How to Lay Bricks: Local-Global Alignment Predicts Preference for Shifted Tile Patterns

We examine the aesthetic characteristics of row tile patterns defined by repeating strips of polygons. In experiment 1 participants rated the perceived beauty of equilateral triangle, square and rectangular tilings presented at vertical and horizontal orientations. The tiles were shifted by one-fourth increments of a complete row cycle. Shifts that preserved global symmetry were liked the most. Local symmetry by itself did not predict ratings but tilings with a greater number of emergent features did. In a second experiment we presented row tiles using all types of three- and four-sided geometric figures: acute, obtuse, isosceles and right triangles, kites, parallelograms, a rhombus, trapezoid, and trapezium. Once again, local polygon symmetry did not predict responding but measures of correspondence between local and global levels did. In particular, number of aligned polygon symmetry axes and number of aligned polygon sides were significantly and positively correlated with beauty ratings. Preference was greater for more integrated tilings, possibly because they encourage the formation of gestalts and exploration within and across levels of spatial scale.

Geometric Locations of Points Equally Distance from Two Given Geometric Figures. Part 4: Geometric Locations of Points Equally Remote from Two Spheres

The article deals with the geometric locations of points equidistant from two spheres. In all variants of the mutual position of the spheres, the geometric places of the points are two surfaces. When the centers of the spheres coincide with the locus of points equidistant from the spheres, there will be spheres equal to the half-sum and half-difference of the diameters of the original spheres. In three variants of the relative position of the initial spheres, one of the two surfaces of the geometric places of the points is a two-sheet hyperboloid of revolution. It is obtained when: 1) the spheres intersect, 2) the spheres touch, 3) the outer surfaces of the spheres are removed from each other. In the case of equal spheres, a two-sheeted hyperboloid of revolution degenerates into a two-sheeted plane, more precisely, it is a second-order degenerate surface with a second infinitely distant branch. The spheres intersect - the second locus of the points will be the ellipsoid of revolution. Spheres touch - the second locus of points - an ellipsoid of revolution, degenerated into a straight line, more precisely into a zero-quadric of the second order - a cylindrical surface with zero radius. The outer surfaces of the spheres are distant from each other - the second locus of points will be a two-sheet hyperboloid of revolution. The small sphere is located inside the large one - two coaxial confocal ellipsoids of revolution. In all variants of the mutual position of spheres of the same diameters, the common geometrical place of equidistant points is a plane (degenerate surface of the second order) passing through the middle of the segment perpendicular to it, connecting the centers of the original spheres. The second locus of points equidistant from two spheres of the same diameter can be either an ellipsoid of revolution (if the original spheres intersect), or a straight (cylindrical surface with zero radius) connecting the centers of the original spheres when the original spheres touch each other, or a two-sheet hyperboloid of revolution (if continue to increase the distance between the centers of the original spheres).

“GEOMETRIC FIGURES” CLUSTER IN THE LANGUAGE PICTURE OF THE WORLD (RUSSIAN-CHUVASH PARALLELS)

Работа посвящена анализу русских и чувашских лексических единиц, репрезентующих кластер «геометрические фигуры», с точки зрения его отражения в сознании двух языковых коллективов. В центре нашего лингвокультурологического анализа паремии, традиционные народные символы, используемые в фольклоре. Лексика данной тематической группы помогает выявить своеобразие менталитета носителей языков, помогает выделить особенности мировосприятия чувашского и русского этносов. Кластер «геометрические фигуры» не исследовался ни в отношении русской, ни в отношении чувашской языковых картин мира. Методы исследования: анализ словарных дефиниций, сопоставительный, концептуальный, лингвокультурологический. Лексемы, обозначающие геометрические фигуры, своеобразно трактуются в их вторичной номинации разными народами. В центре нашего внимания элементарные фигуры, такие как круг, квадрат (прямоугольник), треугольник (угол), шар. Геометрическая фигура «круг» в чувашском языке имеет положительную коннотацию, а в русском языке как положительную, так и отрицательную; шар в обоих анализируемых языках воспринимается отрицательно; угол и в чувашском, и в русском языках имеет и положительную, и отрицательную коннотацию; эмоциональные и оценочные оттенки в высказываниях, содержащих лексему «четырехугольник», имеются только в чувашском языке. Ассоциативно-образное восприятие геометрических фигур связано с особенностями менталитета этноса и раскрывается в национально-культурной коннотации данных лексических единиц. The paper is devoted to the analysis of the Russian and Chuvash lexical units that represent the cluster “geometric figures” from the point of view of its reflection in the minds of two language communities. At the center of our linguistic and cultural analysis are paremias, traditional folk symbols. The vocabulary of this thematic group helps to identify the specificity of the mentality of native speakers, allows us to highlight the peculiarities of the worldview of the Chuvash and Russian ethnic groups. The cluster “geometric shapes” was not studied either in relation to the Russian or Chuvash language pictures of the world. The research methods employed are the analysis of dictionary definitions, comparative, conceptual, linguoculturological analysis. The lexemes denoting geometric figures are uniquely interpreted in their secondary nomination by different peoples. In the study we focus at such elementary figures as circle, square (rectangle), triangle (angle/corner), and sphere. The geometric figure of a circle in the Chuvash language has a positive connotation, and in Russian both positive and negative connotations; the sphere is perceived negatively in both analyzed languages; the angle/corner in both Chuvash and Russian languages has both positive and negative connotations; emotional and evaluative shades in statements containing the lexeme of rectangular are available only in the Chuvash language. The associative-figurative perception of geometric figures is associated with the peculiarities of the mentality of an ethnic group and is revealed in the national-cultural connotation of these lexical units.

