Diagram Geometry

Author : Francis Buekenhout,Arjeh M. Cohen
Publisher : Springer Science & Business Media
Page : 597 pages
File Size : 53,6 Mb
Release : 2013-01-26
Category : Mathematics
ISBN : 9783642344534

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Diagram Geometry by Francis Buekenhout,Arjeh M. Cohen Pdf

This book provides a self-contained introduction to diagram geometry. Tight connections with group theory are shown. It treats thin geometries (related to Coxeter groups) and thick buildings from a diagrammatic perspective. Projective and affine geometry are main examples. Polar geometry is motivated by polarities on diagram geometries and the complete classification of those polar geometries whose projective planes are Desarguesian is given. It differs from Tits' comprehensive treatment in that it uses Veldkamp's embeddings. The book intends to be a basic reference for those who study diagram geometry. Group theorists will find examples of the use of diagram geometry. Light on matroid theory is shed from the point of view of geometry with linear diagrams. Those interested in Coxeter groups and those interested in buildings will find brief but self-contained introductions into these topics from the diagrammatic perspective. Graph theorists will find many highly regular graphs. The text is written so graduate students will be able to follow the arguments without needing recourse to further literature. A strong point of the book is the density of examples.

Author : Malcolm Stewart
Publisher : Simon and Schuster
Page : 591 pages
File Size : 53,7 Mb
Release : 2022-09-27
Category : Body, Mind & Spirit
ISBN : 9781644114315

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Sacred Geometry of the Starcut Diagram by Malcolm Stewart Pdf

• Lavishly illustrated with hundreds of detailed diagrams and technical illustrations exploring the evolution and importance of the starcut diagram • Shows how the starcut diagram underlies the shaman’s dance in China, the Vedic Fire Altar in India, Raphael frescoes, labyrinth designs, the Great Pyramid in Egypt, and the building of ancient cities • Explains how the starcut diagram was used in building and design, how it relates to Pythagoras’s Tetrakys, and how it contains knowledge of the Tree of Life As Malcolm Stewart reveals in this lavishly illustrated study, the simplesquare figure of the Starcut diagram, created only with circles, has extraordinary geometric properties. It allows you to make mathematically exact measurements and build perfectly true level structures without a computer, calculator, slide rule, plumb bob, or laser level. Sharing his extensive research, along with hundreds of detailed diagrams and technical illustrations, the author shows how the Starcut diagram was the key to the building of humanity’s first cities and how it underlies many significant patterns and proportions around the world. Using circles drawn from the vesica piscis, Stewart explains how to create the Starcut diagram and shows how this shape was at the foundation of ancient building and design, illustrating the numerous connections between the diagram and the creation of mandalas and yantras, stained glass windows, architectural ground plans, temples and other sacred buildings, and surveying methods. He also shows how the Starcut diagram reveals ancient geometric knowledge of pi, the Fibonacci sequence, Pythagorean shapes and seals, the golden ratio, the power of 108 and other sacred numbers, and magic squares. Exploring the Starcut diagram’s cosmological and theological implications, Stewart explains how it contains knowledge of the Tree of Life and the Kabbalah. He examines how it relates to the Tetraktys, the key teaching device of Pythagoras, and other cosmograms. Demonstrating the ancient relationships existing between number, geometry, cosmology, and musical harmony, the author shows how the simple shape of the Starcut diagram unifies the many threads of sacred geometry into one beautiful mathematical tapestry.

Author : Mark de Berg
Publisher : Springer Science & Business Media
Page : 388 pages
File Size : 47,5 Mb
Release : 2008-03-07
Category : Computers
ISBN : 9783540779735

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Computational Geometry by Mark de Berg Pdf

This introduction to computational geometry focuses on algorithms. Motivation is provided from the application areas as all techniques are related to particular applications in robotics, graphics, CAD/CAM, and geographic information systems. Modern insights in computational geometry are used to provide solutions that are both efficient and easy to understand and implement.

Author : Reinhard Klette,Azriel Rosenfeld
Publisher : Elsevier
Page : 675 pages
File Size : 43,9 Mb
Release : 2004-09-04
Category : Computers
ISBN : 9780080477268

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Digital Geometry by Reinhard Klette,Azriel Rosenfeld Pdf

Digital geometry is about deriving geometric information from digital pictures. The field emerged from its mathematical roots some forty-years ago through work in computer-based imaging, and it is used today in many fields, such as digital image processing and analysis (with applications in medical imaging, pattern recognition, and robotics) and of course computer graphics. Digital Geometry is the first book to detail the concepts, algorithms, and practices of the discipline. This comphrehensive text and reference provides an introduction to the mathematical foundations of digital geometry, some of which date back to ancient times, and also discusses the key processes involved, such as geometric algorithms as well as operations on pictures. *A comprehensive text and reference written by pioneers in digital geometry, image processing and analysis, and computer vision*Provides a collection of state-of-the-art algorithms for a wide variety of geometrical picture analysis tasks, including extracting data from digital images and making geometric measurements on the data*Includes exercises, examples, and references to related or more advanced work

