Geometric Figures Research Articles

Conscious knowledge of CS-UCS contingency information affects extinction retrieval of conditioned disgust responses: Findings from an online de novo disgust conditioning task.

The present study aimed to establish and develop an online de novo conditioning paradigm for the measurement of conditioned disgust responses. We further explored the effects of explicit instructions about the CS-UCS contingency on extinction learning and retrieval of conditioned disgust responses. The study included a sample of 115 healthy participants. Geometric figures served as conditioned stimuli (CS) and disgust-evoking pictures as unconditioned stimuli (UCS). During disgust conditioning, the CS+ was paired with the UCS (66% reinforcement) and the CS- remained unpaired; during extinction and retrieval, no UCS was presented. Half of the participants (n=54) received instructions prior to the disgust extinction stating that the UCS will not be presented anymore. 1-2 days or 7-8 days later participants performed a retrieval test. CS-UCS contingency, disgust and valence ratings were used as dependent measures. Successful acquisition of conditioned disgust response was observed on the level of CS-UCS contingency, disgust and valence ratings. While some decline in valence and disgust ratings during the extinction stage was observed, contingency instructions did not significantly affect extinction performance. Retrieval one week later revealed that contingency instructions increased the discrimination of the CSs. Extinction of conditioned disgust responses is not affected by explicit knowledge of the CS-UCS contingencies. However, contingency instructions prior to extinction seem to have a detrimental effect on long-term extinction retrieval.

Motor unit placement in a realistic muscle cross section model: performance of a new algorithm and effects of muscle architecture on surface EMG power spectral components

Objetive. Surface electromyogram (sEMG) characteristics are strongly dependent on the spatial localization of motor units (MU). Thus, the definition of the muscle architecture is a crucial step in the simulation of sEMG. Muscles cross section or even the shape of the MU territories is not a regular geometric figure. Moreover, MU may have different fibre densities, and its distribution may not be random but follow a spatial regionalization by type. Despite these prior conditions, the method for MU placement in a muscle model should be able to achieve constant muscle fibre density, which is a generally accepted property of any muscle. Approach. An algorithm was developed that meets the previously established requirements for the distribution of MU in a muscle model. The algorithm considers the muscle cross section and MU territories as bitmaps and encodes the muscle fibre density distribution by pixel brightness. This allowed the use of digital image processing techniques to optimally distribute the MU. The impact of the different muscle architectures on sEMG was investigated using one of the most accepted models of motor unit pool recruitment combined with a model of MU action potential simulation. element-citationitalic Main results. The algorithm produced a completely regionalized architecture with constant muscle fibre density in a muscle with both an irregular cross-section and elliptic MU territory. Significance. In addition to the improvement in the realism of the muscle simulations, the algorithm allowed the investigation of the influence of the spatial distribution of MU on the sEMG power spectrum, thus helping to explain the existing inability to detect changes in motor unit recruitment strategies through the spectral analysis of interference patterns.

Improving the Teaching of Geometric Construction Problems in the Process of Training Future Mathematics Teachers

The article examines the problem of improving the teaching of geometric construction problems using information and communication technology (ICT) tools in the process of training future mathematics teachers at pedagogical universities. During the clarifying experiment, methodological problems in teaching geometric construction problems were identified, and as one of the ways to solve them, the need for methodological training of future mathematics teachers to use applied information and computer resources in teaching geometric construction problems was based. Analysis of information and computer technologies and programs intended for use in teaching geometry courses was performed, and the effectiveness of using the “Live Geometry” program in creating geometric construction problems was shown. Learners are more interested in geometry and construction problems, and can save all work in electronic format for future use. While studying the topic, the tools in the program will help to draw figures and use these figures in solving problems, formulate the properties of geometric figures, and use them to model geometric bodies. In the given article, the authors analyzed the state programs and concepts, the works of domestic and foreign scientists, and the results of an online survey and interviews with students. 54 students of the mathematics education program were involved in a pedagogical experiment, and the results were shown in detail. As the results of the experiment show, after using the “Living Geometry” program in the lesson, students were recognized from a certain personal subjective point of view, which regulates their cognitive and practical activities, and an increase in theoretical knowledge and practical skills was determined. It has been proven by mathematical and statistical methods that the use of the “Living Geometry” program in the teaching of structural problems allows effective and efficient organization of education and increases the methodological training of future mathematics teachers.

