Geometry in Action uses Sketchpad? to awaken student creativity through discovery-based learning. It supplements any college geometry course in which The Geometer's Sketchpad is used. All students must have access to The Geometer's Sketchpad.Each book is packaged with a CD-ROM for students that illustrates what is meant by geometry in action. Students explore 27 sketches prepared by the author to demonstrate Sketchpad's capabilities by dragging points to see shifts in graphs, by animating tesselations to create new patterns, and much, much more! Also included on this CD is the Poincare Disk, a Sketchpad file used to dig deeper into non-Euclidean geometry with The Geometer's Sketchpad.

Approach your problems from the right It isn't that they can't see the solution. It end and begin with the answers. Then, is that they can't see the problem. one day, perhaps you will fmd the final question. G. K. Chesterton, The Scandal of Father Brown 'The Point of a Pin'. 'The Hermit Clad in Crane Feathers' in R. Van Gulik's The Chinese Maze Murders. Growing specialization and diversification have brought a host of monographs and textbooks on increasingly specialized topics. However, the 'tree' of knowledge of mathematics and related fields does not grow only by putting forth new branches. It also happens, quite often in fact, that branches which were thought to be completely disparate are suddenly seen to be related. Further, the kind and level of sophistication of mathematics applied in various sciences has changed drastically in recent years: measure theory is used (non-trivially) in regional and theoretical economics; algebraic geo metry interacts with physics; the Minkowsky lemma, coding theory and the structure of water meet one another in packing and covering theory; quantum fields, crystal defects and mathematical progmmming profit from homotopy theory; Lie algebras are relevant to fIltering; and prediction and electrical engineering can use Stein spaces.

After an introduction to geometric algebra, and the necessary math concepts that are needed, the book examines a variety of applications in the field of cognitive systems using geometric algebra as the mathematical system. There is strong evidence that geobetric albegra can be used to carry out efficient computations at all levels in the cognitive system. Geometric algebra reduces the complexity of algebraic expressions and as a result, it improves algorithms both in speed and accuracy. The book is addressed to a broad audience of computer scientists, cyberneticists, and engineers. It contains computer programs to clarify and demonstrate the importance of geometric algebra in cognitive systems.

Summary A thorough revision of the bestselling Silverlight 4 in Action. This comprehensive guide teaches Silverlight from the ground up, covering all the new v. 5 features in depth. You'll also explore WCF RIA Services, MVVM, and more—with dozens of code samples you can use in Visual Studio 2010 or the free Visual Web Developer 2010 Express. About the Book This hands-on guide explores Silverlight from the ground up, covering every feature in rich, practical detail. It is readable and the coverage is comprehensive. You'll master networking, MVVM, and more—with dozens of code samples you can use in Visual Studio or the free Visual Web Developer Express. Silverlight 5 in Action teaches you how to build desktop-quality applications you can deploy on the web. Beginners will appreciate the progression from simple examples to full applications that employ good design and coding practices. Seasoned . NET developers will love how the sample code embraces and extends what they already know. Purchase of the print book comes with an offer of a free PDF, ePub, and Kindle eBook from Manning. Also available is all code from the book. What's Inside 2D and 3D graphics and animation Business application services, rules, and validation The MVVM pattern and testing Free appendixes (150 pages) available online A background in C# or VB.NET is helpful, but no knowledge of Silverlight or XAML is required. ============================================ Table of Contents PART 1 CORE SILVERLIGHT PART 2 CREATING THE USER INTERFACE PART 3 WORKING WITH DATA AND SERVICES PART 4 2D AND 3D GRAPHICS PART 5 MAKING THE MOST OF THE PLATFORM PART 6 BEST PRACTICES Introducing Silverlight XAML and the property system The application model and the plug-in Working with HTML and browsers Out-of-browser applications The security model and elevated trust Rendering, layout, and transforming Panels Human input Text fundamentals Editing plain and rich text Control basics and UserControls Animation and behaviors Resources, styles, and control templates Extensions, converters, custom controls, and panels Binding Data controls: DataGrid and DataForm Input validation Networking basics Working with SOAP services RESTful services with the ASP.NET Web API Working with XML, JSON, RSS, and Atom Duplex, sockets, and local connections Graphics and effects Working with images Introduction to 3D 3D lighting, texturing, and animation Pop-ups, windows, and full-screen applications Navigation Working with files and directories Printing COM, Native Extensions, and p-invoke Structuring and testing with the MVVM pattern Debugging your application The install experience and preloaders

The dense packing of microscopic spheres (i.e. atoms) is the basic geometric arrangement in crystals of mono-atomic elements with weak covalent bonds, which achieves the optimal ?known density? of B/û18. In 1611, Johannes Kepler had already ?conjectured? that B/û18 should be the optimal ?density? of sphere packings. Thus, the central problems in the study of sphere packings are the proof of Kepler's conjecture that B/û18 is the optimal density, and the establishing of the least action principle that the hexagonal dense packings in crystals are the geometric consequence of optimization of density. This important book provides a self-contained proof of both, using vector algebra and spherical geometry as the main techniques and in the tradition of classical geometry.

