The Image-Based Finite Element Evaluation of the Deformed State

The article presents one of the possible approaches to modeling objects with anisotropic properties based on images of the study area. Data from such images are taken into account when building a numerical model. In this case, material inhomogeneity can be included by integrating the local stiffness matrix of each finite element with a certain weight function. The purpose of the presented work is to develop a finite element for the formation of a computational ensemble and simulation of mechanical behavior taking into account the data of two-dimensional medical images. To implement the proposed approach, we used the assumption that there is a correlation between the values in the image pixels and the elastic properties of the material. Meshing was based on a four-node plane finite element. This approach allows using the quantitative phase or scanning electronic images, as well as computed tomography data. A number of test problems for compression of elementary geometry samples were calculated. The distal part of the rat femur was considered as a model problem. A computed tomography scan of the sample was used to construct a numerical model taking into account the inhomogeneity of the material distribution inside the organ. The distribution field of the nodal displacements based on data obtained from the images of the study area is presented. Within the framework of a model problem, we considered how a computer tomograph resolution influences the quality of the obtained results. For this purpose, calculations were carried out based on compressed input medical images.

Living in Generosity: The Making of a Refugee Resettlement Centre

<p>Generosity naturally reflects the idea of abundance, larger or plentiful. However, generosity as a language in architecture is vaguely understood, as it has neither a particular scheme nor definite form. This thesis focuses on the idea of generosity in architecture by exploring the language of generosity in providing a generous living for refugees resettling in New Zealand. It concerns the condition of living within a refugee resettlement centre when refugees spend their first six-week orientation program to prepare them for a new life in New Zealand. Through design-led research process, the project takes the concept of elementary geometry from children’s drawing of a house and evolves by extracting the language of generosity to form an architecture. Anything that could be simple to us could mean more to others. Hence, the act of provocation in the simplicity of form, scale, scheme, and colour could transform our perception on “generosity”, and thus it gives the potential for architecture to create an ideal condition of living for future refugees resettling in New Zealand.</p>

Living in Generosity: The Making of a Refugee Resettlement Centre

<p>Generosity naturally reflects the idea of abundance, larger or plentiful. However, generosity as a language in architecture is vaguely understood, as it has neither a particular scheme nor definite form. This thesis focuses on the idea of generosity in architecture by exploring the language of generosity in providing a generous living for refugees resettling in New Zealand. It concerns the condition of living within a refugee resettlement centre when refugees spend their first six-week orientation program to prepare them for a new life in New Zealand. Through design-led research process, the project takes the concept of elementary geometry from children’s drawing of a house and evolves by extracting the language of generosity to form an architecture. Anything that could be simple to us could mean more to others. Hence, the act of provocation in the simplicity of form, scale, scheme, and colour could transform our perception on “generosity”, and thus it gives the potential for architecture to create an ideal condition of living for future refugees resettling in New Zealand.</p>

Criteria of Motion Without Slipping for an Omnidirectional Mobile Robot

In this paper we present a study of the dynamics of a mobile robot with omnidirectional wheels taking into account the reaction forces acting from the plane. The dynamical equations are obtained in the form of Newton – Euler equations. In the course of the study, we formulate structural restrictions on the position and orientation of the omnidirectional wheels and their rollers taking into account the possibility of implementing the omnidirectional motion. We obtain the dependence of reaction forces acting on the wheel from the supporting surface on the parameters defining the trajectory of motion: linear and angular velocities and accelerations, and the curvature of the trajectory of motion. A striking feature of the system considered is that the results obtained can be formulated in terms of elementary geometry.

Geometric representations of irrational algebraic numbers in Hungarian high school mathematics education

Irrational numbers are present in our everyday life but their exact values cannot be given in a form that students easily understand. Therefore in this paper we show geometrical constructions and calculations in which non-rational numbers naturally arise and gain meaning. We look at numbers which are expressible with at maximum two roots and are present in the Hungarian curriculum. For each number we present how they appear in Hungarian textbooks, and show multiple problems and solutions in which they arise. These solutions differ in their level of mathematical complexity, from elementary geometry to higher algebra. Introducing these solutions to students, shows them, that the different areas of mathematics are interrelated. This approach may inspire students to use their mathematical knowledge not only from the area in which the problem was presented.

Los problemas espaciales: una propuesta alternativa para enseñar geometría en la Educación Secundaria ObligatoriaSpatial problems: an alternative proposal to teach geometry in Compulsory Secondary Education

ResumenPresentamos un esbozo del problema de investigación que forma parte de un trabajo de tesis. Tras analizar el currículo español de matemáticas y algunos manuales escolares, hemos encontrado una ausencia de las cuestiones a las que responden los conocimientos geométricos propuestos para la Educación Secundaria Obligatoria (alumnos de 12 a 16 años). Después de haber revisado diferentes estudios relacionados con la enseñanza de la geometría, postulamos que los problemas espaciales pueden ayudar a encontrar una posible razón de ser de esos conocimientos geométricos. Así, pretendemos identificar y abordar algunos problemas espaciales a fin de confirmar dicha hipótesis.Palabras-clave: Teoría Antropológica de lo Didáctico, Geometría elemental, Conocimientos geométricos, Problemas espaciales, Modelización Espacio-Geométrica.Abstract.We present an outline of the research problem that is part of a doctoral thesis. After analysing the Spanish mathematics curriculum and some textbooks, we have found an absence of the questions to which the geometric knowledge proposed for high school (students aged 12 to 16 years) answer. After reviewing different studies related to the teaching of geometry, we postulate that spatial problems can help to find a possible justification for such geometric knowledge. Thus, we intend to identify and address some spatial problems in order to confirm this hypothesis.Keywords: Anthropological Theory of Didactics, Elementary Geometry, Geometric Knowledge, Spatial Problems, Space-Geometric Modeling.