Interaction with constraints in 3D modeling

Journal ArticleInteractive geometric modeling is an important part of the industrial product design process. This paper describes how constraints can be used to facilitate the interactive definition of geometric objects and assemblies. We have implemented a geometric modeling system that combines the definition of objects by interactive construction operations and specification of geometric constraints. The modeling operations automatically generate constraints to maintain the properties intended by their invocation, and constraints, in turn, determine the degrees of freedom for further interactive mouse-controlled modeling operations. A symbolic geometry constraint solver is employed for solving systems of constraints

AN INVESTIGATION ABOUT HIGH SCHOOL MATHEMATICS TEACHERS' BELIEFS ABOUT TEACHING GEOMETRY

There continues to exist a dilemma about how, why and when geometry should be taught. The aim of this study was to examine high school mathematics teachers' beliefs about geometry and its teaching with respect to its role in the curriculum, the uses of manipulatives and dynamic geometry software in the classroom, and the role of proofs. In this study belief is taken as subjective knowledge (Furinghetti and Pehkonen, 2002). Data were collected from 520 teachers using questionnaires that included both statements that required responses on a Likert scale and open-ended questions. Also an intervention case study was conducted with one teacher. A three factor solution emerged from the analysis that revealed a disposition towards activities, a disposition towards an appreciation of geometry and its applications and a disposition towards abstraction. These results enabled classification of teachers into one of eight groups depending on whether their scores were positive or negative on the three factors. Knowing the teacher typology allows for appropriate professional development activities to be undertaken. This was done in the case study where techniques for scaffolding proofs were used as an intervention for a teacher who had a positive disposition towards activities and appreciation of geometry and its applications but a negative disposition towards abstraction. The intervention enabled the teacher successfully to teach her students how to understand and construct proofs. The open-ended responses on the questionnaire were analysed to obtain a better understanding of the teachers' beliefs. Four themes, the formal, intuitive, utilitarian and the mathematical, emerged from the analysis, which support the modal arguments given by Gonzalez and Herbst (2006). The findings reveal a disconnect between some high school teachers' beliefs about why geometry is important to study and the current position of the Standards Movement; and between whether geometry should be taught as part of an integrated curriculum or as a one-year course

Surface Comparison with Mass Transportation

We use mass-transportation as a tool to compare surfaces (2-manifolds). In particular, we determine the "similarity" of two given surfaces by solving a mass-transportation problem between their conformal densities. This mass transportation problem differs from the standard case in that we require the solution to be invariant under global M\"obius transformations. Our approach provides a constructive way of defining a metric in the abstract space of simply-connected smooth surfaces with boundary (i.e. surfaces of disk-type); this metric can also be used to define meaningful intrinsic distances between pairs of "patches" in the two surfaces, which allows automatic alignment of the surfaces. We provide numerical experiments on "real-life" surfaces to demonstrate possible applications in natural sciences

A Comparison of Problem-Centered Learning Model and Guided-Practice Model on High-School Students\u27 Mathematics Performance and Attitude

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Psychological Mechanisms Underlying Second Language Fluency

Fluency in a second language is considered important by both learners and teachers, but is not well understood. This paper describes what is known about second language fluency and describes a number of psychological learning mechanisms that might explain how fluency develops. These include the mechanisms underlying the contrast between automatic and controlled processing, the learning mechanisms postulated within Anderson's ACT"' theory of cognition, Bialystok's conception of the control dimension of language development, the notion of restructuring, recent proposals for the redefinition of automaticity as retrieval from memory, both instance and strength versions, and chunking theories. The paper concludes with some suggestions for research into the development of second language fluency itself that can fill gaps in existing knowledge and reduce our dependence on other fields for explanatory principles, while contributing simultaneously to discussion of the mechanisms responsible for skill development in general

Mellin-Barnes Integrals: A Primer on Particle Physics Applications

We discuss the Mellin-Barnes representation of complex multidimensional integrals. Experiments frontiered by the High-Luminosity Large Hadron Collider at CERN and future collider projects demand the development of computational methods to achieve the theoretical precision required by experimental setups. In this regard, performing higher-order calculations in perturbative quantum field theory is of paramount importance. The Mellin-Barnes integrals technique has been successfully applied to the analytic and numerical analysis of integrals connected with virtual and real higher-order perturbative corrections to particle scattering. Easy-to-follow examples with the supplemental online material introduce the reader to the construction and the analytic, approximate, and numeric solution of Mellin-Barnes integrals in Euclidean and Minkowskian kinematic regimes. It also includes an overview of the state-of-the-art software packages for manipulating and evaluating Mellin-Barnes integrals. These lecture notes are for advanced students and young researchers to master the theoretical background needed to perform perturbative quantum field theory calculations.Comment: This is a preprint of the following work: Ievgen Dubovyk, Janusz Gluza and Gabor Somogyi, Mellin-Barnes Integrals: A Primer on Particle Physics Applications, 2022, Springer reproduced with permission of Springer Nature Switzerland AG. 280 page

Aspects of the structure of Modernist poetry, 1908-1918 : a structural and comparative study of the poetic writing of Guillaume Apollinaire, Hans Arp, Hugo Ball, Georg Heym, T.E. Hulme, Max Jacob, Ezra Pound, Pierre Reverdy, and Georg Trakl

This dissertation offers a structural and comparative investigation into some of the 'principles of construction' operative in Modernist poetry in the English, French and German language areas in the first decades of the twentieth century. While the general scope of the study is fairly broad, its thematic focus is restricted to questions of poetic structuration and related theoretical issues. The method of analysis and description leans towards Formalist and Structuralist approaches to literature, and incorporates a diachronic as well as a synchronic dimension. Taking as a starting-point, in chapter 1, the synthetic and idealist conception which informs Mallarmé's Symbolist poetic system, the main body of the work then explores, in the eight chapters which follow, the poetic theories and practices of a representative selection of Modernist poets (Apollinaire, Arp, Ball, Heym, Hulme, Jacob, Pound, Reverdy, Trakl). The central argument pursued throughout these chapters rests on the contention that the diverse and often highly paradoxical modes of Modernist poetic writing are to be understood in relation (in opposition) to the basic categories of the Mallarmean aesthetic. The Modernist repudiation, whether implicit or explicit, of the Symbolist norm represents much more than a stylistic reaction. It implies, within the larger series of 'the Modern', a major theoretical reorientation, the construction of a new, non-idealist poetic, and the replacement of a metaphorical by a metonymic conception of poetic writing. The result is a radically altered approach to the function and finality of poetic language, to the status and nature of the poem, to the relation between poem and poet, between the poem and reality, and between the poet and reality. It is this momentum of reconsideration and reassessment which defines the space within which the various modes of Modernism come into being. In practice, the Modernist poem develops a powerful internal dialectic between on the one hand an impulse towards fragmentation and deconstruction, and, on the other, a tendency to objectivation, control, and reconstruction. In the Expressionist branch, where the role of socio-cultural elements is a contributory factor, the first impulse is particularly in evidence, and reveals strong existential overtones. The more 'constructivist' movements (Cubism, Imagism, Vorticism) appear preoccupied with the notion of the poem as a self-sufficient, self-reflexive entity, appealing at the same time to complementary moments of classicism and exploration. The paradoxes inherent in both branches of Modernism are finally radicalized in the Dadaist venture, which presents the point where the Modernist reconsideration of the categories of poetic writing reaches its ultimate extreme, while simultaneously creating the conditions for its transcendence