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The objective of this research article is the recognition of basic geometry concepts through the design and application of a diagnostic test that involves the use of the dynamic software GeoGebra. This test is part of a research study in which the research question is posed: ¿How can didactic situations mediated by the GeoGebra program lead seventh grade students in an educational institution to the construction and understanding of regular polygons? The test was applied to thirty seventh grade students of an Educational Institution in the department of Boyacá (Colombia). A descriptive qualitative approach is adopted in the study, and the analysis of the information is carried out according to the assumptions of the Theory of Didactic Situations and Van Hiele’s model. Among the results evidenced from the implementation of the diagnostic test are some of the students’ difficulties in the autonomous and complete development of the proposed problem situation and others related to the exchange and comparison of information with other students., El presente artículo tiene como propósito presentar el desarrollo de un trabajo de investigación que tiene entre sus objetivos el reconocimiento de conceptos básicos de geometría por medio del diseño y aplicación de una prueba diagnóstica que involucra la utilización del software dinámico GeoGebra. La pregunta de investigación del estudio corresponde a: ¿Cómo las situaciones didácticas mediadas por el programa GeoGebra pueden conducir a los estudiantes de grado séptimo de una Institución Educativa a la construcción y comprensión de los polígonos regulares? Para dar respuesta a la pregunta planteada, inicialmente se aplicó una prueba a treinta estudiantes de grado séptimo de una Institución Educativa del departamento de Boyacá (Colombia). Se adopta en el estudio un enfoque cualitativo de tipo descriptivo, y se realiza el análisis de la información de acuerdo a las formulaciones de la Teoría de las Situaciones Didácticas y el modelo de Van Hiele. Entre los resultados evidenciados a partir de la implementación de esta prueba diagnóstica, se identificaron algunas dificultades especialmente, en el desarrollo en forma autónoma y completa de situaciones problema y el trabajo en grupo, relacionado con el intercambio y la comparación de la información con los compañeros. Por tanto, luego de los análisis a las situaciones planteadas, se concluye que es importante implementar en el diseño de estas secuencias didácticas, situaciones adidácticas, ya que estas permiten la construcción autónoma del saber matemático, y fortalecen el aprendizaje geométrico y el trabajo en grupo.

In this paper we consider the problem of tracking a mobile target using adaptive estimation while circumnavigating it with a system of Unmanned Surface Vehicles (USVs). The mobile target considered is an irregular dynamic shape approximated by a circle with moving centre and varying radius. The USV system is composed of n USVs of which one is equipped with an Unmanned Aerial Vehicle (UAV) capable of measuring both the distance to the boundary of the target and to its centre. This USV equipped with the UAV uses adaptive estimation to calculate the location and size of the mobile target. The USV system must circumnavigate the boundary of the target while forming a regular polygon. We design two algorithms: One for the adaptive estimation of the target using the UAV’s measurements and another for the control protocol to be applied by all USVs in their navigation. The convergence of both algorithms to the desired state is proved up� to a limit bound. Two simulated examples are provided to verify the performance of the algorithms designed in this paper. © The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2021., QC 20201202

We study a graph coloring problem motivated by a fun Sudoku-style puzzle. Given a bipartition of the edges of a graph into near and far sets and an integer threshold t, a threshold-coloring of the graph is an assignment of integers to the vertices so that endpoints of near edges differ by t or less, while endpoints of far edges differ by more than t. We study threshold-coloring of tilings of the plane by regular polygons, known as Archimedean lattices, and their duals, the Laves lattices. We prove that some are threshold-colorable with constant number of colors for any edge labeling, some require an unbounded number of colors for specific labelings, and some are not threshold-colorable. © 2014 Springer International Publishing.

The paper discusses determining the positions and spatial coordinates of the vertices of polyhedral structures - concave antiprisms of second sort. These polyhedra originate from folding the double row strip of equilateral triangles, closed by two identical regular polygons, the principle akin to the way of the concave cupolae of second sort formation. The paper considers constructive -geometrical solution, including the method of solving the problem using the mechanisms, by application of SolidWorks software package.

In the article the technologies of transformation of a perfect polyhedron (tetrahedron) into semi-perfect one, starlike and imperfect polyhedrons by the methods of computer graphics are presented. The authors have concluded that such transformations of solid models of polyhedrons are most expedient from the known ones in descriptive geometry and engineering graphics., В статье изложены технологии преобразования правильного многогранника (тетраэдра) в полуправильный, звёздчатые и неправильные многогранники методами компьютерной графики. Авторы пришли к выводу, что такие преобразования твёрдотельных моделей правильных многогранников наиболее целесообразны из известных в начертательной геометрии и инженерной графике., В статті викладено технології перетворення правильного многогранника (тетраедра) в напівправильний, зірчасті та неправильні многогранники методами комп’ютерної графіки. Автори дійшли висновку, що такі перетворення твердотільних моделей правильних многогранників найдоцільніші з відомих у нарисній геометрії та інженерній графіці.

In this paper we consider the question whether there is a regular polygon in the Cartesian coordinate system such that all of its coordinates are integers. We are not interested in the case of square since it is trivial. We will show that a regular integer polygon does not exist in the orthogonal coordinate plane.

In this paper we consider the question whether there is a regular polygon in the Cartesian coordinate system such that all of its coordinates are integers. We are not interested in the case of square since it is trivial. We will show that a regular integer polygon does not exist in the orthogonal coordinate plane.