Author(s):  
Scott M. Miller

As is well known, analysis of two surfaces in mesh plays a fundamental role in gear theory. In the past, special coordinate systems, vector algebra, or screw theory was used to analyze the kinematics of meshing. The approach here instead relies on geometric algebra, an extension of conventional vector algebra. The elegance of geometric algebra for theoretical developments is demonstrated by examining the so-called “equation of meshing,” which requires that the relative velocity of two bodies at a point of contact be perpendicular to the common surface normal vector. With surprisingly little effort, several alternative forms of the equation of meshing are generated and, subsequently, interpreted geometrically. Via straightforward algebraic manipulations, the results of screw theory and vector algebra are unified. Due to the simplicity with which complex geometric concepts are expressed and manipulated, the effort required to grasp the general three-dimensional meshing of surfaces is minimized.


Author(s):  
Nazokat Abidova ◽  

The scientific-theoretical bases of interdisciplinary formation of geometric concepts for students with intellectual disabilities are analyzed. The content of pedagogical-corrective work on interdisciplinary formation of geometric concepts for students with intellectual disabilities is covered.


2017 ◽  
Vol 48 (2) ◽  
pp. 177-186 ◽  
Author(s):  
D. W. Joyce ◽  
D. K. Tracy ◽  
S. S. Shergill

Clinical trials in psychiatry inherit methods for design and statistical analysis from evidence-based medicine. However, trials in other clinical disciplines benefit from a more specific relationship between instruments that measure disease state (e.g. biomarkers, clinical signs), the underlying pathology and diagnosis such that primary outcomes can be readily defined. Trials in psychiatry use diagnosis (i.e. a categorical label for a syndrome) as a proxy for the underlying disorder, and outcomes are defined, for example, as a percentage change in a univariatetotal scoreon some clinical instrument. We label this approach to defining outcomesweak aggregationof disease state. Univariate measures are necessary, because statistical methodology is both tractable and well-developed for scalar outcomes, but we show that weak aggregate approaches do not capture disease state sufficiently, potentially leading to loss of information about response to intervention. We demonstrate how multivariate disease state can be captured using geometric concepts of spaces defined over routine clinical instruments, and show how clinically meaningful disease states (e.g. representing different profiles of symptoms, recovery or remission) can be defined as prototypes (geometric locations) in these spaces. Then, we show how to derive univariate (scalar) measures, which capture patient's relationships to these prototypes and argue these representstrong aggregatesof disease state that may be a better basis for outcome measures. We demonstrate our proposal using a large publically available dataset. We conclude by discussing the impact of strong aggregates for analyses in traditional and novel trial designs.


2020 ◽  
pp. 1-14
Author(s):  
Ciaran McMorran

This chapter explores how James Joyce evokes an overarching concern with the linear in his works, both formally (in terms of the Euclidean ideal of rectilinearity) and conceptually (in terms of linear narratives, histories, arguments, modes of thought, etc.). In particular, it considers how the non-linearity of Joyce’s works reflects a wider questioning of the straight line in modernist literature which followed the development of non-Euclidean geometries in the nineteenth and twentieth centuries. This chapter also provides an overview of the geometric babble which entered into the context of Joyce’s writing following the popularization of non-Euclidean geometry in modernist art and literature, as well as the “fashionable nonsense” associated with the application of geometric concepts in contemporary literary criticism. By referring to the source texts which informed Joyce’s articulation of multiple geometric registers, it traces his engagement with non-Euclidean geometry to his early readings of Giordano Bruno’s mathematical and philosophical works, illustrating how notions associated with the curvature of the straight line inform the structural composition of Ulysses and Finnegans Wake.


Author(s):  
Ján Guncaga ◽  
László Budai ◽  
Tibor Kenderessy

There are problems in geometry education in lower and upper secondary school, which students have with the spatial imagination and with the understanding of some geometric concepts. In this article, we want to present tasks that show some advantages of the software GeoGebra. We use this software as a tool to visualize and to explain some geometric concepts, as well as to support students’ spatial imagination. Classification: D30, G10. Keywords: space imagination, GeoGebra, mathematics education at lower and upper secondary level.


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