The Geometry of Creation


Book Description

The flowering of Gothic architecture depended to a striking extent on the use of drawing as a tool of design. By drawing precise "blueprints" with simple tools such as the compass and straightedge, Gothic draftsmen were able to develop a linearized architecture of unprecedented complexity and sophistication. Examination of their surviving drawings can provide valuable and remarkably intimate information about the Gothic design process. Gothic drawings include compass pricks, uninked construction lines, and other telltale traces of the draftsman's geometrically based working method. The proportions of the drawings, moreover, are those actually intended by the designer, uncompromised by errors introduced in the construction process. All of these features make these drawings ideal subjects for the study of Gothic design practice, but their geometry has to date received little systematic attention. This book offers a new perspective on Gothic architectural creativity. It shows, in a series of rigorous geometrical case studies, how Gothic design evolved over time, in two senses: in the hours of the draftsman's labor, and across the centuries of the late Middle Ages. In each case study, a series of computer graphics show in unprecedented detail how a medieval designer could have developed his architectural concept step by step, using only basic geometrical operations. Taken together, these analyses demonstrate both remarkable methodological continuity across the Gothic era, and the progressive development of new and sophisticated permutations on venerable design themes. This rich tradition ultimately gave way in the Renaissance not because of any inherent problem with Gothic architecture, but because the visual language of Classicism appealed more directly to the pretensions of Humanist princes than the more abstract geometrical order of Gothic design, as the book's final chapter demonstrates.




Geometry Creation and Import With COMSOL Multiphysics


Book Description

This book focuses on the geometry creation techniques for use in finite element analysis. Examples are provided as a sequence of fin designs with progressively increasing complexity. A fin was selected as it is a feature widely employed for thermal management. As the content progresses, the reader learns to create or import a geometry into a FEM tool using COMSOL Multiphysics®. The fundamentals may also be applied to other commercial packages such as ANSYS® or AbaqusTM. The content can be utilized in a variety of engineering disciplines including mechanical, aerospace, biomedical, chemical, civil, and electrical. The book provides an overview of the tools available to create and interact with the geometry. It also takes a broader look on the world of geometry, showing how geometry is a fundamental part of nature and how it is interconnected with the world around us. Features: Includes example models that enable the reader to implement conceptual material in practical scenarios with broad industrial applications Provides geometry modeling examples created with built in features of COMSOL Multiphysics® v. 5.4 or imported from other dedicated CAD tools Presents meshing examples and provides practical advice on mesh generation Includes companion files with models and custom applications created with COMSOL Multiphysics® Application Builder.




Sacred Geometry for Artists, Dreamers, and Philosophers


Book Description

An illustrated guide to harmonics--the sacred geometry principles that underlie the natural world--and its practical applications • Demonstrates how the vesica piscis is a matrix from which ideas and forms emanate, connecting cosmic time cycles, measures of space, and musical tones • Provides harmonic analyses of ancient sculpture, architecture, the solar system, the Earth-Moon relationship, and the structure of water and waves • Explains how to apply sacred geometry to create building floor plans, pottery figures, gardens, and sacred ceremonial spaces We are in the midst of a revival of an ancient way of looking at the world--an approach that enabled great civilizations of the past to bring forth inventions of great beauty and power. This school of thought--harmonics--envisioned the natural world and the solar system as an interlocking matrix of harmonious numbers, perfectly woven into the creative fabric of life and the surrounding universe. Exploring the art and science of harmonics, John Oscar Lieben shows how to create harmonious forms using the ancient tools of number, geometry, and musical tone--an approach that resonates with nature’s own ways of creation. He demonstrates many practical applications that result from the study of harmonics, providing analyses of ancient sculpture and architecture, as well as original examples of building floor plans, pottery figures based on planetary proportions, gardens based on harmonic principles, and ceremonial spaces that honor cosmic harmonies and sacred geometric relationships. Showing how harmonics can also be applied to the mysteries of time and space, the author demonstrates how the vesica piscis and many other variations of the vesica shape reveal numerical synchronicities and correspondences that connect cosmic time cycles, measures of space, and musical tones. The author applies harmonics and the “vesica construction” matrix to illustrate many of nature’s wonders, including the Earth-Moon relationship, the interactions of the Golden Number and the musical scale, and how the Flower of Life symbol connects the universal field with the pattern of raindrops falling on a pond. Offering an approach to sacred geometry that pairs the mystical with the practical, the cosmic with the earthly, the author reveals how the art and science of harmonics should be required study for both the artist and the seeker of eternal truths as well as the scientist who seeks an entrance into the sacred foundations of nature.




Sacred Geometry of the Starcut Diagram


Book Description

• 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.




Geometry of Creation


Book Description




Sacred Geometry and Spiritual Symbolism


Book Description

"Unifying spirit and science through geometry and symbolism"--From publisher description.




Sacred Geometry and the Creation of the Universe


Book Description

The classic Sacred Geometrical forms are explained as representations of the successive steps in the creation of the universe.




Geometry by Construction


Book Description

"'Geometry by construction' challenges its readers to participate in the creation of mathematics. The questions span the spectrum from easy to newly published research and so are appropriate for a variety of students and teachers. From differentiation in a high school course through college classes and into summer research, any interested geometer will find compelling material"--Back cover.




Matrix of Creation


Book Description

Sacred numbers arose from ancient man's observation of the heavens, and represent the secrets of cosmic proportion and alignment. The ancients understood that the ripeness of the natural world is the perfection of ratio and that the planetary system--and time itself--is a creation of number. We have forgotten what our ancestors once knew: that numbers and their properties create the forms of the world.




Sacred Geometry


Book Description

Is there a secret visual language all around us? What's so special about the shape of the Great Pyramid? Why is there something so sixy about circles? How many ways can you tile the plane? Lavishly illustrated by the author, this enchanting small introduction to one of the oldest and most widely-used ancient traditions on Earth will forever change the way you look at a triangle, arch, window, fabric repeat, ceramic pattern, graphic design, painting, spiral or flower. WOODEN BOOKS are small but packed with information. "e;Fascinating"e; FINANCIAL TIMES. "e;Beautiful"e; LONDON REVIEW OF BOOKS. "e;Rich and Artful"e; THE LANCET. "e;Genuinely mind-expanding"e; FORTEAN TIMES. "e;Excellent"e; NEW SCIENTIST. "e;Stunning"e; NEW YORK TIMES. Small books, big ideas.