of a “route” for the viewer by means of a well-thought-out arrangement of natural landforms; 3) introduction of vertically and horizontally flowing streams of water on different picture planes; 4) depiction of cloud shadows on a distinctly hilly landscape. The author of the article compares the schemes contained in the manual of J. Littlejohns with the works of G. G. Nissky, which enables readers to comprehend and reflect on the compositions of the masterpieces created by a prominent figure in Soviet art; on the other hand, Nissky’s landscape paintings open for a deeper understanding of the meaning and effectiveness of the methods proposed by J. Littlejohns. The outlined composition techniques are certainly relevant for contemporary artists (painters, graphic artists, animators, designers, etc.) as they make it possible to achieve the plastic expressiveness of a three-dimensional space in a twodimensional image.

Quaternäre Strontium-Kupfer(I)-Lanthanoid(III)-Selenide mit Cer und Praseodym: SrCuCeSe3 und SrCuPrSe3, ein ungleiches Geschwisterpaar / Quaternary Strontium Copper(I) Lanthanoid(III) Selenides with Cerium and Praseodymium: SrCuCeSe3 and SrCuPrSe3, Unequal Brother and Sister

2004 ◽  
Vol 59 (9) ◽  
pp. 985-991 ◽  
Author(s):  
Sabine Strobel ◽  
Thomas Schleid
Keyword(s):  
Single Crystals ◽  
Coordination Number ◽  
Unit Cell ◽  
Structural Relationship ◽  
The Other ◽  
Space Group ◽  
Lattice Constants ◽  
The Third ◽  
Other Hand ◽  
Third Dimension

Quaternary strontium copper(I) lanthanoid(III) selenides are formed by the oxidation of elemental strontium, copper and the corresponding lanthanoid with selenium. Orange to red needle-shaped single crystals of SrCuPrSe3 and SrCuCeSe3 have been synthesized by heating mixtures of Sr, Cu, Pr / Ce and Se with CsI as a flux in evacuated silica tubes to 800°C for 7 d. Both compounds crystallize orthorhombically in space group Pnma with four formula units per unit cell, but with unlike lattice constants (a = 1097.32(6), b = 416.51(2), c = 1349.64(8) pm for SrCuPrSe3 and a = 846.13(5), b = 421.69(2), c = 1663.42(9) pm for SrCuCeSe3) and therefore different structure types. The Pr3+ cations in SrCuPrSe3 are surrounded octahedrally by six Se2− anions forming chains of edge-sharing [PrSe6]9− octahedra that are joined by common vertices. Together with [CuSe4]7− tetrahedra they form [CuPrSe3]2− layers piled up parallel (001). Between those layers the Sr2+ cations are coordinated by seven Se2− anions in the shape of capped trigonal prisms linking the structure in the third dimension. On the other hand in SrCuCeSe3 the Ce3+ cations as well as the Sr2+ cations adopt a coordination number of seven. Since the bonding distances between cerium and selenium match with those of strontium and selenium the two crystallographically independent sites of these cations are occupied statistically by Ce3+ and Sr2+ with equal ratios. Nevertheless, there is a close structural relationship between SrCuPrSe3 and SrCuCeSe3. Similar to SrCuPrSe3 where Cu+ and Pr3+ cations together with Se2− anions form [CuPrSe3]2− layers parallel (001), the Cu+ cations and [(Ce1/Sr1)Se7]11.5− polyhedra in SrCuCeSe3 build strongly puckered layers which are connected by (Ce2)3+/(Sr2)2+ cations. The copper selenium part in both compounds correlates as well, with [CuSe4]7− tetrahedra linked by common vertices to form [CuSe3]5− chains running along [010].

scholarly journals A quadratic transformation of the three-dimensional space of all conics through two points of a projective plane

2009 ◽  
Vol 42 (3) ◽  
Author(s):  
Giorgio Donati
Keyword(s):  
Projective Space ◽  
Projective Plane ◽  
Dimensional Space ◽  
Three Dimensional ◽  
The Other ◽  
Quadratic Transformation ◽  
Pencil Of Conics ◽  
Dimensional Projective Space ◽  
Three Dimensional Space

AbstractUsing the Steiner’s method of projective generation of conics and its dual we define two projective mappings of a double contact pencil of conics into itself and we prove that one is the inverse of the other. We show that these projective mappings are induced by quadratic transformations of the three-dimensional projective space of all conics through two distinct points of a projective plane.

