scholarly journals KONSISTENSI AKSIOMA-AKSIOMA TERHADAP ISTILAH-ISTILAH TAKTERDEFINISI GEOMETRI HIPERBOLIK PADA MODEL PIRINGAN POINCARE

EDUPEDIA ◽  
2018 ◽  
Vol 2 (2) ◽  
pp. 161
Author(s):  
Febriyana Putra Pratama ◽  
Julan Hernadi
Keyword(s):  
Half Plane ◽  
Hyperbolic Geometry ◽  
Euclidean Geometry ◽  
Cross Ratio ◽  
Literature Study ◽  
Disk Model ◽  
Non Euclidean Geometry ◽  
The Cross ◽  
Definition Of ◽  
Poincaré Disk

This research aims to know the interpretation the undefined terms on Hyperbolic geometry and it’s consistence with respect to own axioms of Poincare disk model. This research is a literature study that discusses about Hyperbolic geometry. This study refers to books of Foundation of Geometry second edition by Gerard A. Venema (2012), Euclidean and Non Euclidean Geometry (Development and History)  by Greenberg (1994), Geometry : Euclid and Beyond by Hartshorne (2000) and Euclidean Geometry: A First Course by M. Solomonovich (2010). The steps taken in the study are: (1) reviewing the various references on the topic of Hyperbolic geometry. (2) representing the definitions and theorems on which the Hyperbolic geometry is based. (3) prepare all materials that have been collected in coherence to facilitate the reader in understanding it. This research succeeded in interpret the undefined terms of Hyperbolic geometry on Poincare disk model. The point is coincide point in the Euclid on circle . Then the point onl γ is not an Euclid point. That point interprets the point on infinity. Lines are categoried in two types. The first type is any open diameters of   . The second type is any open arcs of circle. Half-plane in Poincare disk model is formed by Poincare line which divides Poincare field into two parts. The angle in this model is interpreted the same as the angle in Euclid geometry. The distance is interpreted in Poincare disk model defined by the cross-ratio as follows. The definition of distance from  to  is , where  is cross-ratio defined by  . Finally the study also is able to show that axioms of Hyperbolic geometry on the Poincare disk model consistent with respect to associated undefined terms.

The Nature of Arguments Provided by College Geometry Students With Access to Technology While Solving Problems

2010 ◽  
Vol 41 (4) ◽  
pp. 324-350 ◽  
Author(s):  
Karen F. Hollebrands ◽  
AnnaMarie Conner ◽  
Ryan C. Smith
Keyword(s):  
Hyperbolic Geometry ◽  
Euclidean Geometry ◽  
Dynamic Geometry ◽  
Disk Model ◽  
Geometric Objects ◽  
Access To Technology ◽  
Poincaré Disk ◽  
Support Students

Prior research on students' uses of technology in the context of Euclidean geometry has suggested it can be used to support students' development of formal justifications and proofs. This study examined the ways in which students used a dynamic geometry tool, NonEuclid, as they constructed arguments about geometric objects and relationships in hyperbolic geometry. Eight students enrolled in a college geometry course participated in a task-based interview that was focused on examining properties of quadrilaterals in the Poincaré disk model. Toulmin's argumentation model was used to analyze the nature of the arguments students provided when they had access to technology while solving the problems. Three themes related to the structure of students' arguments were identified. These involved the explicitness of warrants provided, uses of technology, and types of tasks.

On the Medians of a Triangle in Hyperbolic Geometry

1958 ◽  
Vol 10 ◽  
pp. 502-506 ◽  
Author(s):  
O. Bottema
Keyword(s):  
Hyperbolic Geometry ◽  
Euclidean Geometry ◽  
Common Point ◽  
Non Euclidean Geometry ◽  
Image Position

In non-Euclidean geometry the three medians of a triangle A 1A2A3 (each joining a vertex A i with the internal midpoint G i of the opposite side) are concurrent; their common point is the centroid G. But the Euclidean theorem ' which depends on similarity, does not hold.

scholarly journals The Topological Reading of Ambiances in the Built Environment: The New Methodology for the Analysis of the Luminous Ambiance in the Museum Space

2019 ◽  
Vol 64 ◽  
pp. 03004
Author(s):  
Selma Saraoui ◽  
Azeddine Belakehal ◽  
Abdelghani Attar ◽  
Amar Bennadji
Keyword(s):  
Sequential Analysis ◽  
Euclidean Geometry ◽  
Essential Element ◽  
Analysis Model ◽  
Architectural Space ◽  
Spatial Features ◽  
Non Euclidean Geometry ◽  
Metric Dimensions ◽  
Definition Of ◽  
Shed Light

