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Mathematics
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New Insights into Geometrical Transformations
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New Insights into Geometrical Transformations

A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "Algebra, Geometry and Topology".

Deadline for manuscript submissions: closed (31 May 2021) | Viewed by 9008

Special Issue Editors

Prof. Dr. Joaquin Giménez

E-Mail Website
Guest Editor
University of Barcelona, Faculty of Teacher Education, Campus Mundet Passeig de la Vall d’Hebron 171, 08035 Barcelona, Spain
Interests: mathematics education; geometry education; teacher training; culture of mathematic education; mathematics reasoning; mathematics activities
Prof. Dr. Xhevdet Thaqi

E-Mail Website
Guest Editor
Public University "Kadri Zeka", Faculty of Applied Sciences, str. "Z. Shemsiu", n.n. 60000 Gjilan, Kosovo
Interests: geometry; geometrical transformations; equivalent geometrical transformations; isoperimetrical transformations; mathematics education; applied geometrical transformations

Special Issue Information

Dear Colleagues,

The discussion about geometrical transformation is usually associated with a way of re-elaborating answers to the big question about what geometry is, where answers have been given by Hilbert, Klein, Yaglom, and others. From the works of Hoffer, Hiebert et al., we identify six elements to consider in the analysis of geometrical transformation: The geometrical transformation as an object, terminology and types of geometrical transformations, relationships and hierarchy in the notion of transformations, transformations as process or change, communication and reasoning with geometrical transformations, and cultural and historical elements in geometrical transformations.

The identification of each of these categories is based on the indicators that must be obtained in the various investigations that we seek to present in this Special Issue.

This process of generating indicators allows us to establish a stable analysis scheme that is finally the one we are trying to present to the scientific community of the Mathematics journal of MDPI. We invite researchers and scientists to contribute with the conceptual and empirical manuscripts in the Special Issue that should represent significant contributions in which different research perspectives of analysis should be adopted developing specific topics, such as New Insights into Geometrical Transformations.

This Special Issue focuses on a multidisciplinary research approach, in which several research areas have been involved: mathematical logic and mathematical foundation; algebraic geometry; geometry; computational mathematics; combinatorial mathematics; fuzzy mathematics; applied mathematics; and other areas of mathematical sciences.

Prof. Dr. Joaquin Giménez
Prof. Dr. Xhevdet Thaqi
Guest Editors

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Mathematics is an international peer-reviewed open access semimonthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2600 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • Geometrical transformations
  • Terminology and types of geometrical transformations
  • Relationships and hierarchy in the notion of transformations
  • Transformations as process or change
  • Communication and reasoning with geometrical transformations
  • Cultural and historical elements in geometrical transformations
  • Equivalent geometrical transformations
  • Interactive geometry software

Published Papers (3 papers)

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Research

15 pages, 2058 KiB  
Article
The Structure of n Harmonic Points and Generalization of Desargues’ Theorems
by Xhevdet Thaqi and Ekrem Aljimi
Mathematics 2021, 9(9), 1018; https://doi.org/10.3390/math9091018 - 30 Apr 2021
Cited by 1 | Viewed by 2594
Abstract
In this paper, we consider the relation of more than four harmonic points in a line. For this purpose, starting from the dependence of the harmonic points, Desargues’ theorems, and perspectivity, we note that it is necessary to conduct a generalization of the [...] Read more.
In this paper, we consider the relation of more than four harmonic points in a line. For this purpose, starting from the dependence of the harmonic points, Desargues’ theorems, and perspectivity, we note that it is necessary to conduct a generalization of the Desargues’ theorems for projective complete n-points, which are used to implement the definition of the generalization of harmonic points. We present new findings regarding the uniquely determined and constructed sets of H-points and their structure. The well-known fourth harmonic points represent the special case (n = 4) of the sets of H-points of rank 2, which is indicated by P42. Full article
(This article belongs to the Special Issue New Insights into Geometrical Transformations)
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30 pages, 4804 KiB  
Article
Networked Analysis of a Teaching Unit for Primary School Symmetries in the Form of an E-Book
by Angel Gutiérrez, Adela Jaime and Pablo Gutiérrez
Mathematics 2021, 9(8), 832; https://doi.org/10.3390/math9080832 - 11 Apr 2021
Cited by 3 | Viewed by 2820
Abstract
In mathematics education, technology offers many opportunities to enrich curricular contents. Plane symmetries is a topic often skipped by primary teachers. However, it is important and may be worked in attractive ways in dynamic geometry software environments. In any regular classroom there are [...] Read more.
In mathematics education, technology offers many opportunities to enrich curricular contents. Plane symmetries is a topic often skipped by primary teachers. However, it is important and may be worked in attractive ways in dynamic geometry software environments. In any regular classroom there are students with different levels of mathematical attainment, some needing easy tasks while others, particularly mathematically-gifted students, need challenging problems. We present a teaching unit for plane symmetries, adequate for upper primary school grades, implemented in a fully interactive electronic book, with most activities solved in GeoGebra apps. The book allows student to choose which itinerary to follow and attention is paid to different levels of students’ mathematical attainment. The research objective of the paper is to make a networked analysis of the structure and contents of the teaching unit based on the Van Hiele levels of mathematical reasoning and the levels of cognitive demand in mathematical problem solving. The analysis shows the interest of networking both theories, the suitability of the teaching unit, as the Van Hiele levels and the cognitive demand of the activities increases, and its usefulness to fit the needs of each student, from low attainers to mathematically-gifted students. Full article
(This article belongs to the Special Issue New Insights into Geometrical Transformations)
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26 pages, 364 KiB  
Article
Blown-Up Hirzebruch Surfaces and Special Divisor Classes
by Jae-Hyouk Lee and YongJoo Shin
Mathematics 2020, 8(6), 867; https://doi.org/10.3390/math8060867 - 28 May 2020
Viewed by 2803
Abstract
We work on special divisor classes on blow-ups F p , r of Hirzebruch surfaces over the field of complex numbers, and extend fundamental properties of special divisor classes on del Pezzo surfaces parallel to analogous ones on surfaces [...] Read more.
We work on special divisor classes on blow-ups F p , r of Hirzebruch surfaces over the field of complex numbers, and extend fundamental properties of special divisor classes on del Pezzo surfaces parallel to analogous ones on surfaces F p , r . We also consider special divisor classes on surfaces F p , r with respect to monoidal transformations and explain the tie-ups among them contrast to the special divisor classes on del Pezzo surfaces. In particular, the fundamental properties of quartic rational divisor classes on surfaces F p , r are studied, and we obtain interwinded relationships among rulings, exceptional systems and quartic rational divisor classes along with monoidal transformations. We also obtain the effectiveness for the rational divisor classes on F p , r with positivity condition. Full article
(This article belongs to the Special Issue New Insights into Geometrical Transformations)
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