The Greek Neoplatonist Commentators on Aristotle

2018 ◽  
pp. 894-920
Author(s):  
Michael Griffin
Keyword(s):  
Dimensional Space ◽  
Three Dimensional ◽  
The Third ◽  
Natural Place ◽  
Biological Reproduction ◽  
Three Dimensional Space

Greek Neoplatonist commentators on Aristotle practiced philosophy and science in the third through seventh centuries ce by performing innovative exegesis of Aristotle’s works. To investigate nature is, for the commentators, to read with understanding Aristotle’s treatises in a set curriculum, with a commentary and teacher. Therefore, a mature philosopher would often prove to be a capable commentator, or interpreter, who could foster the reading of the primary texts with charity and objectivity, eliciting the author’s meaning through paraphrase, lemmatized discussion, and a critically evaluated doxography of the puzzles presented by the text. On the Neoplatonist account, the system expounded in Aristotle’s treatises is uniform and consistent, and is harmonious with the philosophy expounded in Plato’s dialogues. This chapter surveys concepts in the commentators including nature (phusis), biological reproduction, the five or four elements, dynamics and Philoponus’ impetus, natural place and three-dimensional space, modes of causation, teleology, time, cosmogony, and cosmology.

The Content of Descriptive Geometry Course For High Educational Institution’s In the Third Industrial Revolution’s Era

2018 ◽  
Vol 6 (3) ◽  
pp. 49-55 ◽  
Author(s):  
Юрий Поликарпов ◽  
Yuriy Polikarpov
Keyword(s):  
Industrial Revolution ◽  
Dimensional Space ◽  
Three Dimensional ◽  
Descriptive Geometry ◽  
Cad Systems ◽  
Course Content ◽  
The Third ◽  
Stage Of Development ◽  
High Educational ◽  
Three Dimensional Space

A brief journey into the history of industrial revolutions has been presented. It is noted that our society has entered the third industrial revolution’s era. In this regard, the main consequences of the third industrial revolution have been noted. The stages of development for design methods and the basic science providing the design process have been considered. The historical necessity and significance of Gaspar Monge’s descriptive geometry appearance has been considered as well. Modern products design approaches using CAD systems are described. It is stated that design has again returned to three-dimensional space, in fact prior to the Monge’s era, but at a new stage of development. The conclusion is drawn that, taking into account the realities and needs of modern production, it is necessary to modernize the descriptive geometry course for technical high educational institutions. The author's suggestions on course content changing are presented related to extension of one sections and reducing of another ones, taking into account the fact that in real design practice the designer solves geometric problems in three-dimensional space, rather than in a complex drawing. It is noted that in connection with the extensive use of CAD systems, the design stages and the composition of design documentation developed at each stage are changed. Such concepts as "electronic model" and "electronic document" have appeared and are widely used, that is confirmed by adoption of new USDD standards. In such a case the role and significance of some types of drawings may change in the near future, since modern CAD systems allow transfer to production not 2D drawings, but electronic models and product drawings.

scholarly journals УНІФІКАЦІЯ ТА ГАРМОНІЗАЦІЯ ІНФОРМАЦІЇ В АРТРОЛОГІЇ ДЛЯ СТВОРЕННЯ СИСТЕМИ ПРОГНОЗУВАННЯ РЕЗУЛЬТАТІВ ОПЕРАТИВНОГО ВТРУЧАННЯ

2014 ◽  
Author(s):  
M. M. Ryhan
Keyword(s):  
Dimensional Space ◽  
Three Dimensional ◽  
Automated Diagnosis ◽  
Information Base ◽  
The Third ◽  
Class 1 ◽  
The Creation ◽  
Three Dimensional Space