The shape of you: do individuals associate particular geometric shapes with identity?

For more than a century, psychologists have been interested in how visual information can arouse emotions. Several studies have shown that rounded shapes evoke positive feelings due to their link with happy/baby-like expressions, compared with sharp angular shapes, usually associated with anger and threatening objects having negative valence. However, to date, no-one has investigated the preference to associate simple geometric shapes to personal identities, including one’s own, that of a close acquainted, or that of a stranger. Through 2 online surveys we asked participants to associate a geometric shape, chosen among a circle, a square and a triangle, to each of three identities, namely “you” (the self), “your best friend” or “a stranger”. We hypothesized that the circle would be more associated with the self, the square with the friend and the triangle with the stranger. Moreover, we investigated whether these associations are modulated by 3 personality traits: aggressivity, social fear and empathy. As predicted, we found that participants associate more often the circle with the self, both the circle and the square with the best friend, whereas they matched angular shapes (both the triangle and the square) to the stranger. On the other hand, the possibility that personality traits can modulate such associations was not confirmed. The study of how people associate geometric figures with the self or with other identities giving them an implicit socio-affective connotation, is interesting for all the disciplines interested in the automatic affective processes activated by visual stimuli.

Programming Robots by Demonstration Using Augmented Reality

The world is living the fourth industrial revolution, marked by the increasing intelligence and automation of manufacturing systems. Nevertheless, there are types of tasks that are too complex or too expensive to be fully automated, it would be more efficient if the machines were able to work with the human, not only by sharing the same workspace but also as useful collaborators. A possible solution to that problem is on human–robot interaction systems, understanding the applications where they can be helpful to implement and what are the challenges they face. This work proposes the development of an industrial prototype of a human–machine interaction system through Augmented Reality, in which the objective is to enable an industrial operator without any programming experience to program a robot. The system itself is divided into two different parts: the tracking system, which records the operator’s hand movement, and the translator system, which writes the program to be sent to the robot that will execute the task. To demonstrate the concept, the user drew geometric figures, and the robot was able to replicate the operator’s path recorded.

Tangram – Guardado a sete chaves – Construção e Atividades

Este trabalho tem como objetivo mostrar curiosidades sobre a origem do Tangram, bem como a construção de suas sete peças. Serão propostas atividades baseadas nas peças que compõe o Tangram, com o intuito de desenvolver as habilidades e competências dos alunos do ensino fundamental acerca do conteúdo de áreas de figuras, além da congruência de algumas figuras geométricas. This work aims to show curiosities about the origin of Tangram, as well as the construction of its seven pieces. Activities based on the pieces that make up the Tangram will be proposed, in order to develop the skills and competencies of elementary school students about the content of figure areas, as well as the congruence of some geometric figures.

DEVELOPMENT OF SPATIAL PERCEPTIONS IN PRESCHOOL AGE THROUGH GEOMETRIC TRANSFORMATIONS IN THE APPLICATION OF A COMPETENCE APPROACH

During preschool age a number of notions are formed related to the development of the child’s personality. Orienteering within space is part of the mathematical preparation of children in kindergarten. This section is one of the most difficult to master. A specific feature of childhood is the concrete-image thinking. To perceive the world around them, children need many examples. Preschoolers handle objects – they rotate, move, but do not analyze their actions. This paper describes the need and role of setting appropriate cognitive tasks to promote the development of spatial orientation of preschool children. The main part of the cognitive tasks related to the formation of spatial perceptions is intended to be mastered through the mathematical educations. Insufficient provision of materials and difficulty in perception by children do not motivate teachers to prefer to work in time for additional activities. It is this fact that provokes us to show that many resources can be created that are interesting for children and at the same time have great cognitive value. Practical developments about the topic are presented, which are realized in the education of students – future pedagogues. Various options are proposed, related to translation or transfer of an object, construction of objects and counting of geometric figures. The presented practical results are part of a study of the possibilities for applying a competency approach in kindergarten. In order to achieve a change in the educational system, it is necessary the University to prepare young educators for a new way of pedagogical interaction.

Ideas for improving mathematics teaching in fourth grade of primary school by using the mathematical software GeoGebra

In the paper studying some spatial geometric figures in 4th grade mathematics education is explored. To do this the possibilities of GeoGebra are used. For each of the figures – rectangular parallelepiped, cube, pyramid, cylinder, cone, sphere, drawings are given in order to illustrate the geometric figure as well as to ensure following the basic rule in learning and understanding mathematical concepts – varying the insignificant properties of the concept to make its significant ones stand out.