Kategoria BISAC: Mathematics >> Geometry - General

This fascinating title reviews the teaching and learning of school geometry from the perspective of both the new teacher and the more experienced teacher. It is designed to extend and deepen subject knowledge and to offer practical advice and ideas for the classroom in the context of current practice and research. Particular emphasis is given to the following elements: Understanding the key ideas of the geometry curriculum. Learning geometry effectively: lessons from research and current practice. Misconceptions and errors. Geometry reasoning: problem solving and proving. The role of...

Based on the latest historical research, Worlds Out of Nothing is the first book to provide a course on the history of geometry in the 19th century. Topics covered in the first part of the book are projective geometry, especially the concept of duality, and non-Euclidean geometry. The book then moves on to the study of the singular points of algebraic curves (Plucker s equations) and their role in resolving a paradox in the theory of duality; to Riemann s work on differential geometry; and to Beltrami s role in successfully establishing non-Euclidean geometry as a rigorous mathematical...

An easily accessible introduction to over three centuries of innovations in geometry

Praise for the First Edition

-. . . a welcome alternative to compartmentalized treatments bound to the old thinking. This clearly written, well-illustrated book supplies sufficient background to be self-contained.- --CHOICE

This fully revised new edition offers the most comprehensive coverage of modern geometry currently available at an introductory level. The book strikes a welcome balance between academic rigor and accessibility, providing a complete and cohesive...

"This book covers many interesting topics not usually covered in a present day undergraduate course, as well as certain basic topics such as the development of the calculus and the solution of polynomial equations. The fact that the topics are introduced in their historical contexts will enable students to better appreciate and understand the mathematical ideas involved...If one constructs a list of topics central to a history course, then they would closely resemble those chosen here."

(David Parrott, Australian Mathematical Society)

This book...

This book is a comprehensive collection of known results about the Lozi map, a piecewise-affine version of the Henon map. Henon map is one of the most studied examples in dynamical systems and it attracts a lot of attention from researchers, however it is difficult to analyze analytically. Simpler structure of the Lozi map makes it more suitable for such analysis. The book is not only a good introduction to the Lozi map and its generalizations, it also summarizes of important concepts in dynamical systems theory such as hyperbolicity, SRB measures, attractor types, and more.

Written by students for students, Bridging the Gap to University Mathematics is a refreshing, new approach to making the transition into undergraduate-level mathematics or a similar numerate degree. Suitable for students of all backgrounds, whether A-level, Scottish Higher, International Baccalaureate or similar, the book helps readers to shape their existing knowledge and build upon current strengths in order to get the most out of their undergraduate studies.

The book can be used as a source of private study before embarking on a degree or as a textbook for an introductory...

Cinderella.2, the new version of the well-known interactive geometry software, has become an even more versatile tool than its predecessor. The geometry component extends the functionality to such spectacular objects as dynamic fractals, and the software includes two major new components: physical simulation such as of mechanical objects, virtual electronic devices, and electromagnetic properties. Cinderella.2 Documentation offers complete instruction and techniques for using Cinderella.2.

By virtue of their special algebraic structures, Pythagorean-hodograph (PH) curves offer unique advantages for computer-aided design and manufacturing, robotics, motion control, path planning, computer graphics, animation, and related fields. This book offers a comprehensive and self-contained treatment of the mathematical theory of PH curves, including algorithms for their construction and examples of their practical applications. Special features include an emphasis on the interplay of ideas from algebra and geometry and their historical origins, detailed algorithm descriptions, and many...