<p class="1">This article discusses the possibility of establishing an information base for automated diagnosis and predicting the outcomes of surgery in gonarthrosis. The unified information document provides the creation of three-dimensional space for decision­making system. Recorded on the same plane the primary symptoms of the disease, the second - the results of pre­processing the information obtained using internationally accepted questionnaires. Finally, the third presents the results of “voting” for final conclusions decision.</p>

scholarly journals Constructive Geometric Models with Imaginary Objects

2020 ◽  
pp. short27-1-short27-9
Author(s):  
Denis Voloshinov ◽  
Alexandra Solovjeva
Keyword(s):  
Projective Geometry ◽  
Dimensional Space ◽  
Three Dimensional ◽  
Higher Order ◽  
Second Order ◽  
The Other ◽  
Significant Obstacle ◽  
The Relationship ◽  
Planar Drawing ◽  
Three Dimensional Space

The article is devoted to the consideration of a number of theoretical questions of projective geometry related to specifying and displaying imaginary objects, especially, conics. The lack of development of appropriate constructive schemes is a significant obstacle to the study of quadratic images in three-dimensional space and spaces of higher order. The relationship between the two circles, established by the inversion operation with respect to the other two circles, in particular, one of which is imaginary, allows obtain a simple and effective method for indirect setting of imaginary circles in a planar drawing. The application of the collinear transformation to circles with an imaginary radius also makes it possible to obtain unified algorithms for specifying and controlling imaginary conics along with usual real second-order curves. As a result, it allows eliminate exceptional situations that arise while solving problems with quadratic images in spaces of second and higher order.

scholarly journals Minimum action principle and shape dynamics

2017 ◽  
Vol 14 (130) ◽  
pp. 20170031 ◽  
Author(s):  
Patrice Koehl
Keyword(s):  
Elastic Energy ◽  
Dimensional Space ◽  
Shape Recognition ◽  
Three Dimensional ◽  
The Other ◽  
Success Rates ◽  
Evolutionary Patterns ◽  
The Cost ◽  
Better Than ◽  
Three Dimensional Space

In this paper, we propose a new method for computing a distance between two shapes embedded in three-dimensional space. Instead of comparing directly the geometric properties of the two shapes, we measure the cost of deforming one of the two shapes into the other. The deformation is computed as the geodesic between the two shapes in the space of shapes. The geodesic is found as a minimizer of the Onsager–Machlup action, based on an elastic energy for shapes that we define. Its length is set to be the integral of the action along that path; it defines an intrinsic quasi-metric on the space of shapes. We illustrate applications of our method to geometric morphometrics using three datasets representing bones and teeth of primates. Experiments on these datasets show that the variational quasi-metric we have introduced performs remarkably well both in shape recognition and in identifying evolutionary patterns, with success rates similar to, and in some cases better than, those obtained by expert observers.

Geometry in three dimensions over GF (3)

1954 ◽  
Vol 222 (1149) ◽  
pp. 262-286 ◽  
Keyword(s):  
Dimensional Space ◽  
Three Dimensional ◽  
Galois Field ◽  
The Other ◽  
Three Dimensions ◽  
Common Vertex ◽  
Line Geometry ◽  
Fundamental Properties ◽  
The Common ◽  
Three Dimensional Space

