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The Intuitive Geometry method is a basic set of principles for using overlapping circles to create and design anything. The method includes the circle, square, triangle, hexagon, pentagon, spirals, waves, and scaling. The 2nd Edition of the book includes more detailed step by step instructions for the Intuitive Geometry method, ten examples of applying the method with detailed step by step instructions, and forty artworks to showcase the Intuitive Geometry method. The ten examples are: Bees, Butterflies, Flowers (3 fold), Flowers (4 fold), Flowers (5 fold), Human Body, Human Eye, Human Face, Snowflakes, and Spiders. For more information visit www.nathaliestrassburg.com.
Self-realization is the process of unifying our consciousness into a harmonious whole. This guide is based on the sixty-four lessons from the I Ching that we can master to expand our awareness, discover our authentic self, realize our inner truth, and live our unique destiny. When we balance our physical, emotional, spiritual, and mental aspects we become more self-empowered, and can achieve greater self-fulfillment. Following the Preface and Introduction, the book includes an Overview of the spectrum of ourselves, archetypes, roles, skill, spheres of awareness, principles, the learning spectrum, numbers, geometry, feminine and masculine expressions, self-realization, needs, relationships, and transformation. The book is then organized into four aspects: Physical, Emotional, Spiritual, and Mental. Each section contains the numbers, geometry, spheres of awareness, principles, traits, abilities, skills, and the learning spectrum. Each aspect has sixteen lessons. The sixty-four lessons in the learning spectrum are the lessons we can master to be an individual that takes empowered action, capable of empowered responses, based on empowered perspectives, and empowered thinking. They are tools that cultivate inner truth, emotional intelligence, and mental freedom that allow us to embrace whatever happens in life. Each lesson has a theme with an introduction, feminine and masculine expressions, and a spectrum: affirmation, wisdom, compassion, contemplation, investigation, sensation, observation, and visualization. For more information, art, images, designs, books, and other resources visit www.nathaliestrassburg.com
This volume features a collection of papers dedicated to "Canons of Form-Making", in honor of the 500th anniversary of the birth of architect Andrea Palladio (1508-1580). Theorist as well as practitioner, Palladio's architecture was based on well-defined canons that he had gleaned from studying the treatises as well as the remains of architecture from antiquity. Palladio himself left to posterity not only his large corpus of built works, but his Quattro libri d'architettura. Three of the papers in this issue are specifically about Palladio and his work. The other papers deal with canons of form-making, ancient and contemporary.
Many students have trouble the first time they take a mathematics course in which proofs play a significant role. This new edition of Velleman's successful text will prepare students to make the transition from solving problems to proving theorems by teaching them the techniques needed to read and write proofs. The book begins with the basic concepts of logic and set theory, to familiarize students with the language of mathematics and how it is interpreted. These concepts are used as the basis for a step-by-step breakdown of the most important techniques used in constructing proofs. The author shows how complex proofs are built up from these smaller steps, using detailed 'scratch work' sections to expose the machinery of proofs about the natural numbers, relations, functions, and infinite sets. To give students the opportunity to construct their own proofs, this new edition contains over 200 new exercises, selected solutions, and an introduction to Proof Designer software. No background beyond standard high school mathematics is assumed. This book will be useful to anyone interested in logic and proofs: computer scientists, philosophers, linguists, and of course mathematicians.
The book, revised, consists of XI Parts and 28 Chapters covering all areas of mathematics. It is a tool for students, scientists, engineers, students of many disciplines, teachers, professionals, writers and also for a general reader with an interest in mathematics and in science. It provides a wide range of mathematical concepts, definitions, propositions, theorems, proofs, examples, and numerous illustrations. The difficulty level can vary depending on chapters, and sustained attention will be required for some. The structure and list of Parts are quite classical: I. Foundations of Mathematics, II. Algebra, III. Number Theory, IV. Geometry, V. Analytic Geometry, VI. Topology, VII. Algebraic Topology, VIII. Analysis, IX. Category Theory, X. Probability and Statistics, XI. Applied Mathematics. Appendices provide useful lists of symbols and tables for ready reference. Extensive cross-references allow readers to find related terms, concepts and items (by page number, heading, and objet such as theorem, definition, example, etc.). The publisher’s hope is that this book, slightly revised and in a convenient format, will serve the needs of readers, be it for study, teaching, exploration, work, or research.