Revisiting manipulatives in the learning of geometric figures

Over time, teaching materials, such as manipulatives, have acquired a key role in promoting students’ understanding of mathematical knowledge. These materials play an important resource in student learning, including a recreational role that promotes motivation and a dynamic role in the understanding of concepts in which students are involved in the learning activities. Based on these assumptions, this study aims to investigate the contribution of manipulative materials in the learning of geometric figures by elementary school students. Adopting a qualitative and interpretative approach, data were collected through students’ written records, and audio and video record of students’ activities. The results show that students explored, manipulated, and constructed representations of triangles, squares, rectangles, circles, and other geometric figures, distinguishing them from each other through shape and properties. In particular, through manipulation of shapes with manipulatives students realized that a square is a rectangle but the inverse is not true.

Confirmation of the Acquired Knowledge for Recognition of the Geometric Triangle Figure Using Information Technologies

The article is dedicated to the use of information technology in the creation of educational games for acquiring novelties in primary school. Specialized Scratsh software for the inclusion of children in computer culture is considered. The basis for the developed animated modules is the textbook in mathematics for third grade with authors Prof. Dr. Vladimira Angelova and Jana Koleva, Prosveta Plus Publishing House, Sofia, 2017

Comparison of planimetric CT‑based volumetry with simplified models for determining the size of intrapelvic hematomas due to pelvic fractures in emergency room diagnostics

Bleeding in the pelvis can lead to acirculatory problem. The widely used whole-body computed tomography (WBCT) scan in the context of treatment in the trauma resuscitation unit (TRU) can give an idea of the source of bleeding (arterial vs. venous/osseous); however, the volume determination of an intrapelvic hematoma by volumetric planimetry cannot be used for aquick estimation of the blood loss. Simplified measurement techniques using geometric models should be used to estimate the extent of bleeding complications. To determine whether simplified geometric models can be used to quickly and reliably determine intrapelvic hematoma volume in fractures type Tile B/C during emergency room diagnostics or whether the time-consuming planimetric method must always be used. Retrospectively, 42 intrapelvic hemorrhages after pelvic fractures Tile B + C (n = 8:B, 34:C) at two trauma centers in Germany were selected (66%men, 33%women; mean age 42 ± 20 years) and the CT scans obtained during the initial trauma scan were analyzed in more detail. The CT datasets of the included patients with 1-5 mm slice thickness were available for analysis. By area labelling (ROIs) of the hemorrhage areas in the individual slice images, the volume was calculated by CT volumetrically. Comparatively, volumes were calculated using simplified geometric figures (cuboid, ellipsoid, Kothari). Acorrection factor was determined by calculating the deviation of the volumes of the geometric models from the planimetrically determined hematoma size. The median planimetric bleeding volume in the total collective was 1710 ml (10-7152 ml). Relevant pelvic bleeding with atotal volume > 100 ml existed in 25patients. In 42.86% the volume was overestimated in the cuboid model and in 13cases (30.95%) there was asignificant underestimation to the planimetrically measured volume. Thus, we excluded this volume model. In the models ellipsoid and measuring method according to Kothari, an approximation to the planimetrically determined volume could be achieved with acorrection factor calculated via amultiple linear regression analysis. The time-saving and approximate quantification of the hematoma volume using amodified ellipsoidal calculation according to Kothari makes it possible to assess the extent of bleeding in the pelvis after trauma if there are signs of aC-problem. This measurement method, as asimple reproducible metric, could be embedded in trauma resuscitation units (TRU) in the future.

Pain and related suffering reduce attention toward others.