The object of this paper is to give some account of the geometry of the three-dimensional space S wherein the co-ordinates belong to a Galois field K of 3 marks. A description of the fundamental properties of quadrics is sufficiently long for one paper, and so an account of the line geometry is deferred. The early paragraphs (§§ 1 to 4) are necessarily concerned with geometry on a line or in a plane. A line consists of 4 points; these are self-projective under all 4! permutations. A plane consists of 13 points and has the same number, 234, of triangles, quadrangles, quadri-laterals and non-singular conics. A diagram is helpful, especially when we consider sections by planes in S . The space S has 40 points. Non-singular quadrics are of two kinds: either ruled, when we call them hyperboloids, or non-ruled, when we call them ellipsoids. A hyperboloid H consists of 16 points and has a pair of reguli; the 24 points of S not on H are the vertices of 6 tetra-hedra that form two allied desmic triads. The ellipsoid F is introduced in § 12; it consists of 10 points, the other 30 points of S being separated into two batches of 15 between which there is a symmetrical (3, 3) correspondence. Either batch can be arranged as a set of 6 pentagons, each of the 15 points being the common vertex of 2 of these. The pentagons of either set have all their edges tangents of F and, with their polar pentahedra, have significant properties and interrelations. By no means their least important attribute is that they afford, with F , so apposite a domain of operation for the simple group of order 360. In §§ 23 to 26 are described the operations of the group in this setting. Thereafter the 36 separations of the 10 points of F into complementary pentads are discussed, no 4 of either pentad being coplanar. During the work constructions for an ellipsoid are encountered; one is in § 16, another in § 30.

On Pedal Quadrics in Non-Euclidean Hyperspace

1925 ◽  
Vol 22 (5) ◽  
pp. 751-758
Author(s):  
J. P. Gabbatt
Keyword(s):  
Orthogonal Projection ◽  
Euclidean Plane ◽  
Dimensional Space ◽  
Three Dimensional ◽  
The Other ◽  
Elementary Geometry ◽  
Orthogonal Projections ◽  
Point Pair ◽  
Straight Line ◽  
Three Dimensional Space

1. The following are well-known theorems of elementary geometry: Given any euclidean plane triangle, A0 A1 A2, and any pair of points, X, Y, isogonally conjugate q. A0 A1 A2; then the orthogonal projections of X, Y on the sides of A0 A1 A2 lie on a circle, the pedal circle of the point-pair. If either of the points X,- Y describe a (straight) line, m, then the other describes a conic circumscribing A0 A1 A2, and the pedal circle remains orthogonal to a fixed circle, J; thus the pedal circles in question are members of an ∞2 linear system of circles of which the circle J and the line at infinity constitute the Jacobian. In particular, if the line m meet Aj Ak at Lt (i, j, k = 0, 1, 2), then the circles on Ai Li as diameter, which are the pedal circles of the point-pairs Ai, Li, are coaxial; the remaining circles of the coaxial system being the director circles of the conics, inscribed in the triangle A0 A1 A2, which touch the line m. If Mi denote the orthogonal projection on m of Ai, and Ni the orthogonal projection on Aj Ak of Mi, then the three lines Mi Ni meet at a point (Neuberg's theorem), viz. the centre of the circle J. Analogues for three-dimensional space of most of these theorems are also known ‖.

scholarly journals Nontrivial Isometric Embeddings for Flat Spaces

Universe ◽  
2021 ◽  
Vol 7 (12) ◽  
pp. 477
Author(s):  
Sergey Paston ◽  
Taisiia Zaitseva
Keyword(s):  
Minkowski Space ◽  
Dimensional Space ◽  
Equations Of Motion ◽  
Three Dimensional ◽  
Ambient Space ◽  
The Other ◽  
Field Limit ◽  
Isometric Embeddings ◽  
Weak Gravitational Field ◽  
Three Dimensional Space

Nontrivial isometric embeddings for flat metrics (i.e., those which are not just planes in the ambient space) can serve as useful tools in the description of gravity in the embedding gravity approach. Such embeddings can additionally be required to have the same symmetry as the metric. On the other hand, it is possible to require the embedding to be unfolded so that the surface in the ambient space would occupy the subspace of the maximum possible dimension. In the weak gravitational field limit, such a requirement together with a large enough dimension of the ambient space makes embedding gravity equivalent to general relativity, while at lower dimensions it guarantees the linearizability of the equations of motion. We discuss symmetric embeddings for the metrics of flat Euclidean three-dimensional space and Minkowski space. We propose the method of sequential surface deformations for the construction of unfolded embeddings. We use it to construct such embeddings of flat Euclidean three-dimensional space and Minkowski space, which can be used to analyze the equations of motion of embedding gravity.

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