Three Vertex and Parallelograms in the Affine Plane: Similarity and Addition Abelian Groups of Similarly <i>n</i>-Vertexes in the Desargues Affine Plane

Orgest Zaka

doi:doi:10.11648/j.mma.20180301.12

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Three Vertex and Parallelograms in the Affine Plane: Similarity and Addition Abelian Groups of Similarly n-Vertexes in the Desargues Affine Plane

Orgest Zaka

Published in Mathematical Modelling and Applications (Volume 3, Issue 1)

Received: 14 May 2017 Accepted: 18 December 2017 Published: 8 January 2018

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Abstract

In this article will do a’ concept generalization n-gon. By renouncing the metrics in much axiomatic geometry, the need arises for a new label to this concept. In this paper will use the meaning of n-vertexes. As you know in affine and projective plane simply set of points, blocks and incidence relation, which is argued in [1], [2], [3]. In this paper will focus on affine plane. Will describe the meaning of the similarity n-vertexes. Will determine the addition of similar three-vertexes in Desargues affine plane, which is argued in [1], [2], [3], and show that this set of three-vertexes forms an commutative group associated with additions of three-vertexes. At the end of this paperare making a generalization of the meeting of similarity n-vertexes in Desargues affine plane, also here it turns out to have a commutative group, associated with additions of similarity n-vertexes.

Published in	Mathematical Modelling and Applications (Volume 3, Issue 1)
DOI	10.11648/j.mma.20180301.12
Page(s)	9-15
Creative Commons	This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.
Copyright	Copyright © The Author(s), 2018. Published by Science Publishing Group

Keywords

n-vertexes, Desargues Affine Plane, Similarity of n-Vertexes, Abelian Group

References

[1]	Dr. Orgest ZAKA, Prof. Dr. Kristaq FILIPI, (2017) "An Application of Finite Affine Plane of Order n, in an Experiment Planning", International Journal of Science and Research (IJSR), http://www.ijsrpublications.com/ijsr.net/archive/v6i6/v6i6.php, Volume 6 Issue 6, June 2017, 1744 - 1747, DOI: 10.21275/ART20174592
[2]	Zaka, O., Flipi, K. (2016). One construction of an affine plane over a corps. Journal of Advances in Mathematics, Council for Innovative Research. Volume 12 Number 5. 6200-6206.
[3]	Zaka, O., Filipi, K. (2016). “The transform of a line of Desargues affine plane in an additive group of its points”, International Journal of Current Research, 8, (07), 34983-34990.
[4]	FRANCIS BORCEUX (2014). An Axiomatic Approach to Geometry&An Algebraic Approach to Geometry (Geometric Trilogy I& Geometric Trilogy II). Springer International Publishing Switzerland.
[5]	Grrillet, P. A (2007). Abstract Algebra(Second Edition). Graduate Texts in Mathematics v242. ISBN-13: 978-0-387-71567-4Springer Science + Business Media, LLC (Grrillet, P. A, et al, 2007).
[6]	Hilbert. D, Vossen. S. C (1990). Geometry And The Imagination. Chelsea Publishing Company.
[7]	Buenkenhout, F, (Editors)(1995). HANDBOOK OF INCIDENCE GEOMETRY. Elsevier Science B. V. ISBN: 0 444 88355 X.
[8]	Hungerford, TH. W (1974). Algebra (Graduate Text in Mathematics vol 73). Springer-Verlag New York, Inc. ISBN 0-387-90518-9.
[9]	Lang, S (2002). Abstract Algebra (Third Edition). Springer-verlag new york, inc. ISBN 0-387-95385-X.
[10]	Ueberberg, Johannes (2011), Foundations of Incidence Geometry, Springer Monographs in Mathematics, Springer, doi:10.1007/978-3-642-20972-7, ISBN 978-3-642-26960-8.

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APA Style

Orgest Zaka. (2018). Three Vertex and Parallelograms in the Affine Plane: Similarity and Addition Abelian Groups of Similarly n-Vertexes in the Desargues Affine Plane. Mathematical Modelling and Applications, 3(1), 9-15. https://doi.org/10.11648/j.mma.20180301.12

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ACS Style

Orgest Zaka. Three Vertex and Parallelograms in the Affine Plane: Similarity and Addition Abelian Groups of Similarly n-Vertexes in the Desargues Affine Plane. Math. Model. Appl. 2018, 3(1), 9-15. doi: 10.11648/j.mma.20180301.12

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AMA Style

Orgest Zaka. Three Vertex and Parallelograms in the Affine Plane: Similarity and Addition Abelian Groups of Similarly n-Vertexes in the Desargues Affine Plane. Math Model Appl. 2018;3(1):9-15. doi: 10.11648/j.mma.20180301.12

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@article{10.11648/j.mma.20180301.12,
  author = {Orgest Zaka},
  title = {Three Vertex and Parallelograms in the Affine Plane: Similarity and Addition Abelian Groups of Similarly n-Vertexes in the Desargues Affine Plane},
  journal = {Mathematical Modelling and Applications},
  volume = {3},
  number = {1},
  pages = {9-15},
  doi = {10.11648/j.mma.20180301.12},
  url = {https://doi.org/10.11648/j.mma.20180301.12},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.mma.20180301.12},
  abstract = {In this article will do a’ concept generalization n-gon. By renouncing the metrics in much axiomatic geometry, the need arises for a new label to this concept. In this paper will use the meaning of n-vertexes. As you know in affine and projective plane simply set of points, blocks and incidence relation, which is argued in [1], [2], [3]. In this paper will focus on affine plane. Will describe the meaning of the similarity n-vertexes. Will determine the addition of similar three-vertexes in Desargues affine plane, which is argued in [1], [2], [3], and show that this set of three-vertexes forms an commutative group associated with additions of three-vertexes. At the end of this paperare making a generalization of the meeting of similarity n-vertexes in Desargues affine plane, also here it turns out to have a commutative group, associated with additions of similarity n-vertexes.},
 year = {2018}
}

