Connecting Spatial Reasoning Process to Geometric Problem

The field of spatial reasoning has seen a lot of research. The process of spatial reasoning, on the other hand, needs to be investigated further. The goal of this study is to capture an elementary school student's spatial reasoning process when solving geometric problems. The spatial skills used in solving geometric problems were also identified in this study. A geometric test was given to seventeen elementary school students. Three participants were chosen as the study's subjects based on their written responses. According to the findings, the subject's spatial reasoning process always begins with the processing of information in mental visualization. Mental visualization is used to help with orientation and selecting the appropriate visual perspective. The spatial skills of spatial visualization and spatial orientation are critical in spatial reasoning. Furthermore, this research initiated the emphasis on the focus of spatial reasoning in the process.

Evaluation of the performance between post process kinematic and static technique in the forest environment

A GNSS involves a constellation of satellites orbiting Earth, continuously transmitting signals that enable users to determine their three-dimensional (3D) position with global coverage. The positioning principle is based on solving an elemental geometric problem, involving the distances (ranges) of a user to a set of at least 4-5 GNSS satellites with known coordinates. These ranges and satellite coordinates are determined by the user’s receiver using signals and navigation data transmitted by the satellites; the resulting user coordinates can be computed to an accuracy of several metres. However, centimetre-level positioning can be achieved using more advanced techniques (kinematic). GPS/GLONASS technique is becoming compulsory for many applications concerning forest management and inventory. This paper aims to comparing the coordinates resulted from Post Process Kinematic with the resulted coordinates for the same points resulted from static technique. Nonetheless, it appears that forest measurements with ± 1 cm accuracy cannot be guaranteed on all occasions, since difficult situations may lead to greater errors (about ±10 cm accuracy for horizontal components and about ± (20-100) cm accuracy for vertical components).

Generation of Tubular and Membranous Shape Textures with Curvature Functionals

Tubular and membranous shapes display a wide range of morphologies that are difficult to analyze within a common framework. By generalizing the classical Helfrich energy of biomembranes, we model them as solutions to a curvature optimization problem in which the principal curvatures may play asymmetric roles. We then give a novel phase-field formulation to approximate this geometric problem, and study its Gamma-limsup convergence. This results in an efficient GPU algorithm that we validate on well-known minimizers of the Willmore energy; the software for the implementation of our algorithm is freely available online. Exploring the space of parameters reveals that this comprehensive framework leads to a wide continuum of shape textures. This first step towards a unifying theory will have several implications, in biology for quantifying tubular shapes or designing bio-mimetic scaffolds, but also in computer graphics, materials science, or architecture.

Plimpton 322: A Study of Rectangles

Plimpton 322 is one of the most sophisticated and interesting mathematical objects from antiquity. It is often regarded as teacher’s list of school problems, however new analysis suggests that it relates to a particular geometric problem in contemporary surveying.

BIM based decision-support tool for automating design to fabrication process of freeform lattice space structure

Complex freeform surfaces and structures are increasingly designed and used in the product and building industry due to the advances in mathematics and digital design tools. However, there is still a gap between designing freeform surfaces and fabricating them. The process of preparing freeform surfaces’ shop drawings is complicated, time-consuming, and lacks the mutual understanding among the stakeholders. Computational design and Building Information Modeling (BIM) can serve as a mediator agent for the integration of design goals with the geometric logic of constructability. They can also facilitate creating platforms for designing and evaluating freeform structures. This open-ended qualitative research attempts to develop a systematic methodology for automating the design and construction drafting process of freeform lattice space structure. Solving this complex geometric problem aims to benefit the design for construction and manufacturers and shrink the cost and time of the process. The study employs a 3D computer-aided design (CAD) tool and introduces an algorithm that generates a BIM model. The BIM model contains shop drawings and suggests the specifications of the main elements, such as beams, glass panels, and nodes.

Visualization of Selected Sangaku Problem as Didactical Phenomenon in GeoGebra

In this article, we will focus on visualization solutions within specific geometric problem of the category Sangaku - historical mathematical problems from Japan. We also highlight didactical advantages of experimental activities in the teaching of mathematics and the role of the visualization via using dynamical geometry software GeoGebra.

Student’s Anticipation Profile at Rigor Level in Determining Papaya Tree Root Dimensions

Students with a rigor level of geometric thinking can analytically solve problems, yet the ability may not be readily observable. Thus, an example of how students solve problems merits explorations. Inspired by student’s problem solving, this study aimed to examine the student’s anticipatory profile in determining Papaya tree roots' dimensions. This qualitative research utilized tests and interview. Two tests were carried out: van Hiele geometric level grouping test for selecting the research participants and the report-based test for the actual project. Seventeen students took the van Hiele test, and one of them, who achieved the rigor level, was selected for the interview. Data obtained from the interview were then analyzed qualitatively. The study showed that students with a rigor level of geometric thinking anticipated analytically. The subject was able to explain a geometric problem systematically, starting from analyzing problems, clarifying detailss, to presenting arguments clearly and precisely. The findings in this study generate useful information for teachers who train their students to analyze a geometric problem correctly and adequately.

Cell Resistance and in Antimicrobial Resistance with Waning Vaccination

Viruses are obligatory minute intra-cellular infectious agents with very simple composition. They are nonliving macro molecules outside the host cell while turned into living active organisms inside host cells. The genetic material (DNA or RNA) carrying the information crucial for virus replication and enforces the cell to approve virus replication. Consequently, it is cellular resistance against the virus that determines whether a cell at any site is infected or not. In this study, we interest in the resistance of cell which may be infected by some disturbance such as a function of [Formula: see text] or as a random variable. Antimicrobial resistance (AMR) is the wider word for resistance in various kinds of microorganisms and includes resistance to antibacterial, antiviral, anti-parasitic, and anti-fungal medicines. Here we study the AMR problem and also, the waning vaccination in the Percolation area. Percolation is a purely geometric problem in which clusters of connected sites or bonds are clearly defined static objects. We are studying cellular automata from Domany–Kinzel on the population of AMRs as on the spreading network. Each connection is rewired on a one-dimensional chain and combined with any probability p node. Additionally, the Domany–Kinzel model will be applied for AMR and waning vaccination in two dimensions.

Overconstrained Cable-Driven Parallel Manipulators Statics Analysis based on Simplified Static Cable Model

In recent years, cable-driven parallel manipulators (CDPM) become more and more interesting topics of robot researchers due to its outstanding advantages. Unlike traditional parallel robots, CDPMs use many flexible cables in order to connect the robot fixed frame and the moving platform instead of using conventional rigid links. Since cables used in CDPM is very light compared to rigid links, its workspace can be very large. Besides, CDPMs are often enhanced load capacity by adding redundant actuators. They also help to widen the singularity-free workspace of CDPM. On the other hand, the redundant actuators produce the underdetermined system i.e. the system has non-unique solutions. Moreover, the elasticity and bendability of flexible cable caused by self-weight and external forces act on it, resulting in the kinematic problem of CDPMs are no longer related to the geometric problem. Therefore, the system of CDPM become non-linear when the deformation of cable is considered. In this study, we introduce the simplified static cable model and use it to linearize the static model of redundantly actuated CDPM. The algorithm to solve the force distribution problem is proposed in Sect. 4. The static-workspace and the performance of those are analyzed in a numerical test.