Local Mathematics and No Information at a Distance; Some Effects on Physics and Geometry

Local mathematics consists of a collection of mathematical systems located at each space and time point. The collection is limited to the systems that include numbers in their axiomatic description. A scalar map between systems at different locations is based on the distinction of two conflated concepts, number and number value. The effect that this setup has on theory descriptions of physical and geometric systems is described. This includes a scalar spin 0 field in gauge theories, expectation values in quantum mechanics and path lengths in geometry. The possible relation of the scalar map to consciousness is noted.

Local Mathematics and No Information at a Distance; Some Effects on Physics and Geometry

Local mathematics consists of a collection of mathematical systems located at each space and time point. The collection is limited to the systems that include numbers in their axiomatic description. A scalar map between systems at different locations is based on the distinction of two conflated concepts, number and number value. The effect that this setup has on theory descriptions of physical and geometric systems is described. This includes a scalar spin 0 field in gauge theories, expectation values in quantum mechanics and path lengths in geometry. The possible relation of the scalar map to consciousness is noted.

S-Shaped Transition Curves as an Element of Reverse Curves in Road Design

A road designing involves horizontal and vertical alignment. The horizontal geometry is formed by straight and curvilinear sections that are traditionally formed using circular and transition curves (mainly the clothoid). Different geometric systems that are designed using circular and transition curves are between others circular curves with symmetrical or unsymmetrical clothoids, combined curves, oval curves and reverse curves. Designing these systems is quite complex. Therefore, so-called S-shaped transition curves are an alternative to traditional approaches. These curves are known from literature and are modern geometric tools for the shaping of reverse curves. The paper analyses the basic geometric properties of these curves as well as compare to the geometry of the appropriate geometric systems, which are formed with clothoid or using S-shaped transition curves. In addition, a procedure for designing reverse curves using S-shaped transition curves was proposed. Another research topic was the comparison of the analysed reverse curves (created using polynomial transition curves) with traditional curves (created using the clothoid). The results of the studies, despite the noticeable differences in the geometry of the compared components, confirm the practical usefulness of the S-shaped transition curves for designing the geometry of the route.

Eficacia del Diseño Universal de Aprendizaje para el fortalecimiento del pensamiento espacial y sistemas geométricos en estudiantes de primer grado / Effectiveness of the Universal Learning Design for the Strengthening of Space Thought and Geometric Systems in First Grade Students

ABSTRACTThis document approach the research phase of the Master's degree in mathematics didactics at the Caldas University, called comparative study between universal learning design and conventional methods as a strategy for strengthening spatial thinking and geometric systems in the children of the first grade of the Institución Educación Nuestra Señora del Rosario in Manzanares, (Caldas). The objective of this preliminary analysis is to evaluate the effectiveness of learning through the DUA and compare it with the traditional method.RESUMENEste documento abordó la fase de indagación del trabajo de grado de la Maestría en didáctica de la matemática de la Universidad de Caldas, denominado estudio comparativo entre el diseño universal de aprendizaje y los métodos convencionales como estrategia para el fortalecimiento del pensamiento espacial y los sistemas geométricos en los niños del grado primero de la Institución educativa Nuestra Señora del Rosario del municipio de Manzanares, (Caldas). El objetivo de este análisis preliminar consistió en evaluar la eficacia del aprendizaje por medio del DUA y compararlo con el método tradicional.

Studying the impact of amendments in the Polish guidelines on the values of basic geometric parameters of railway lines

The article discusses changes in domestic regulations related to de-signing geometric systems of railway lines. Also, a model of calculating the basic parameters of geometric systems performed for three different (extreme) design examples was presented. The calculations were performed according to two guidelines