Author : Mark Ryan
Publisher : John Wiley & Sons
Page : 218 pages
File Size : 41,7 Mb
Release : 2019-04-19
Category : Mathematics
ISBN : 9781119590460

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Geometry Essentials For Dummies by Mark Ryan Pdf

Geometry Essentials For Dummies (9781119590446) was previously published as Geometry Essentials For Dummies (9781118068755). While this version features a new Dummies cover and design, the content is the same as the prior release and should not be considered a new or updated product. Just the critical concepts you need to score high in geometry This practical, friendly guide focuses on critical concepts taught in a typical geometry course, from the properties of triangles, parallelograms, circles, and cylinders, to the skills and strategies you need to write geometry proofs. Geometry Essentials For Dummies is perfect for cramming or doing homework, or as a reference for parents helping kids study for exams. Get down to the basics — get a handle on the basics of geometry, from lines, segments, and angles, to vertices, altitudes, and diagonals Conquer proofs with confidence — follow easy-to-grasp instructions for understanding the components of a formal geometry proof Take triangles in strides — learn how to take in a triangle's sides, analyze its angles, work through an SAS proof, and apply the Pythagorean Theorem Polish up on polygons — get the lowdown on quadrilaterals and other polygons: their angles, areas, properties, perimeters, and much more

Author : Hoon Hong,Dongming Wang
Publisher : Springer
Page : 213 pages
File Size : 44,6 Mb
Release : 2006-02-08
Category : Computers
ISBN : 9783540313632

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Automated Deduction in Geometry by Hoon Hong,Dongming Wang Pdf

This book presents the thoroughly refereed post-proceedings of the 5th International Workshop on Automated Deduction in Geometry, ADG 2004, held at Gainesville, FL, USA in September 2004. The 12 revised full papers presented aurvey current issues theoretical and methodological topics as well as applications thereof - in particular automated geometry theorem proving, automated geometry problem solving, problems of dynamic geometry, and an object-oriented language for geometric objects.

Author : Mateusz Hohol
Publisher : Routledge
Page : 188 pages
File Size : 40,6 Mb
Release : 2019-09-12
Category : Psychology
ISBN : 9780429508592

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Foundations of Geometric Cognition by Mateusz Hohol Pdf

The cognitive foundations of geometry have puzzled academics for a long time, and even today are mostly unknown to many scholars, including mathematical cognition researchers. Foundations of Geometric Cognition shows that basic geometric skills are deeply hardwired in the visuospatial cognitive capacities of our brains, namely spatial navigation and object recognition. These capacities, shared with non-human animals and appearing in early stages of the human ontogeny, cannot, however, fully explain a uniquely human form of geometric cognition. In the book, Hohol argues that Euclidean geometry would not be possible without the human capacity to create and use abstract concepts, demonstrating how language and diagrams provide cognitive scaffolding for abstract geometric thinking, within a context of a Euclidean system of thought. Taking an interdisciplinary approach and drawing on research from diverse fields including psychology, cognitive science, and mathematics, this book is a must-read for cognitive psychologists and cognitive scientists of mathematics, alongside anyone interested in mathematical education or the philosophical and historical aspects of geometry.

Author : Dave Barker-Plummer,Richard Cox,Nik Swoboda
Publisher : Springer
Page : 304 pages
File Size : 43,9 Mb
Release : 2006-06-29
Category : Computers
ISBN : 9783540356240

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Diagrammatic Representation and Inference by Dave Barker-Plummer,Richard Cox,Nik Swoboda Pdf

Proceedings of the 4th International Conference on Theory and Application of Diagrams, Stanford, CA, USA in June 2006. 13 revised full papers, 9 revised short papers, and 12 extended abstracts are presented together with 2 keynote papers and 2 tutorial papers. The papers are organized in topical sections on diagram comprehension by humans and machines, notations: history, design and formalization, diagrams and education, reasoning with diagrams by humans and machines, and psychological issues in comprehension, production and communication.