It has been proposed that the expression of pain-related suffering may lead to an enhanced focus on oneself and reduced attention toward the external world. This study aimed at investigating whether experimentally induced painrelated suffering may lead persons to withdraw into themselves, causing a reduced focus on external stimuli as reflected by impaired performance in a facial recognition task and heightened perception of internal stimuli measured by interoceptive awareness. Thirty-two participants had to recognize different emotional facial expressions (neutral, sad, angry, happy), or neutral geometrical figures under conditions of no pain, low, and high prolonged pain intensities. Interoceptive accuracy was measured using a heartbeat-detection task prior to and following the pain protocol. Males but not females were slower to recognize facial expressions under the condition of high painful stimulation compared to the condition of no pain. In both, male and female participants, the difficulty in recognizing another person's emotions from a facial expression was directly related to the level of suffering and unpleasantness experienced during pain. Interoceptive accuracy was higher after the pain experiment. However, neither the initial interoceptive accuracy nor the change were significantly related to the pain ratings. Our results suggest that long-lasting and intense painful stimuli, which induce suffering, lead to attentional shifts leading to withdrawal from others. These findings contribute to a better understanding of the social dynamics of pain and pain-related suffering.

Multimodal Presentation of Interactive Audio-Tactile Graphics Supporting the Perception of Visual Information by Blind People

Due to the limitations in the perception of graphical information by blind people and the need to substitute the sense of sight with other senses, the correct use of multimedia in the presentation of graphics is particularly important. The aim of the authors was to correctly present visual information in the tactile and audio form and to provide contextually selected information to reduce the existing cognitive barriers. In this article, the authors decided to research the method of exploring a tactile picture by a blind person and providing contextual and semantic information about the touched image elements using the developed tool for multimodal presentation of interactive audio-tactile graphics supporting the perception of blind people. The use of multimedia should improve the perception of the conveyed content. Therefore, the effectiveness of interpreting the information contained in the tactile image is verified by analyzing the tactile, audio, and contextual perceptions during the experiments. The following issues were considered in detail from the point of view of the blind and visually impaired: the recognition of shapes of image elements depending on their size and properties, the optimal width of elements displayed on the tablet screen, the time intervals between taps on an image element, and the acceptable length of graphic element audio description. The results from this study suggest the need to select the image presentation parameters in various perception channels to the user's needs. The findings of our research on tactile shape perception of geometric figures indicate potential problems in recognizing the shapes of figures in the case of wrong preparation of tactile pictures. In the case of a small difference in the proportions of the length of the sides of the figure or a slight difference in the measures of the angles of the figure sides, we have noticed that most blind people fail to recognize its shape. Considerable progress in improving such perception can be achieved by increasing the proportions in the lengths of the sides and the measures of the angles between the sides of the figure. Further steps concern introducing an alternative audio description of the properties of the figure so as to improve the interpretability of the figure shape. For most users, the width of a virtual line in a digital image displayed on a tablet should be around 5 mm for a corresponding 1 mm tactile line. The configuration of the time intervals defining the user's gestures (two-taps, three-taps) should be about 340 ms. Applying audio descriptions to tactile picture elements improves the understanding and interpretation of the information presented on it. Most participants in the test group accepted 5 to 10 seconds of voice prompts. Longer messages were incomprehensible, and details were hard to remember. In the proposed solution, the audio description can be divided into two or three different descriptions available to the user after tapping two or three times on an image element. It allows the user to decide on the amount of contextual information needed about the touched tactile picture element. The research attempted to show the typical values of various image presentation parameters and their ranges of values and indicated effective methods of their selection for a specific system user.

Écrire pour guérir. Les formules magiques écrites dans la médecine populaire roumaine (XVIIe-XXe siècles)

In traditional Romanian society, where the vast majority of the population was illiterate, writing remained mysterious and inaccessible. For the peasants from the Romanian village, writing and the book have acquired separate meanings, being used in a particular way through magico-religious rituals. In order to defend against the action of evil forces and for the healing of the sick body, the traditional community instituted ceremonial, apotropaic and thaumaturgical practices, involving a set of alternative uses of writing. The clerics played an important role in consolidating these practices. The village priests made the written amulets (apocryphal texts, prayers and incantations) intended to be worn closest to the body to ward off unclean spirits which could cause harm to women who had just given birth and to the new-born. Books and writing were seen as repositories of healing forces that could ward off disease and trouble. In the Romanian rural society, between the two World Wars, it was still believed that evil spirits, agents of disease, could be drawn from the sick person's body with the help of “healing letters” (rom. “răvașe de leac”), containing prayers, various religious symbols, names of saints but also magic formulas, often presented in an enigmatic and incomprehensible way. The formulas are written upside down, from right to left, then from left to right (like the famous palindrome “Sator arepo tenet opera rotas” or “Abracadabra”) or distributed in geometric figures (spirals, triangles, crosses). These “healing papers”, with a strong iconic charge, were applied to the body or the text and the image were drawn directly on the skin of the sufferer. Drinking water in which one had washed a plate on the surface of which healing formulas had been written or swallowing the paper on which magic formulas were written were other common practices. Romanian ethnologists have documented the survival of these practices until the mid1970s. Similar practices are found in other parts of Europe.