Manifolds, the higher-dimensional analogs of smooth curves and surfaces, are fundamental objects in modern mathematics. Combining aspects of algebra, topology, and analysis, manifolds have also been applied to classical mechanics, general relativity, and quantum field theory. In this streamlined introduction to the subject, the theory of manifolds is presented with the aim of helping the reader achieve a rapid mastery of the essential topics. By the end of the book the reader should be able to compute, at least for simple spaces, one of the most basic topological invariants of a manifold, its de Rham cohomology. Along the way, the reader acquires the knowledge and skills necessary for further study of geometry and topology. The requisite point-set topology is included in an appendix of twenty pages; other appendices review facts from real analysis and linear algebra. Hints and solutions are provided to many of the exercises and problems. This work may be used as the text for a one-semester graduate or advanced undergraduate course, as well as by students engaged in self-study. Requiring only minimal undergraduate prerequisites, 'Introduction to Manifolds' is also an excellent foundation for Springer's GTM 82, 'Differential Forms in Algebraic Topology'.
From the reviews: "This book offers a coherent treatment, at the graduate textbook level, of the field that has come to be known in the last decade or so as computational geometry. ... ... The book is well organized and lucidly written; a timely contribution by two founders of the field. It clearly demonstrates that computational geometry in the plane is now a fairly well-understood branch of computer science and mathematics. It also points the way to the solution of the more challenging problems in dimensions higher than two." #Mathematical Reviews#1 "... This remarkable book is a comprehensive and systematic study on research results obtained especially in the last ten years. The very clear presentation concentrates on basic ideas, fundamental combinatorial structures, and crucial algorithmic techniques. The plenty of results is clever organized following these guidelines and within the framework of some detailed case studies. A large number of figures and examples also aid the understanding of the material. Therefore, it can be highly recommended as an early graduate text but it should prove also to be essential to researchers and professionals in applied fields of computer-aided design, computer graphics, and robotics." #Biometrical Journal#2
Developed from celebrated Harvard statistics lectures, Introduction to Probability provides essential language and tools for understanding statistics, randomness, and uncertainty. The book explores a wide variety of applications and examples, ranging from coincidences and paradoxes to Google PageRank and Markov chain Monte Carlo (MCMC). Additional application areas explored include genetics, medicine, computer science, and information theory. The print book version includes a code that provides free access to an eBook version. The authors present the material in an accessible style and motivate concepts using real-world examples. Throughout, they use stories to uncover connections between the fundamental distributions in statistics and conditioning to reduce complicated problems to manageable pieces. The book includes many intuitive explanations, diagrams, and practice problems. Each chapter ends with a section showing how to perform relevant simulations and calculations in R, a free statistical software environment.
From bestselling author of Fermat's Last Theorem, a must-have for number lovers and Simpsons fans
The content of Geometry with an Introduction to Cosmic Topology is motivated by questions that have ignited the imagination of stargazers since antiquity. What is the shape of the universe? Does the universe have and edge? Is it infinitely big? Dr. Hitchman aims to clarify this fascinating area of mathematics. This non-Euclidean geometry text is organized intothree natural parts. Chapter 1 provides an overview including a brief history of Geometry, Surfaces, and reasons to study Non-Euclidean Geometry. Chapters 2-7 contain the core mathematical content of the text, following the ErlangenProgram, which develops geometry in terms of a space and a group of transformations on that space. Finally chapters 1 and 8 introduce (chapter 1) and explore (chapter 8) the topic of cosmic topology through the geometry learned in the preceding chapters.