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.

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 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.

ABOUT THE PROBLEM OF CLASSIFICATION OF THE CONCEPTS OF INFORMATICS STUDIED AT SECONDARY SCHOOL

2018 ◽  
pp. 4-7
Author(s):  
S. I. Zenko
Keyword(s):  
Secondary School ◽  
Foreign Language ◽  
Computer Science ◽  
Parts Of Speech ◽  
The Third ◽  
The Cross ◽  
Definition Of

The article raises the problem of classification of the concepts of computer science and informatics studied at secondary school. The efficiency of creation of techniques of training of pupils in these concepts depends on its solution. The author proposes to consider classifications of the concepts of school informatics from four positions: on the cross-subject basis, the content lines of the educational subject "Informatics", the logical and structural interrelations and interactions of the studied concepts, the etymology of foreign-language and translated words in the definition of the concepts of informatics. As a result of the first classification general and special concepts are allocated; the second classification — inter-content and intra-content concepts; the third classification — stable (steady), expanding, key and auxiliary concepts; the fourth classification — concepts-nouns, conceptsverbs, concepts-adjectives and concepts — combinations of parts of speech.

Suggested Notation for Ratios and Cross-Ratios

1912 ◽  
Vol 6 (98) ◽  
pp. 294-296
Author(s):  
Alfred Lodge
Keyword(s):  
Cross Ratio ◽  
The Cross

I wish to call attention to the value, for some purposes, ot the notation for the ratio ; and for the cross-ratio . For instance: in Menelaus’ theorem for the property of a transversal meeting the sides of a triangle ABC in the points P, Q, R, the first mentioned notation makes the property shine out very clearly The equation in the form is , which conspicuously separates the points on the transversal from the angular points of the triangle.

DEVELOPMENT OF THE APPENDIX FOR CHECKING RESIDUAL KNOWLEDGE OF STUDENTS

2021 ◽  
Author(s):  
Анна Юрьевна Белякова ◽  
Алена Алексеевна Самохвалова
Keyword(s):  
Quality Assessment ◽  
High Quality ◽  
Applied Informatics ◽  
Definition Of

В статье рассматривается определение остаточных знаний студентов. Для более эффективной и качественной оценки знаний по дисциплинам профессионального блока у студентов направления 09.03.03 - Прикладная информатика предлагается автоматизировать данный процесс. The article discusses the definition of residual knowledge of students. For a more efficient and high-quality assessment of knowledge in the disciplines of the professional block among students of the direction 09.03.03 - Applied Informatics, it is proposed to automate this process.

Equivariant Forms: Structure and Geometry

2013 ◽  
Vol 56 (3) ◽  
pp. 520-533 ◽  
Author(s):  
Abdelkrim Elbasraoui ◽  
Abdellah Sebbar
Keyword(s):  
Riemann Surface ◽  
Line Bundle ◽  
Modular Forms ◽  
Differential Forms ◽  
Cross Ratio ◽  
Canonical Line Bundle ◽  
The Cross

Abstract.In this paper we study the notion of equivariant forms introduced in the authors' previous works. In particular, we completely classify all the equivariant forms for a subgroup of SL2(ℤ) by means of the cross-ratio, weight 2 modular forms, quasimodular forms, as well as differential forms of a Riemann surface and sections of a canonical line bundle.

scholarly journals Angular Vectors in the Theory of Vectors

2017 ◽  
Vol 9 (5) ◽  
pp. 71
Author(s):  
Yevhen Mykolayovych Kharchenko
Keyword(s):  
Angular Velocity ◽  
Cross Product ◽  
Vector Form ◽  
Coordinate Vector ◽  
The Cross ◽  
Definition Of ◽  
Physical Quantities

The theory of angular vectors, which allows modelling of the properties of angular physical quantities, is considered. The meaning of the cross product of vectors was radically revised and changed. Formulas for finding torque and angular velocity in a coordinate-vector form with a correct mapping of their directions were deduced. Described definition of the inverse vector and its properties. The inversed vector allows us to perform vector division operations.

Sign in / Sign up

Export Citation Format

Share Document