Development of a Learning Model of Quadric Surfaces With Augmented Reality and Didactic Engineering

<p class="0abstract">Augmented reality (AR) is an emerging technology that has permeated different spheres of life, one of them is education, and specifically the teaching-learning process at different educational levels and objects of study. For this reason, this paper presents the development of a learning model of quadric surfaces mediated by a mobile AR application and based on didactic engineering. The model was applied to a group of environmental engineering students of the Catholic University of Manizales. To obtain information on the use of the application and the learning results obtained, some intervention instruments were developed. The students stated that the use of AR allowed them to better understand the concepts of quadric surfaces, even more so in a time of pandemic by COVID-19, where education was highly measured by ICTs.</p>

Design of Low Cross-Polarization Tri-Reflector CATR with Standard Quadric Surfaces Working in Terahertz

In this paper, a tri-reflector compact antenna test range (CATR) consisting of a main parabolic reflector with a square aperture of 3 m in side length and two sub-reflectors of rotationally standard quadric surfaces working in terahertz is proposed. By using the equivalent paraboloid theory and cross-polarization elimination conditions and then combining with the appropriate shaped feed, the low cross-polarization and good quiet zone (QZ) performance of the system are achieved. The simulated results demonstrate that a cross-polarization isolation of >37 dB and a peak-to-peak amplitude (phase) ripple of <1.8 dB (13°) can be achieved on the principal cuts of the QZ at 100–500 GHz. At the same time, the QZ usage ratio of the CATR can reach 75%. The proposed tri-reflector CATR composed of standard quadric surfaces not only exhibits good quiet zone performance but also greatly reduces the manufacturing difficulty of the sub-reflectors and the construction cost of the system.

Study on the impact of calculation radius on IDW gravity modelling

Gravity modelling is a necessary process of applying gravity data to practice, and a vital research area in resource exploring and geodesy. Inverse distance weighted (IDW) interpolation is a widely used algorithm in gravity modelling and many other griding procedures. Based on the gravity anomaly data acquired from the airborne gravimetry over a region in the Northwest of China, IDW method is analysed and implemented with varying calculation radius in gravity modelling. The results show that over the study area, with a proper calculation radius, the IDW can give a more precise prediction than quadric surfaces fitting (QSF) method. The distances between sampled points and unsampled points are the only information taken into consideration in the IDW interpolation, so the analysis of the influence by changing the calculation radius of the unsampled points in this test provides a new research direction of error eliminating when using IDW.

A abordagem de interpretação global no ensino e na aprendizagem das superfícies quádricasThe global interpretation approach in the teaching and learning of quadric surfaces

Neste trabalho analisamos o ensino e a aprendizagem das superfícies quádricas (não cilíndricas e não degeneradas) na perspectiva da Teoria dos Registros de Representações Semióticas de Raymond Duval, principalmente, no que diz respeito à abordagem de interpretação global de propriedades figurais. Indicamos as articulações semio-cognitivas envolvendo os registros em língua natural, cartesiano e simbólico de maneira explícita, modo não encontrado em livros didáticos consultados. Além dessas articulações, em especial, sugerimos o recurso das interseções com planos articulado à ideia de que os valores visuais dependem ou são condicionados ao conjunto e à combinação das unidades significantes simbólicas da equação correspondente, o que é fundamental para a reconhecimento dos diferentes casos de quádricas ou de uma quádrica em diferentes posições. Com isso pensamos contribuir ainda mais para o estudo do reconhecimento das quádricas, acrescentando, com o uso do Geogebra, as reflexões que permitem que as análises feitas para uma quádrica em uma das posições denominada, em livros didáticos, de posição padrão poderão ser estendidas a essa mesma quádrica em suas outras posições. Veremos que elementos semio-cognitivos discutidos neste trabalho trazem novas contribuições para o estudo da identificação das quádricas.In this work we analyze the teaching and learning of quadric (non-cylindrical and non-degenerated) surfaces from the perspective of Raymond Duval's Theory of Semiotic Representations, especially with regard to the global interpretation approach of figurative properties. We indicate the semi-cognitive articulations involving the natural, cartesian and symbolic language registers in an explicit way, a method not found in accessed textbooks. In addition to these articulations, in particular, we suggest the use of intersections with concepts linked to the idea that visual values depend or are conditioned on the set and the combination of the symbolic units of the corresponding equation, which is essential for the recognition of the different cases of quadrics or a quadric in different positions. With this in mind, we intend to contribute even more to the study of quadric recognition, adding, with the use of a GeoGebra, that the reflections that allow the analyzes made for a quadric in one of the positions denominated, in textbooks, as standard position, can be extended to this same quadric in its other positions. We will notice that the semi-cognitive elements discussed in this work bring new contributions to the study of quadrics identification. As a result of this path, we can semiotically understand why the symbolic and cartesian registers of the quadrics correspond in the way we know it.