Author : Antonio Pasini
Publisher : Unknown
Page : 280 pages
File Size : 50,9 Mb
Release : 2003
Category : Mathematics
ISBN : UOM:39015058702609

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Topics in Diagram Geometry by Antonio Pasini Pdf

Author : John C. Dixon
Publisher : John Wiley & Sons
Page : 434 pages
File Size : 40,5 Mb
Release : 2009-10-27
Category : Technology & Engineering
ISBN : 0470682892

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Suspension Geometry and Computation by John C. Dixon Pdf

Revealing suspension geometry design methods in unique detail, John Dixon shows how suspension properties such as bump steer, roll steer, bump camber, compliance steer and roll centres are analysed and controlled by the professional engineer. He emphasizes the physical understanding of suspension parameters in three dimensions and methods of their calculation, using examples, programs and discussion of computational problems. The analytical and design approach taken is a combination of qualitative explanation, for physical understanding, with algebraic analysis of linear and non-linear coefficients, and detailed discussion of computer simulations and related programming methods. Includes a detailed and comprehensive history of suspension and steering system design, fully illustrated with a wealth of diagrams Explains suspension characteristics and suspension geometry coefficients, providing a unique and in-depth understanding of suspension design not found elsewhere. Describes how to obtain desired coefficients and the limitations of particular suspension types, with essential information for suspension designers, chassis technicians and anyone else with an interest in suspension characteristics and vehicle dynamics. Discusses the use of computers in suspension geometry analysis, with programming techniques and examples of suspension solution, including advanced discussion of three-dimensional computational geometry applied to suspension design. Explains in detail the direct and iterative solutions of suspension geometry.

Author : Brendan Hassett,James McKernan,Jason Starr,Ravi Vakil
Publisher : American Mathematical Soc.
Page : 614 pages
File Size : 54,7 Mb
Release : 2013-09-11
Category : Mathematics
ISBN : 9780821889831

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A Celebration of Algebraic Geometry by Brendan Hassett,James McKernan,Jason Starr,Ravi Vakil Pdf

This volume resulted from the conference A Celebration of Algebraic Geometry, which was held at Harvard University from August 25-28, 2011, in honor of Joe Harris' 60th birthday. Harris is famous around the world for his lively textbooks and enthusiastic teaching, as well as for his seminal research contributions. The articles are written in this spirit: clear, original, engaging, enlivened by examples, and accessible to young mathematicians. The articles in this volume focus on the moduli space of curves and more general varieties, commutative algebra, invariant theory, enumerative geometry both classical and modern, rationally connected and Fano varieties, Hodge theory and abelian varieties, and Calabi-Yau and hyperkähler manifolds. Taken together, they present a comprehensive view of the long frontier of current knowledge in algebraic geometry. Titles in this series are co-published with the Clay Mathematics Institute (Cambridge, MA).

Author : Anonim
Publisher : Springer Science & Business Media
Page : 540 pages
File Size : 43,7 Mb
Release : 2024-06-28
Category : Electronic
ISBN : 0387953744

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Lectures on Discrete Geometry by Anonim Pdf

Author : Harold Abelson,Andrea Disessa
Publisher : MIT Press
Page : 502 pages
File Size : 43,7 Mb
Release : 1986-07-09
Category : Computers
ISBN : 0262510375

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Turtle Geometry by Harold Abelson,Andrea Disessa Pdf

Turtle Geometry presents an innovative program of mathematical discovery that demonstrates how the effective use of personal computers can profoundly change the nature of a student's contact with mathematics. Using this book and a few simple computer programs, students can explore the properties of space by following an imaginary turtle across the screen. The concept of turtle geometry grew out of the Logo Group at MIT. Directed by Seymour Papert, author of Mindstorms, this group has done extensive work with preschool children, high school students and university undergraduates.

Author : Michael Joswig,Nobuki Takayama
Publisher : Springer Science & Business Media
Page : 332 pages
File Size : 48,6 Mb
Release : 2013-03-14
Category : Mathematics
ISBN : 9783662051481

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Algebra, Geometry and Software Systems by Michael Joswig,Nobuki Takayama Pdf

A collection of surveys and research papers on mathematical software and algorithms. The common thread is that the field of mathematical applications lies on the border between algebra and geometry. Topics include polyhedral geometry, elimination theory, algebraic surfaces, Gröbner bases, triangulations of point sets and the mutual relationship. This diversity is accompanied by the abundance of available software systems which often handle only special mathematical aspects. This is why the volume also focuses on solutions to the integration of mathematical software systems. This includes low-level and XML based high-level communication channels as well as general frameworks for modular systems.

Author : Antonio Pasini
Publisher : Oxford University Press on Demand
Page : 488 pages
File Size : 43,9 Mb
Release : 1994
Category : Literary Criticism
ISBN : 0198534973

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Diagram Geometries by Antonio Pasini Pdf

Diagram geometry provides a range of techniques that enable an interaction between group theory and geometry. These techniques allow the mathematician to get information on a multi-dimensional geometric object from some knowledge of its bi-dimensional properties. This book introduces thesetechniques and provides a survey of the development of the subject of diagram geometry.The first three chapters are descriptive; a number of examples are presented, basic concepts are explained, and the reader is introduced to the language of diagram geometries.The theory is developed in the next three chapters and in chapter 7 a number of characterizations are proved. This is continued in later chapters following a survey of more advanced concepts and techniques.