The Geometry of Creation


Book Description

This book offers a new perspective on Gothic architectural creativity. It shows, in a series of geometrical case studies, how Gothic design evolved over time, in two senses: in the hours of the draftsman's labour, and across the centuries of the late Middle Ages. In each case, a series of computer graphics show how a medieval designer could have developed his architectural concept step by step, using only basic geometrical operations. Taken together, these analyses demonstrate remarkable methodological continuity across the Gothic era, and the development of sophisticated permutations on venerable design themes.




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 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

Reveals the ancient mathematical principles refuting the notion of the solar system as an accidental creation • Reveals how ancient civilizations encoded their secret knowledge of the sky in mythology, music, and sacred measures • Shows how modern culture can benefit from the ancient astronomical and astrological worldview based on number • Shows the role of ratio and harmonic proportions in the creation of the material world Humanity’s understanding of number was deeper and richer when the concept of creation was rooted in direct experience. But modern sensibility favors knowledge based exclusively on physical laws. We have forgotten what our ancestors once knew: that numbers and their properties create the forms of the world. Ancient units of measurement held within them the secrets of cosmic proportion and alignment that are hidden by the arbitrary decimal units of modern mathematical thinking. Sacred numbers arose from ancient man’s observations of the heavens. Just as base ten numbers relate to the fingers and toes in terms of counting, each celestial period divides into the others like fingers revealing the base numbers of planetary creation. This ancient system made the art of counting a sacramental art, its units being given spiritual meanings beyond just measurement. The imperial yard, for example, retains a direct relationship to the Equator, the length of a day and a year, and the angular values of Earth, Moon, and Jupiter. The ancients encoded their secret knowledge of the skies within mythology, music, monuments, and units of sacred measurement. They understood that the ripeness of the natural world is the perfection of ratio and realized that the planetary environment--and time itself--is a creation of number.




Euclid—The Creation of Mathematics


Book Description

Euclid presents the essential of mathematics in a manner which has set a high standard for more than 2000 years. This book, an explanation of the nature of mathematics from its most important early source, is for all lovers of mathematics with a solid background in high school geometry, whether they be students or university professors.




Sacred Geometry Book of History, Meanings and How to Create Them


Book Description

Why is it that we are so drawn to and enticed by sacred geometry? They start with simple mathematical shapes, that combine to create elaborate illustrations of such beauty and elegance that we marvel at them. Beliefs, religious, spiritual and cultural, have been historically attached to them. The specific design and creation of each individual sacred geometric pattern is thought, among many cultures, not only to demonstrate an understanding of specific universal concepts, but to hold powers of mystical possibilities. The aim of this book is to provide an understanding of the history, creation and meanings of sacred geometry for those who are new to the subject, and to open an insight into the beliefs placed upon them with the hope that it will inspire the reader's interest and imagination and increase their enthusiasm. Enjoy learning how such simple shapes can evolve into inspiring and powerful patterns that weave through the fabric of our entire universe and reality.




Sacred Geometry and Spiritual Symbolism


Book Description

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




Sacred Geometry


Book Description

Originally published: Presteigne, Powys, Wales: Wooden Books Ltd., 1998.