바이오필릭 디자인 접근법을 활용한 Stella McCartney의 친환경 패션 분석

This study aimed to examine cases of clothing in Stella McCartney"s most recent collection a sustainable eco-friendly brand and understand the biophilic fashion design approach based on the attributes that represent the indirect experience of nature. The study found that the number of cases of biophilic fashion showing such attributes in Stella McCartney"s collection during the most recent 4 years was 293. The study examined the characteristics of selected cases by classifying them into 6 types of biophilic fashion such as ‘images of nature’, ‘natural material’, ‘shapes evoking nature’, ‘information richness’, ‘patina of time’, and ‘natural geometries’ based on the standard of the advanced studies. As a result of an examination of the types of biophilic fashion shown in Stella McCartney"s collection during the most recent 4 years, ‘shapes evoking nature’ represented the majority of cases in each season. The characteristics of the types of biophilic fashion appearing in this Stella McCartney Collection were found to be as follows: ‘Images of nature’ was expressed as clothing details reminiscent of natural object-patterned print and natural objects. As for ‘natural material’, this was expressed as old and worn material with an unartificial texture or semitransparency representing the textures of nature and material with stains or rough textures. The characteristic of ‘shapes evoking nature’ was expressed as a flexible curve taking after nature in the overall silhouette or detail. ‘Information richness’ appeared with the repeated arrangement of natural objects or abstract expression of environmental images. The ‘patina of time’ theme was expressed through the use of washed-out dyeing, color fades, or dusty processing to give the feeling of old clothes and the natural passing of time. ‘Natural geometries’ brought geometric beauty as a curve expressed in the geometric pattern representing different-sized geometric figure, sound waves, or the shape of the human body.

Reinstatement of thought conditioning following extinction and counterconditioning

Pairing a cue (e.g., an image of a geometrical figure) with an outcome (e.g., an image with aversive content) can result in the cue eliciting thoughts of that outcome (i.e., thought conditioning). Previous research suggests an advantage of counterconditioning over extinction in reducing thoughts of (aversive) outcomes. However, it is unclear how robust this effect is. This study aimed to (1) replicate the previously observed advantage of counterconditioning over extinction and (2) test whether counterconditioning leads to less reinstatement of thoughts of an aversive outcome relative to extinction. Participants (N = 118) underwent a differential conditioning procedure and were then assigned to one of three conditions: extinction (i.e., the aversive outcome was no longer presented), no extinction (i.e., the aversive outcome continued to be presented) and counterconditioning (i.e., the aversive outcome was replaced with positive images). After three unsignaled outcome presentations, participants indicated in a return of fear test the extent to which they thought of the aversive outcome. As predicted, counterconditioning was more successful in reducing thinking of the aversive outcome than extinction. Yet, there were no differences in return of thoughts of the aversive outcome between the two conditions. Future research should consider other return of fear procedures.

Can We Identify the Theorem in Metaphysics 9, 1051a24-27 with Euclid’s Proposition 32? Geometric Deductions for the Discovery of Mathematical Knowledge

This paper has two specific goals. The first is to demonstrate that the theorem in Metaphysics Θ 9, 1051a24-27 is not equivalent to Euclid’s Proposition 32 of book I (which contradicts some Aristotelian commentators, such as W. D. Ross, J. L. Heiberg, and T. L. Heith). Agreeing with Henry Mendell’s analysis, I argue that the two theorems are not equivalent, but I offer different reasons for such divergence: I propose a pedagogical-philosophical reason for the Aristotelian theorem being shorter than the Euclidean one (and the previous Aristotelian versions). Aristotle wants to emphasize the deductive procedure as a satisfactory method to discover scientific knowledge. The second objective, opposing some consensus about geometrical deductions/theorems in Aristotle, is to briefly propose that the theorem, exactly as we found it in Metaphysics and without any emendation to the text (therefore opposing Henry Mendell’s suggested amendments), allows the ancient philosopher to demonstrate that universal mathematical knowledge is in potence in geometrical figures. This tentatively proves that Aristotle emphasizes that geometrical deduction is sufficient to actualize mathematical knowledge.