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TY  - JOUR
T1  - Three Vertex and Parallelograms in the Affine Plane: Similarity and Addition Abelian Groups of Similarly n-Vertexes in the Desargues Affine Plane
AU  - Orgest Zaka
Y1  - 2018/01/08
PY  - 2018
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DO  - 10.11648/j.mma.20180301.12
T2  - Mathematical Modelling and Applications
JF  - Mathematical Modelling and Applications
JO  - Mathematical Modelling and Applications
SP  - 9
EP  - 15
PB  - Science Publishing Group
SN  - 2575-1794
UR  - https://doi.org/10.11648/j.mma.20180301.12
AB  - In this article will do a’ concept generalization n-gon. By renouncing the metrics in much axiomatic geometry, the need arises for a new label to this concept. In this paper will use the meaning of n-vertexes. As you know in affine and projective plane simply set of points, blocks and incidence relation, which is argued in [1], [2], [3]. In this paper will focus on affine plane. Will describe the meaning of the similarity n-vertexes. Will determine the addition of similar three-vertexes in Desargues affine plane, which is argued in [1], [2], [3], and show that this set of three-vertexes forms an commutative group associated with additions of three-vertexes. At the end of this paperare making a generalization of the meeting of similarity n-vertexes in Desargues affine plane, also here it turns out to have a commutative group, associated with additions of similarity n-vertexes.
VL  - 3
IS  - 1
ER  -

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Author Information

Orgest Zaka

Department of Mathematics, Faculty of Technical Science, University “Ismail QEMALI”of Vlora, Vlora, Albania

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Plain Text BibTeX RIS

APA Style

Orgest Zaka. (2018). Three Vertex and Parallelograms in the Affine Plane: Similarity and Addition Abelian Groups of Similarly n-Vertexes in the Desargues Affine Plane. Mathematical Modelling and Applications, 3(1), 9-15. https://doi.org/10.11648/j.mma.20180301.12

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ACS Style

Orgest Zaka. Three Vertex and Parallelograms in the Affine Plane: Similarity and Addition Abelian Groups of Similarly n-Vertexes in the Desargues Affine Plane. Math. Model. Appl. 2018, 3(1), 9-15. doi: 10.11648/j.mma.20180301.12

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AMA Style

Orgest Zaka. Three Vertex and Parallelograms in the Affine Plane: Similarity and Addition Abelian Groups of Similarly n-Vertexes in the Desargues Affine Plane. Math Model Appl. 2018;3(1):9-15. doi: 10.11648/j.mma.20180301.12

Copy | Download

@article{10.11648/j.mma.20180301.12,
  author = {Orgest Zaka},
  title = {Three Vertex and Parallelograms in the Affine Plane: Similarity and Addition Abelian Groups of Similarly n-Vertexes in the Desargues Affine Plane},
  journal = {Mathematical Modelling and Applications},
  volume = {3},
  number = {1},
  pages = {9-15},
  doi = {10.11648/j.mma.20180301.12},
  url = {https://doi.org/10.11648/j.mma.20180301.12},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.mma.20180301.12},
  abstract = {In this article will do a’ concept generalization n-gon. By renouncing the metrics in much axiomatic geometry, the need arises for a new label to this concept. In this paper will use the meaning of n-vertexes. As you know in affine and projective plane simply set of points, blocks and incidence relation, which is argued in [1], [2], [3]. In this paper will focus on affine plane. Will describe the meaning of the similarity n-vertexes. Will determine the addition of similar three-vertexes in Desargues affine plane, which is argued in [1], [2], [3], and show that this set of three-vertexes forms an commutative group associated with additions of three-vertexes. At the end of this paperare making a generalization of the meeting of similarity n-vertexes in Desargues affine plane, also here it turns out to have a commutative group, associated with additions of similarity n-vertexes.},
 year = {2018}
}

Copy | Download

TY  - JOUR
T1  - Three Vertex and Parallelograms in the Affine Plane: Similarity and Addition Abelian Groups of Similarly n-Vertexes in the Desargues Affine Plane
AU  - Orgest Zaka
Y1  - 2018/01/08
PY  - 2018
N1  - https://doi.org/10.11648/j.mma.20180301.12
DO  - 10.11648/j.mma.20180301.12
T2  - Mathematical Modelling and Applications
JF  - Mathematical Modelling and Applications
JO  - Mathematical Modelling and Applications
SP  - 9
EP  - 15
PB  - Science Publishing Group
SN  - 2575-1794
UR  - https://doi.org/10.11648/j.mma.20180301.12
AB  - In this article will do a’ concept generalization n-gon. By renouncing the metrics in much axiomatic geometry, the need arises for a new label to this concept. In this paper will use the meaning of n-vertexes. As you know in affine and projective plane simply set of points, blocks and incidence relation, which is argued in [1], [2], [3]. In this paper will focus on affine plane. Will describe the meaning of the similarity n-vertexes. Will determine the addition of similar three-vertexes in Desargues affine plane, which is argued in [1], [2], [3], and show that this set of three-vertexes forms an commutative group associated with additions of three-vertexes. At the end of this paperare making a generalization of the meeting of similarity n-vertexes in Desargues affine plane, also here it turns out to have a commutative group, associated with additions of similarity n-vertexes.
VL  - 3
IS  - 1
ER  -

Copy | Download