The question of finding the shortest distance between two points of different diversity

Digital education at the university implies application of information technologies, active learning methods and comprehensive algorithmizing of the process of solving various tasks. It is also supposed to create application software packages, which can find their application at the junction of various disciplines. (1) One area of digital education is to solve the problems of motion optimization and localization of various objects. In particular, the question of finding the shortest distance between points lying on two different varieties (curves, plane, etc.) is frequently solved (more than 10) Here are examples of the solving. The first example describes an algorithm for finding the shortest distance between two parabolas lying in the same plane; the second example suggests a solution course for an elliptical paraboloid and a point on the coordinate axis. Finally, the third example deals with the distance between a cube parabola and a hemisphere with the center at the beginning of the coordinates.

The Self-Calibration Method for the Vertex Distance of the Elliptical Paraboloid Array

The elliptical paraboloid array plays an important role in precision measurement, astronomical telescopes, and communication systems. The calibration of the vertex distance of elliptical paraboloids is of great significance to precise 2D displacement measurement. However, there are some difficulties in determining the vertex position with contact measurement. In this study, an elliptical paraboloid array and an optical slope sensor for displacement measurement were designed and analyzed. Meanwhile, considering the geometrical relationship and relative angle between elliptical paraboloids, a non-contact self-calibration method for the vertex distance of the elliptical paraboloid array was proposed. The proposed self-calibration method was verified by a series of experiments with a high repeatability, within 3 μ m in the X direction and within 1 μ m in the Y direction. Through calibration, the displacement measurement system error was reduced from 100 μ m to 3 μ m . The self-calibration method of the elliptical paraboloid array has great potential in the displacement measurement field, with a simple principle and high precision.

A Novel 2D Micro-Displacement Measurement Method Based on the Elliptical Paraboloid

The micro-displacement measurement system with 2D/3D has become increasingly important in the field of scientific research and technology application. In order to explore the application of an optical surface in micro-displacement measurement, a novel and simple 2D micro-displacement measurement method based on the elliptical paraboloid was designed and subjected to experiment. The measurement system takes advantage of the elliptical paraboloid instead of a plane mirror in the optical structure of an autocollimator which has been ameliorated to adapt to curved surface measurement. Through the displacement of the light spot on the CCD (Charge Coupled Device) detector, the displacement of the target could be measured with a linear correlation coefficient of 0.9999. The accuracy of the system is about ± 0.3 μm in a wide range in two dimensions. The results were in good agreement with the theoretical analysis and indicated the potential applicability of the proposed system in the detection of geometric errors of CNC (Computerized Numerical Control) machine tools.

Aprehensiones y modificaciones en el registro gráfico dinámico del paraboloide elípticoApprehensions and modifications into the Dynamic-Graphical register of the elliptical paraboloid

El presente artículo tiene como objetivo estudiar las aprehensiones y modificaciones del paraboloide elíptico en el Registro Gráfico Dinámico (RGD) por medio del ambiente de representaciones dinámicas Geogebra 3D. Para ello, tomamos como base aspectos de la investigación previa, realizada por el primer autor, sobre visualización del paraboloide elíptico que se fundamenta en la Teoría de Registros de Representación Semiótica de Duval, configuramos el RGD del paraboloide elíptico y analizamos cómo se desarrollan sus aprehensiones y modificaciones. Concluimos afirmando que el desarrollo de aprehensiones en tareas que involucran la noción de paraboloide elíptico puede ser realizado en el RGD y entendemos que es posible investigar otros objetos matemáticos que puedan ser representados en dicho registro. This paper aims at studying the apprehensions and modifications of an elliptic paraboloid in the Dynamic-Graphic Register (DGR) through the environment of dynamic representations Geogebra 3D. To do that, we take aspects from Duval’s Theory of Registers of Semiotic Representation as well as a study on paraboloid visualization as a benchmark. We configured the DGR of the elliptic paraboloid and analyzed how apprehensions and modifications develop in such register. We concluded stating that developing apprehensions in tasks that involve the notion of elliptic paraboloid can be done in the DGR, and we empathize that this type of research can be realized with other mathematical objects that may be represented in such register.

Repairing and Strengthening of Elliptical Paraboloid Reinforced Concrete Shells with Openings

This investigation is carried out to evaluate the repair and strengthening the techniques of elliptical paraboloid reinforced concrete shells with openings. An experimental program of several different techniques in repair and strengthening is executed. The materials, which are considered for strengthening, are; Glass fiber reinforced polymers GFRP at different position of the shell bottom surface, steel strip and external tie. They loaded by four concentrated loads affected on the corners of the opening. The initial and failure loads as well as the crack propagation for the tested shells at different loading stages, deflections and failure load for repaired and shells are recorded. A non-linear computer program based on finite element techniques is used to study the behavior of these types of shells. Geometric and materials nonlinearities are considered in the analysis. The efficiency and accuracy of computer program are verified by comparing the program results with those obtained experimentally for the control shell with opening and strengthened shells.

Analytical Solutions for Moving Elliptical Paraboloid Heat Source in Semi-Infinite Plate

An attempt has been made in this paper to findout the trainsent temperature distribution on the welded plates through analytical as well as numerical method considering double elliptic paraboloid moving heat source volume.It has been assumed that heat is distributed through gaussian manner on the welded plates and modes of heat transfer for welded plates are conduction as well as convection.With the help of these solutions dimnesions of weld bead geometry,HAZ width and thermal stress have been predicted and validated with the experimental data.