Category: GOLDEN RATIO

From Sunflowers to God’s Divine Architecture of Life.

By 3D THINKING, 3D THINKING IN DESIGN AND ARCHITECTURE, ABJAD SYSTEM, ALTAIR DESIGNS, Architecture, Arts, CREATIVE GEOMETRY, DIVINE PROPORTIONS, DYNAMIC SPHERE GEOMETRY, EARLY ISLAMIC PERIOD, FRACTALS, GEOMETRY OF ANCIENT EGYPT, GEOMETRY THROUGH TIME, GOLDEN RATIO, INDUS VALLEY, ISLAMIC ART, LE CORBUSIER, NESTING POLYGONS, PATTERNS OF PERCEPTION, PERCEPTION, PYTHAGOREANS, SACRED ARCHITECTURE, SACRED GEOMETRY, VISUAL LOGIC, VISUAL THINKING

In response to questions from readers of the “Visual Thinking, Seeing Through Time” book series (ebook and print formats) I’ve added a SUPPLEMENTS page to this website. This is the first! “From Sunflowers to God’s Divine Architecture of Life.” This supplement relates to Book 1, Chapter 5, Ancient Egypt. It also covers Book 2, Chapter […]

Book Covers

Explore Visual Thinking Through Time

By 3D THINKING, 3D THINKING IN DESIGN AND ARCHITECTURE, ABJAD SYSTEM, ALTAIR DESIGNS, Architecture, Arts, CREATIVE GEOMETRY, DIVINE PROPORTIONS, EARLY ISLAMIC PERIOD, GEOMETRY OF ANCIENT CHINA, GEOMETRY OF ANCIENT EGYPT, GEOMETRY THROUGH TIME, GOLDEN RATIO, INDUS VALLEY, ISLAMIC ART, LABYRINTHS, LE CORBUSIER, NESTING POLYGONS, PATTERNS OF PERCEPTION, PERCEPTION, PYTHAGOREANS, SACRED ARCHITECTURE, SACRED GEOMETRY, VISUAL LOGIC

Overview Visual Thinking, Seeing Through Time is a five-book series. It explores the development of visual logic from archaic humans through early civilizations. It continues into the age of artificial intelligence. The series examines how visual‑cognitive structures shape human reasoning across the arts. These structures affect architecture and geometry. This reveals deep connections between perception, culture, […]

Book Covers

Launch of ‘Visual Thinking’: Five Books on Art and Geometry

By 3D THINKING, 3D THINKING IN DESIGN AND ARCHITECTURE, ABJAD SYSTEM, ALTAIR DESIGNS, Architecture, Arts, CREATIVE GEOMETRY, DIVINE PROPORTIONS, DYNAMIC SPHERE GEOMETRY, EARLY ISLAMIC PERIOD, FRACTALS, GEOMETRY OF ANCIENT CHINA, GEOMETRY OF ANCIENT EGYPT, GEOMETRY THROUGH TIME, GOLDEN RATIO, IMAGES DESIGN BOOKS, INDUS VALLEY, INTERACTIVE LEARNING, ISLAMIC ART, LABYRINTHS, LE CORBUSIER, NESTING POLYGONS, PATTERNS OF PERCEPTION, PERCEPTION, PYTHAGOREANS, SACRED ARCHITECTURE, SACRED GEOMETRY, SHAPE CHANGING POLYHEDRA, VISUAL LOGIC

“Visual Thinking, Seeing Through Time” is a five-book odyssey through the human experience in Architecture, the Arts, and Geometry from the dawn of consciousness to the frontiers of artificial intelligence.

The Story of Visual Thinking—Geometry, Architecture, and the Arts. AI Audio Review.

By 3D THINKING, 3D THINKING IN DESIGN AND ARCHITECTURE, Architecture, Arts, CREATIVE GEOMETRY, DIVINE PROPORTIONS, EARLY ISLAMIC PERIOD, GEOMETRY OF ANCIENT EGYPT, GEOMETRY THROUGH TIME, GOLDEN RATIO, IMAGES DESIGN BOOKS, INDUS VALLEY, INTERACTIVE LEARNING, ISLAMIC ART, LE CORBUSIER, PATTERNS OF PERCEPTION, PERCEPTION, PYTHAGOREANS, SACRED ARCHITECTURE, SACRED GEOMETRY, VISUAL LOGIC

An AI-generated 30 minute audio review of my latest book.

Presentations & Workshops

By 3D THINKING, 3D THINKING IN DESIGN AND ARCHITECTURE, ABJAD SYSTEM, ALTAIR DESIGNS, CREATIVE GEOMETRY, DIVINE PROPORTIONS, DYNAMIC SPHERE GEOMETRY, EARLY ISLAMIC PERIOD, GEOMETRY OF ANCIENT CHINA, GEOMETRY OF ANCIENT EGYPT, GEOMETRY THROUGH TIME, GOLDEN RATIO, IMAGES DESIGN BOOKS, INDUS VALLEY, ISLAMIC ART, LABYRINTHS, LE CORBUSIER, LECTURES PRESENTATIONS, MIND DOODLES, NESTING POLYGONS, PATTERNS OF PERCEPTION, PERCEPTION, PYTHAGOREANS, SACRED GEOMETRY, SHAPE CHANGING POLYHEDRA, VISUAL LOGIC

PRESENTATIONS WORKSHOPS

DYNAMIC SPHERES: GOLDEN RATIO ARCHITECTURE

By DYNAMIC SPHERE GEOMETRY, GOLDEN RATIO

“3D Thinking” Page 288: A “Golden Ratio” structure extracted from a 3D lattice generated by the sphere cluster, HP1.3. See Page 271, “3D THINKING ANIMATIONS.” The lattice is created by connecting the centers of the “Golden Ratio” spheres. The illustration shows how the lattice is generated and then how the  structure is extracted from the space-filling […]

Dynamic Sphere Geometry – Updated Page

By 3D THINKING, CREATIVE GEOMETRY, DYNAMIC SPHERE GEOMETRY, GOLDEN RATIO

Have updated the “Dynamic Sphere Geometry” page. Applications are architectural, design, new materials. Revised page has updated animations showing how close packing sphere arrangements (of different sized spheres) are generated, examples of sequences and an example of an architectural lattice generated by the geometry.