Daylight is currently at the centre of discourse on architectural space. The definition of architectural space takes essence from Euclidean geometry related to metric dimensions. The present study is an attempt to shed light on topology which is a non-Euclidean geometry. It can support non-metric components of space such as light to define architectural space. A corpus of six European museums has been chosen to study the immaterial or material relationships between form and daylight, since light is an essential element for the success of the exhibition. It also seeks to highlight discontinuity reports, and to confirm their existence through their software visualizations Therefore, the current study has taken into account an analysis model based on the notions of "route" and "sequence". The contemporary architectural project focused on taking into account human postures, both physical and psychological, within the architectural space. The results obtained show that light can release other spatial features for the museum space that can be highlighted by visualization with sequential analysis.

scholarly journals An Unsupervised Learning Method for Attributed Network Based on Non-Euclidean Geometry

Symmetry ◽  
2021 ◽  
Vol 13 (5) ◽  
pp. 905
Author(s):  
Wei Wu ◽  
Guangmin Hu ◽  
Fucai Yu
Keyword(s):  
Ricci Curvature ◽  
Hyperbolic Geometry ◽  
Euclidean Geometry ◽  
Structural Information ◽  
Information Aggregation ◽  
Network Embedding ◽  
Heterogeneous Information ◽  
Non Euclidean Geometry ◽  
Attributed Network ◽  
Attribute Information

Many real-world networks can be modeled as attributed networks, where nodes are affiliated with attributes. When we implement attributed network embedding, we need to face two types of heterogeneous information, namely, structural information and attribute information. The structural information of undirected networks is usually expressed as a symmetric adjacency matrix. Network embedding learning is to utilize the above information to learn the vector representations of nodes in the network. How to integrate these two types of heterogeneous information to improve the performance of network embedding is a challenge. Most of the current approaches embed the networks in Euclidean spaces, but the networks themselves are non-Euclidean. As a consequence, the geometric differences between the embedded space and the underlying space of the network will affect the performance of the network embedding. According to the non-Euclidean geometry of networks, this paper proposes an attributed network embedding framework based on hyperbolic geometry and the Ricci curvature, namely, RHAE. Our method consists of two modules: (1) the first module is an autoencoder module in which each layer is provided with a network information aggregation layer based on the Ricci curvature and an embedding layer based on hyperbolic geometry; (2) the second module is a skip-gram module in which the random walk is based on the Ricci curvature. These two modules are based on non-Euclidean geometry, but they fuse the topology information and attribute information in the network from different angles. Experimental results on some benchmark datasets show that our approach outperforms the baselines.

Graphic-Analytical Researches of Involution

2017 ◽  
Vol 5 (1) ◽  
pp. 3-11 ◽  
Author(s):  
Графский ◽  
O. Grafskiy ◽  
Усманов ◽  
A. Usmanov ◽  
Холодилов ◽  
...  
Keyword(s):  
Cross Ratio ◽  
Rectangular Coordinate System ◽  
Projective Transformations ◽  
Coordinate Axis ◽  
Graphic Editor ◽  
Applied Informatics ◽  
The Cross ◽  
Pass Through ◽  
Definition Of ◽  
Straight Lines

Known projective transformations, namely their private types such as harmonism and involution are considered. It is known that projective transformations are collinear, at their performance the order, the cross ratio of fours of elements (on a straight line — the cross ratio of four points, in a bunch of straight lines — the cross ratio of this bunch’s four straight lines, this property (invariant) is similarly preserved for a bunch of planes, i.e. in considering of first step forms) is preserved. At a constructive approach to such transformations there are some ways for definition of position for corresponding elements which students use when studying discipline "Affine and projective geometry" on preparation profiles 09.03.01 — “CAD Systems" and 09.03.03 — “Applied Informatics in Design”. The received constructions are checked by analytical calculations, proceeding from known dependences for harmonism and involutions. In such a case results both for a range of points, and for a bunch of straight lines which pass through these points are analytically compared. The provided computational and graphic work contains three sections: prospects, harmonism and involution, and is carried out by students on individual options with application of the graphic editor Microsoft Visio or the graphic package CO MPAS voluntary. In the present paper some constructions in definition of corresponding points in elliptic and hyperbolic involution are considered, some of these constructions are published for the first time. Besides, a proposition has been formulated: in a rectangular coordinate system the work for coordinates of two points related to a circle intersection with one coordinate axis is equal to the product for coordinates of two other points related to this circle intersection with the other coordinate axis. This proposition is fairly for imaginary points of circle intersection with coordinate axes as well.

The Use of the Cross-Ratio in Aetiological Surveys

1975 ◽  
Vol 12 (S1) ◽  
pp. 349-355
Author(s):  
P. Armitage
Keyword(s):  
Relative Risk ◽  
Case Control ◽  
Cross Ratio ◽  
Matched Pairs ◽  
Case Control Studies ◽  
Standard Methods ◽  
Relative Risks ◽  
The Cross ◽  
Definition Of ◽  
Measure Of Association

The use of the cross-ratio as a measure of association in a 2×2 table is closely related to Bartlett's (1935) definition of interaction in a higher-order table. Inference about aetiological associations from case-control studies is most naturally done in terms of the cross-ratio, as a measure of relative risk. Standard methods of statistical analysis, for the comparison and combination of relative risks and for matched pairs, are reviewed, and some new results noted.

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