PostGIS in Action, Third Edition shows you how to solve real-world geodata problems. You’ll go beyond basic mapping, and explore custom functions for your applications. Summary In PostGIS in Action, Third Edition you will learn: An introduction to spatial databases Geometry, geography, raster, and topology spatial types, functions, and queries Applying PostGIS to real-world problems Extending PostGIS to web and desktop applications Querying data from external sources using PostgreSQL Foreign Data Wrappers Optimizing queries for maximum speed Simplifying geometries for greater efficiency PostGIS in Action, Third Edition teaches readers of all levels to write spatial queries for PostgreSQL. You’ll start by exploring vector-, raster-, and topology-based GIS before quickly progressing to analyzing, viewing, and mapping data. This fully updated third edition covers key changes in PostGIS 3.1 and PostgreSQL 13, including parallelization support, partitioned tables, and new JSON functions that help in creating web mapping applications. Purchase of the print book includes a free eBook in PDF, Kindle, and ePub formats from Manning Publications. About the technology PostGIS is a spatial database extender for PostgreSQL. It offers the features and firepower you need to take on nearly any geodata task. PostGIS lets you create location-aware queries with a few lines of SQL code, then build the backend for mapping, raster analysis, or routing application with minimal effort. About the book PostGIS in Action, Third Edition shows you how to solve real-world geodata problems. You’ll go beyond basic mapping, and explore custom functions for your applications. Inside this fully updated edition, you’ll find coverage of new PostGIS features such as PostGIS Window functions, parallelization of queries, and outputting data for applications using JSON and Vector Tile functions. What's inside Fully revised for PostGIS version 3.1 and PostgreSQL 13 Optimize queries for maximum speed Simplify geometries for greater efficiency Extend PostGIS to web and desktop applications About the reader For readers familiar with relational databases and basic SQL. No prior geodata or GIS experience required. About the author Regina Obe and Leo Hsu are database consultants and authors. Regina is a member of the PostGIS core development team and the Project Steering Committee. Table of Contents PART 1 INTRODUCTION TO POSTGIS 1 What is a spatial database? 2 Spatial data types 3 Spatial reference systems 4 Working with real data 5 Using PostGIS on the desktop 6 Geometry and geography functions 7 Raster functions 8 Spatial relationships PART 2 PUTTING POSTGIS TO WORK 9 Proximity analysis 10 PostGIS TIGER geocoder 11 Geometry and geography processing 12 Raster processing 13 Building and using topologies 14 Organizing spatial data 15 Query performance tuning PART 3 USING POSTGIS WITH OTHER TOOLS 16 Extending PostGIS with pgRouting and procedural languages 17 Using PostGIS in web applications

This volume presents the proceedings of the 2nd International Workshop on - gebraic Frames for the Perception and Action Cycle. AFPAC 2000. held in Kiel, Germany, 10–11 September 2000. The presented topics cover new results in the conceptualization, design, and implementation of visual sensor-based robotics and autonomous systems. Special emphasis is placed on the role of algebraic modelling in the relevant disciplines, such as robotics, computer vision, theory of multidimensional signals, and neural computation. The aims of the workshop are twofold: ?rst, discussion of the impact of algebraic embedding of the task at hand on the emergence of new qualities of modelling and second, facing the strong relations between dominant geometric problems and algebraic modelling. The ?rst workshop in this series, AFPAC’97. inspired several groups to i- tiate new research programs, or to intensify ongoing research work in this ?eld, and the range of relevant topics was consequently broadened, The approach adopted by this workshop does not necessarily ?t the mainstream of worldwide research-granting policy. However, its search for fundamental problems in our ?eld may very well lead to new results in the relevant disciplines and contribute to their integration in studies of the perception–action cycle.

Over the last twenty-five years Ernst von Glasersfeld has had a tremendous impact on mathematics and science education through his fundamental insights into the nature of knowledge and knowing. Radical Constructivism in Action is a new volume of papers honouring his work by building on his model of knowing. The contributions by leading researchers present constructivism in action, tying the authors' actions regarding practical problems of mathematics and science education, philosophy, and sociology to their philosophical constraints, giving meaning to constructivism operationally. The book begins with a retrospective analogy between radical constructivism's emergence and changes in what is thought of as "certain" scientific knowledge. It aims to increase understanding of constructivism and Glasersfeld's achievement, and is vibrant evidence of the continued vitality of research in the constructivism tradition.

This study provides a historical analysis of Freudenthal’s didactic ideas and his didactic career. It is partly biographical, but also contributes to the historiography of mathematics education and addresses closely related questions such as: what is mathematics and where does it start? Which role does mathematics play in society and what influence does it have on the prevailing views concerning its accompanying didactics?. Hans Freudenthal (1905–1990), professor in mathematics, scientist, literator, but above all mathematics-educator, was inextricably linked to the changes which took place in mathematics education and didactics during the second half of the last century. His diversity as a scientist and his inexhaustible efforts to establish the didactics of mathematics as a seriously pursued science, made Freudenthal's influence in this area considerable. He foresaw an essential, practical role for mathematics in everyone’s life, encouraging students to discover and create mathematics themselves, instead of imposing a ready-made mathematical system. The theory of mathematics education thus developed in the Netherlands would gain world fame in the following decades. Today, in the light of the discussions about mathematics education, in which the call for `genuine’ mathematics instead of the so-called 'kindergarten'-mathematics can be heard, Freudenthal's approach seems to be passé. However, the outcome of this study (which is mainly based on documents from Freudenthal’s vast personal archive) shows a more refined picture. The direct identification of 'kindergarten'-mathematics with Freudenthal’s view on mathematics education is not justified. 'Realistic mathematics' as advocated by Freudenthal includes more than just a practical introductory and should, among other things, always aim at teaching 'genuine' mathematics in the end.