Influence of spatial imagery and imagery control on geometric form location in paintings

The study of artistic works requires an educated vision, a certain way of looking that unveils potential relations amongst objects. Fine art students develop skills that are resultant of their training in finding possible connections amongst elements in a painting. One of the abilities related to the observation and analysis of a work of art is the capacity to form mental images. The present study involved 188 fine art students (105 first-year students and 83 fourth-year students) and was meant to find out whether their education level, their spatial imagery ability and their imagery control had any influence on the location of geometric forms in a painting. We assessed hits minus errors. Results showed Results showed that fine arts students’ spatial ability and imagery control explained a significant percentage of score variation in the task of locating geometric figures in Velázquez's paintings. The significance of these results is consistent with those obtained in previous studies, spatial capacity, and imagery control influence on the achievement of skills in the artistic field.

Invariant Percolation Properties in Random Isotropic Systems of Conductive Discorectangles on a Plane: From Disks to Sticks

Nanorod‐ and nanowire‐based films are promising 2D materials for the transparent conductive electrodes, including flexible and stretchable ones. To mimic the shape of elongated conductive nanoparticles and, at the same time, simplify the simulations, different simple geometrical figures are used. During simulation, the shape and the aspect ratio of the particles affect the electrical and optical properties of films. However, some features of the conductive films may be insensitive both to the shape of particles and to their aspect ratio. 2D random systems of isotropically placed, overlapping, identical discorectangles (stadia) with aspect ratios ranging from 1 (disks) to ∞ (zero‐width sticks) are studied. The particular case when only the junction resistance between conductive particles is taken into account is considered. The effect of the aspect ratio and the number density of conductive discorectangles on the behavior of the electrical conductivity, the local conductivity exponent, and the current‐carrying backbone is analyzed. The computer simulations demonstrate that some of the properties of random, isotropic 2D systems of conductive discorectangles are insensitive to the aspect ratios of the particles.

A hub-and-spoke model of geometric concepts

The cognitive basis of geometry is still poorly understood, even the ‘simpler’ issue of what kind of representation of geometric objects we have. In this work, we set forward a tentative model of the neural representation of geometric objects for the case of the pure geometry of Euclid. To arrive at a coherent model, we found it necessary to consider earlier forms of geometry. We start by developing models of the neural representation of the geometric figures of ancient Greek practical geometry. Then, we propose a related model for the earliest form of pure geometry – that of Hippocrates of Chios. Finally, we develop the model of the neural representation of the geometric objects of Euclidean geometry. The models are based on the hub-and-spoke theory. In our view, the existence of specific models opens the possibility of addressing the relationship between geometric figures and geometric objects, in a novel way, in terms of their neural representation.

Closed Form Solution in the Buckling Optimization Problem of Twisted Shafts

The counterpart for Euler’s buckling problem is Greenhill’s problem, which studies the forming of a loop in an elastic beam under torsion. In the context of twisted shafts, the optimal shape of the beam along its axis is searched. A priori form of the cross-section remains unknown. For the solution of the actual problem, the stability equations take into account all possible convex and simply connected shapes of the cross-section. The cross-sections are similar geometric figures related by a homothetic transformation with respect to a homothetic center on the axis of the beam and vary along its axis. The distribution of material along the length of a twisted shaft is optimized so that the beam is of the constant volume and will support the maximal moment without spatial buckling. The applications of the variational method for stability problems are illustrated in this manuscript.

