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This book aims to make the subject of geometry and its applications easy and comfortable to understand by students majoring in mathematics or the liberal arts, architecture and design. It can be used to teach students at different levels of computational ability and there is also sufficient novel material to interest students at a higher cognitive level. While the book goes deeply into the applications of geometry, it contains much introductory material which up to now may not have been known to the student. The constructive approach using compass and straightedge engages students, not just on an intellectual level, but also at a tactile level. This may be the only rigorous book offering geometry that attempts to engage students outside of the mathematics discipline.
This book is meant to serve either as a textbook for an interdisciplinary course in Mathematics of Design, or as a trade book for designers. It will also be of interest for people interested in recreational mathematics showing the connection between mathematics and design. Topics from the book can also be adapted for use in pre-college mathematics. Each chapter will provide the user with ideas that can be incorporated in a design. Background materials will be provided to show the reader the mathematical principles that lie behind the designs.
Extensive work is a result of four year research within the international project Women's Creativity since the Modern Movement, and brings new insights into women in architecture, construction, design, urban planning and landscape architecture in Europe and in the rest of the world. It is divided into eight chapters that combine 116 articles on topics: A. Women’s education and training: National and international mappings; B. Women’s legacy and heritage: Protection, restoration and enhancement; C. Women in communication and professional networks; D. Women and cultural tourism; E. Women’s achievements and professional attainments: Moving boundaries; F. Women and sustainability: City and Landscape; G. Women ‘as subjects’: Documentation, methodology, interpretation and enhancement; SG. Design drawings. / Obsežno delo je plod štiriletnih raziskav v okviru mednarodnega projekta MoMoWo - Ženska ustvarjalnost od modernizma dalje in prinaša nova spoznanja na področju žensk v arhitekturi, gradbeništvu, oblikovanju, urbanizmu in krajinski arhitekturi v Evropi in širše. Razdeljena je v osem poglavij, ki združujejo 116 prispevkov na temo o njihovi izobraženosti, kulturni zapuščini, vključevanju v stanovska združenja ali njihovim prispevkom h kulturnemu turizmu in stroki ter raziskovanju njihovega dela. Zaključi jo poglavje z grafičnimi prilogami.
The geometry of Hessian structures is a fascinating emerging field of research. It is in particular a very close relative of Knhlerian geometry, and connected with many important pure mathematical branches such as affine differential geometry, homogeneous spaces and cohomology. The theory also finds deep relation to information geometry in applied mathematics. This systematic introduction to the subject first develops the fundamentals of Hessian structures on the basis of a certain pair of a flat connection and a Riemannian metric, and then describes these related fields as applications of the theory."
This book consists of essays that stand on their own but are also loosely connected. Part I documents how numbers and geometry arise in several cultural contexts and in nature: scale, proportion in architecture, ancient geometry, megalithic stone circles, the hidden pavements of the Laurentian library, the shapes of the Hebrew letters, and the shapes of biological forms. Part II shows how many of the same numbers and number sequences are related to the modern mathematical study of numbers, dynamical systems, chaos, and fractals.
Virtual reality (VR) is one of the technologies with the highest expectations for future growth. By creating realistic images and objects, a VR environment gives the user the impression that they are completely engrossed in their surroundings. VR applications that go beyond leisure, tourism, and marketing are now in high demand and thus the technology must be user-friendly and economical. The major technology firms are already striving to create headsets that do not require cables and that allow for high-definition viewing. Artificial intelligence is being used to control VR headsets that have far more powerful CPUs. The new standard will also offer some intriguing capabilities, like the ability to connect huge user communities and additional gadgets. Customers will be able to get photos in real-time in corporate settings, almost as if they were seeing them with their own eyes. This book presents a comprehensive overview of VR applications in medicine, electric vehicles, aviation, architecture, and more.
This book explores democracy beyond the governmental structures and focuses on participatory governance in particular. It demonstrates that we need to change the way we think about democracy and our notion of democracy has to be re-conceptualised.
This volume covers many topics, including number theory, Boolean functions, combinatorial geometry, and algorithms over finite fields. It contains many new, theoretical and applicable results, as well as surveys that were presented by the top specialists in these areas. New results include an answer to one of Serre's questions, posted in a letter to Top; cryptographic applications of the discrete logarithm problem related to elliptic curves and hyperelliptic curves; construction of function field towers; construction of new classes of Boolean cryptographic functions; and algorithmic applications of algebraic geometry.
Energy of knots is a theory that was introduced to create a "canonical configuration" of a knot - a beautiful knot which represents its knot type. This book introduces several kinds of energies, and studies the problem of whether or not there is a "canonical configuration" of a knot in each knot type. It also considers this problem in the context of conformal geometry. The energies presented in the book are defined geometrically. They measure the complexity of embeddings and have applications to physical knotting and unknotting thorough numerical experiments.
Number Theory Through Inquiry is an innovative textbook that leads students on a carefully guided discovery of introductory number theory. The book has two equally significant goals. One goal is to help students develop mathematical thinking skills, particularly, theorem-proving skills. The other goal is to help students understand some of the wonderfully rich ideas in the mathematical study of numbers. This book is appropriate for a proof transitions course, for an independent study experience, or for a course designed as an introduction to abstract mathematics. Math or related majors, future teachers, and students or adults interested in exploring mathematical ideas on their own will enjoy Number Theory Through Inquiry. Number theory is the perfect topic for an introduction-to-proofs course. Every college student is familiar with basic properties of numbers, and yet the exploration of those familiar numbers leads us to a rich landscape of ideas. Number Theory Through Inquiry contains a carefully arranged sequence of challenges that lead students to discover ideas about numbers and to discover methods of proof on their own. It is designed to be used with an instructional technique variously called guided discovery or Modified Moore Method or Inquiry Based Learning (IBL). Instructors' materials explain the instructional method. This style of instruction gives students a totally different experience compared to a standard lecture course. Here is the effect of this experience: Students learn to think independently: they learn to depend on their own reasoning to determine right from wrong; and they develop the central, important ideas of introductory number theory on their own. From that experience, they learn that they can personally create important ideas, and they develop an attitude of personal reliance and a sense that they can think effectively about difficult problems. These goals are fundamental to the educational enterprise within and beyond mathematics.