Originally published in 1971 The Geometry of Environment is a fusion of art and mathematics introducing stimulating ideas from modern geometry, using illustrations from architecture and design. The revolution in the teaching of mathematics and the advent of the computer in design challenge traditional ways of appreciating the space about us, and expand the ‘structural’ understanding of our surroundings through such concepts as transformations, symmetry groups, sets and graphs. This book aims to show the relevance of ‘new maths’ and encourages exploration of the widening intellectual horizons of environmental design and architecture.
This textbook provides a thorough introduction to the differential geometry of parametrized curves and surfaces, along with a wealth of applications to specific architectural elements. Geometric elements in architecture respond to practical, physical and aesthetic needs. Proper understanding of the mathematics underlying the geometry provides control over the construction. This book relates the classical mathematical theory of parametrized curves and surfaces to multiple applications in architecture. The presentation is mathematically complete with numerous figures and animations illustrating the theory, and special attention is given to some of the recent trends in the field. Solved exercises are provided to see the theory in practice. Intended as a textbook for lecture courses, Parametric Geometry of Curves and Surfaces is suitable for mathematically-inclined students in engineering, architecture and related fields, and can also serve as a textbook for traditional differential geometry courses to mathematics students. Researchers interested in the mathematics of architecture or computer-aided design will also value its combination of precise mathematics and architectural examples.
A fully illustrated inspirational art book from visionary painter Francene Hart • Includes more than 80 full-color reproductions of Hart’s intricate watercolor paintings and the stories behind them • Recounts the evolution of her art and her discovery of the hidden order of Nature that led to her masterful artistic integrations of Nature, Spirit, and Sacred Geometry • Explores how to tap into the energies provided by spirit guides and power animals, like Jaguar, Raven, Octopus, and Dolphin, and harness the intelligence of the heart for creative inspiration and vision Every one of us possesses the potential to receive visionary experiences and integrate them into our lives. Artists become visionaries by cultivating their instinctive creative spark and sharing their profound visions with the world. In this lavishly illustrated memoir, including more than 80 full-color reproductions of her intricate watercolor paintings and the stories behind them, Francene Hart recounts the evolution of her art from formative influences to her masterful integrations of Nature, Spirit, and Sacred Geometry. Opening with her early work on mandalas and her explorations of the work of Joseph Campbell and C. G. Jung, Hart explains how her first works of art were in response to the solitary life she led in the forest, where she discovered the hidden order of Nature. She reveals how she learned to center her artistic explorations on the intelligence of the heart rather than the intellect, utilizing the wisdom and imagery of Sacred Geometry, reverence for the natural environment, and the interconnectedness between all things as her inspirations. She describes the shamanic lessons that accompanied her discoveries and shaped her understanding of sacred relationships with the self, others, and Mother Earth. She explores how to tap into the energies provided by spirit guides and power animals, like Jaguar, Raven, Octopus, and Dolphin, and explains her profound affinity for the ocean, including her discovery of water consciousness in Hawaii. Offering chronicles of her inspiring travels and transformational encounters around the world, Hart shares her experiences at sacred sites in the Amazon, Central America, Egypt, England, Scotland, Paris, Cambodia, and the Himalayas and how these places influenced her art. Exploring what is revealed as inspiration arises, Spirit informs, and vision is transformed into art, Francene Hart’s journey offers a window into the secret order of Nature, the power of sacred symbols for evolving consciousness, and a visionary artistic path that perfectly blends the mathematical rigors of sacred geometry and the numinous.
"The structural designs that occur in nature - in molecules, in crystals, in living cells - appear in this fully illustrated book as a source of inspiration and study of design of man-made structures" -- BOOK JACKET.
Suitable for advanced undergraduate and graduate students of engineering, physics, and mathematics and scientific researchers of all types, this is the first authoritative text on invisibility and the science behind it. More than 100 full-color illustrations, plus exercises with solutions. 2010 edition.
"Form Geometry Structure is an architecture and generative design guide that introduces a scientific framework in the exploration of forms in nature and design. From their geometric definition to their structural potential, forms are created and transformed by simple computing algorithms following growth patterns found in nature. In the natural world, these geometric forms can provide great inspiration in the design of the man-made world. Although software independent, this book presents several digital models of parametric forms built in Bentley's generative design software GenerativeComponents. While the relationship between geometry and forces in nature has been explored for millennia, contemporary computational tools bring new insights and methodologies. Form Geometry Structure is beautifully illustrated and rigorously researched and will bridge the gap between art and science, bringing to contemporary terms the tradition of the treatises on art and architecture." -- Publisher's site.
Encompassing nature, science, art, architecture, and spirituality, and illustrated with over 700 photographs and line drawings, The Hidden Geometry of Life illuminates the secret underpinnings of existence. In her trademark easy-to-understand style, mathematician Karen French shows how sacred geometry permeates every level of being, manifesting itself in simple shapes and numbers, music and sounds, light and color, even in the mysteries of creation itself. But these geometrical archetypes are more than the building blocks of reality: they are gateways to profound new levels of awareness.
From the simplest observations in nature to detailed measuring of intricate forms, we find geometry everywhere in the world around us.In this magnificent book, John Blackwood explores different kinds of symmetry in the diverse realms of nature. He considers the fundamental forms of minerals, plants, animals and humans, before going on to look at spirals, vortices, buds and other complex shapes. Using projective geometry as a basis, he shows how many forms in nature are generated by the same basic geometrical process, but significant disparities lead to the wondrous variety found in our universe.Fully illustrated with over 500 photographs, drawings and diagrams, this is both a beautiful and inspirational book.
