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Group action analysis developed and applied mainly by Louis Michel to the study of N-dimensional periodic lattices is the central subject of the book. Di erent basic mathematical tools currently used for the description of lattice geometry are introduced and illustrated through applications to crystal structures in two- and three-dimensional space, to abstract multi-dimensional lattices and to lattices associated with integrable dynamical systems. Starting from general Delone sets the authors turn to di erent symmetry and topological classi- cations including explicit construction of orbifolds for two- and three-dimensional point and space groups. Voronoï and Delone cells together with positive quadratic forms and lattice description by root systems are introduced to demonstrate alternative approaches to lattice geometry study. Zonotopes and zonohedral families of 2-, 3-, 4-, 5-dimensional lattices are explicitly visualized using graph theory approach.
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In the theory of stationary spatial point processes, Palm distributions are used to describe the point process seen from one of its points. Such an intrinsic frame of reference is not only interesting for theoretical considerations, but also useful in related fields such as queuing theory and stochastic geometry.
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To celebrate the 270th anniversary of the De Gruyter publishing house, the company is providing permanent open access to 270 selected treasures from the De Gruyter Book Archive. Titles will be made available to anyone, anywhere at any time that might be interested. The DGBA project seeks to digitize the entire backlist of titles published since 1749 to ensure that future generations have digital access to the high-quality primary sources that De Gruyter has published over the centuries.
Geometry, Hyperbolic. --- Hyperbolic geometry --- Lobachevski geometry --- Lobatschevski geometry --- Geometry, Non-Euclidean
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This open access book covers the main topics for a course on the differential geometry of curves and surfaces. Unlike the common approach in existing textbooks, there is a strong focus on variational problems, ranging from elastic curves to surfaces that minimize area, or the Willmore functional. Moreover, emphasis is given on topics that are useful for applications in science and computer graphics. Most often these applications are concerned with finding the shape of a curve or a surface that minimizes physically meaningful energy. Manifolds are not introduced as such, but the presented approach provides preparation and motivation for a follow-up course on manifolds, and topics like the Gauss-Bonnet theorem for compact surfaces are covered.
Geometria diferencial --- Geometry, Differential. --- Differential Geometry.
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O livro "GEOMETRIA E TECNOLOGIA: visitando alternativas metodológicas para a sala de aula" tem por objetivo discutir perspectivas metodológicas para o ensino de geometria, em especial, no contexto da educação básica. Busca a ressignificação do ensino das noções sobre Espaço e Forma, ainda marcado por simbolismo lógico-formal precoce e raramente apropriado pelos educandos. Situando o trabalho didático-pedagógico no contexto da modelagem de situações matemáticas e de uso de ferramentas tecnológicas como o GeoGebra, um software livre cuja funcionalidade permite aos estudantes relacionar teoria e prática no contexto da resolução de problemas, adota a geometria como objeto de estudo e de investigação. Trata-se de obra de interesse tanto para professores que ensinam Matemática nas diversas instâncias da educação como para profissionais das redes de ensino envolvidos com orientação técnico-pedagógica e formação inicial ou continuada de educadores. Concebendo a apropriação significativa do fato geométrico como resultante de um processo de investigação e de resolução de problemas, procura evidenciar que a aprendizagem matemática pode ser prazerosa, quando compreendida como fazer humano criativo cuja gênese se situa na geração de ideias, articulação e negociação de significados.
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The aim of this book is to present recent results in both theoretical and applied knot theory-which are at the same time stimulating for leading researchers in the field as well as accessible to non-experts. The book comprises recent research results while covering a wide range of different sub-disciplines, such as the young field of geometric knot theory, combinatorial knot theory, as well as applications in microbiology and theoretical physics.
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Title in English: Construction Tasks: Textbook for Students of Mathematics Teaching at the 2nd Level of Primary School. The publication presents the problems of solving construction problems at primary school. It shows ways of solving basic construction problems and complex construction problems that are given at primary or secondary school. It deals with problems of solving construction problems in Geogebra.
Geometry --- construction problems --- geometry --- basic construction problems --- GeoGebra
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Geometry. --- Mathematics --- Euclid's Elements
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Despite being present in the National Indications, the teaching of solid geometry is often put in the background in common teaching practice for its conceptual difficulties and broad theoretical prerequisites. This volume aims to offer a proposal of constructive teaching of solid geometry based on the use of ZOMETOOL, an innovative teaching tool suitable for constructing both two-dimensional and three-dimensional figures. The methodology adopted is that of the mathematics laboratory, guided by cards, in order to stimulate discussion among students in individual groups, focusing both on the motivational lever given by the discovery and on the autonomous construction of mathematical meanings. The volume presents the activities proposed in the 2013/14 and 2014/15 school years in various secondary schools in the province of Turin and the results of the students and the critical issues that emerged during the work are analyzed. This work is therefore configured as a tool to guide the teacher in carrying out the activities in the classroom and to provide useful tips for the design of new learning courses.
Mathematics. --- Geometry. --- matematica --- zoometrol --- geometria
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