Transitions Between Domains of Activity as “Domestications of the Eye” for the Learning of Mathematics with GGBot

We present a theoretical study that allows us to attempt framing in an embodied perspective the effectiveness of the drawing robot GGBot in the learning of geometry. The aim of the article is to set the intertwining of activity, semiotics, perception, and knowledge at the crossover of Radford’s theory of objectification (TO) and Borba and Villareal’s notion of humans-with-media. Such a crossover is articulated in four building blocks: (1) processes of objectification and the role of semiotic means of objectification, where we state that digital artifacts such as the GGBot change the topology of the semiotic means of objectification; (2) cognition is sensuous and learning is a process of domestication of the eye, where perception is theoretically shaped by the interaction with GGBot; (3) GGBot and humans-with-media, where we outline new thinking collectives and their modes of activity; (4) domestication of the eye triggered by transitions between domains of activity. Each building block of our theoretical discussion is empirically anchored to four episodes involving primary school students’ learning geometrical figures using the GGBot. To conclude, we focus on two basic concepts of geometrical thinking that unfold in the shift between domains.

Mathematical Creativity: Student Geometrical Figure Apprehension in Geometry Problem-Solving Using New Auxiliary Elements

<p style="text-align:justify">The definition of creativity among professional mathematicians and the definition of mathematical creativity in the classroom context are significantly different. The purpose of this study was to investigate the relationship between students’ mathematical creativity (i.e., cognitive flexibility) and figure apprehension when solving geometric problems with novel auxiliary features such as straight lines and curved lines. In other words, this study determined if geometry knowledge influenced mathematical creativity (cognitive flexibility) in problem-solving. Grade-12 students participated in the intervention. The high school that is the research topic attempts to equip students with academic abilities and is, except for vocational schools, the most popular form of high school among all other types. Such a school was chosen for the study so that a significant proportion of students in Makassar could be represented. In this study, we discovered a relationship between cognitive flexibility and the geometric ability of pupils while solving problems involving auxiliary lines. This indicates that the usage of auxiliary lines as a reference for developing pupils’ creative thinking skills must be advocated. In addition, good geometric abilities (e.g., visual thinking, geometrical reasoning) will encourage pupils to generate various problem-solving concepts. This finding contributes significantly to future research by focusing on auxiliary lines.</p>

The Shape Entropy of Small Bodies

The irregular shapes of small bodies usually lead to non-uniform distributions of mass, which makes dynamic behaviors in the vicinities of small bodies different to that of planets. This study proposes shape entropy (SE) as an index that compares the shapes of small bodies and spheres to describe the shape of a small body. The results of derivation and calculation of SE in two-dimensional and three-dimensional cases show that: SE is independent of the size of geometric figures but depends on the shape of the figures; the SE difference between a geometric figure and a circle or a sphere, which is the limit of SE value, reflects the difference between this figure and a circle or a sphere. Therefore, the description of shapes of small bodies, such as near-spherical, ellipsoid, and elongated, can be quantitatively described via a continuous index. Combining SE and the original inertia index, describing the shape of small bodies, can define the shapes of small bodies and provide a reasonably simple metric to describe a complex shape that is applicable to generalized discussion and analysis rather than highly detailed work on a specific, unique, polyhedral model.

Comparison of Seed Images with Geometric Models, an Approach to the Morphology of Silene (Caryophyllaceae)

Seed morphological description is traditionally based on adjectives, which originated from the comparison with other shapes, including geometric figures. Nevertheless, descriptions based on this feature are not quantitative and measurements giving the percentage of similarity of seeds with reference figures are not available in the literature. Lateral views of Silene seeds resemble the cardioid and cardioid-derived figures. Dorsal views, nonetheless, resemble ellipses and derivatives, allowing seed shape quantification by comparison with defined geometric figures. In this work, we apply already-described models as well as new models to the morphological analysis of 51 Silene species. Our data revealed the existence of a link between lateral and dorsal models. Lateral models closed in the hilum region (models LM2 and LM4) were associated with those convex models of the dorsal seed views (DM1-DM4, DM10). Lateral models more open around the hilum region adjusted to seeds characterized as dorso canaliculata type better, i.e., to those geometric models with partial concavities in their dorsal views. The relationship between lateral and dorsal models, as well as between the models to their utility in taxonomy, is discussed.