Golden Ratio

Dymaxion Map by Buckminster Fuller

Dymaxion
The Dymaxion map by Buckminster Fuller is a projection of a world map onto the surface of a icosahedron, which can be unfolded and flattened to two dimensions. Read More...

Temporal Fractal of the Cardiac Cycle

Cardiac
Phi-damping implosion cycle of the heart as a function of Mandelbrot geometry.
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Fibonacci Spiral of a Pine Tree

Pine
A dead pine tree I found that had split along its Fib spiral growth path as it dried out. If you look closely you can see how the branches resonated out along either side of the spiral. Read More...

Inosculation of a Tree Trunk

Inosculation
When two trees grow together it's called inosculation. Read More...

The DNA Egg Model

DNAEgg
There are two geometric models found in DNA that help explain the geometry of the human body. The first is the Yang Quasi-28-gon Eggshell and the second is the White G-ball Yolk. Read More...

Phi-Damping Locations in a Standing Wave

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The Phi-Damping Well

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The Pentagram & Fibonacci Series

Pentagram
One way to view the Fibonacci Series is as a recursive approximation of golden ratios in the Harmonic Series, together represented geometrically as a set of phi-recursive pentagrams. Read More...

Golden Triangle of the Larynx

Larynx
Those interested in the anatomy of the larynx and process of vocalization will like the following anatomy lesson. Read More...

How to Build an Anechoic Chamber

Anechoic
Echoes in rooms and speaker enclosures are created by harmonic wave reflection over-resonating within a cavity. This can be easily prevented by creating an enclosure using the dimensions of the golden ratio and its inverse. Read More...

Mutually Orthogonal Isometric Hexagons

Isometric
The geometric figure on the cover of INTERFERENCE was part of a graphic art series entitled Cubing the Human Archetype. Read More...

Golden Spiral of a Flower

Spiral
Given that every form of life on Earth grows out of a spiral and that indeed weather systems, planetary systems, solar systems and galaxies also form out of spiral formations, why is it that spirals are excluded entirely from the study of geometry and in fact much of the study of mathematics? Read More...

Mineral Crystallization and the Golden Ratio

Mineral
Ancient philosophers believed God slept in rocks. These golden spirals in a Bismuth crystal form little G's as if searching for God. Read More...

Permittivity of Free Space

Free
Isometric projection of an orthogonal harmonic lattice introduces a gap, enabling energy to articulate and travel through space. Without this little bit of slack, nothing could move or bond and the universe would be dead. Read More...

Forbidden Apple of Harmony

Apple
The Apple of Knowledge symbolism is very old and appears to be related to the ancient belief that all life is harmonically organized. Here is a simple illustration showing how the golden mean is at the bottom of both horizontal and vertical geometries of the apple. Read More...

Constructing the Vitruvian Man

Vitruvian
Reverse engineering the geometry of the human body. Read More...

The 13:8 Crystallization of a Leaf

Leaf
The 13:8 Crystallization of a Leaf. Read More...

The Harmonic Jupiter Hypothesis

Jupiter
The Harmonic Jupiter Hypothesis… Read More...

The CBS Eye

CBS
A simple harmonic model for the human face...
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Golden Ratio in Pythagorean Tetrachords

Tetrachords
Dual golden ratios in the tritone function of a diatonic scale (relative to C major / A minor).
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