Mission
explore the architecture of all that is
- seek to understand the ordering principles of the universe
- demonstrate the merging of divine logic and natural order
- discern patterns in the systems
- introduction
- mission
- call to action
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GEOMETOR
exploring the architecture of all that is
Create tools for geometric exploration
animations and interactions
Create a knowledge archive
collection of foundational information on the order of things
Explore the wonders of the Golden Ratio
connect systems of logic with natural systems
Projects
manifestations of the mission
GEOMETOR Explorer
symbolic algebra constructive geometry engine
GEOMETOR Explorer is an essential tool of the GEOMETOR Project. The goal is to establish a system for generating constructive geometric figures and finding instance of golden sections.
All of the learning within GEOMETOR should be embodied within explorer.
Deep Field Project
Finding Golden Sections within a blank canvas
Like the Hubble Deep Field Experiment which searched for galaxies in an empty spot in space, we are are planning to turn Geometor Explorer to a blank canvas to see how many unique instances of golden ratios we can find.
Studies and Animations
hand drawings, geogebra models, browser-based animations
all constructive geometry is motion in time
Geogebra Models
work leading up to Geometor Explorer
base construction template
numerous settings and tools
Base
Svg
Four Circles
one of the simplest golden sections
From two points, we can draft a line with through them or scribe two circle where each point is a center for a circle passing through the other point.
Unique External
6 unique constructions of the golden ratio
Demonstrates 6 ways to construct golden ratio points external to a unit segment
Export
Root 3
constructions inside a circumscribed equilateral triangle
Root3f
Root3f_
Root 3 resonance
resonant golden sections emerge
Root 3 external
golden sections outside of a circumscribed equilateral triangle
Root3 Harmonics
harmonic pencil within a circumscribed equilateral triangle projects the golden ratio
Root 5
golden sections from the double square
Star of Truth
lines which section the unit into the golden ratio
Geometor Logo
Circles and Squares
Triangle and Square
Hyperbolic
Heptagon
Algebra
Euclid
Elements and other studies
parsing original texts for study in photon
Fundamentals
concepts in constructive geometry
The geometric studies of Fred Seelig
Morphology
forms from the natural world
- crystals
- plants
- animals
- colonies / collections
Harmonics
proportion, vibration, resonance, cymatics
Log
Latest updates on this project
Articles
concepts, philosophy, documentation
A collection of articles
The Golden Ratio
perfection in balance and growth
- divine proportion
- golden ratio
- extreme and mean ratio
Logical Systems
arithmetic, geometry, algebra
- Phi emerges at the outset when exploring the simplest of logical relationships
Extreme and Mean Ratio
The Golden Ratio is also a Golden Mean
\[ \large \frac{a}{b} = \frac{b}{a+b}\]
Identities
Algebraic Expressions related to PHI
A study of the algebraic attributes and identities of the Divine Proportion
Continuous Fractions
Continuos Fractions
Golden Sections
Geometric constructions which derive the Golden Ratio
A Golden Section is the ratio of two segments within a construction where the proportion of their measures is PHI.
Constructive-geometry
base constructions
3 primary Golden Ratio section instances based on the root 5, root 3 and root2 proportions
√3 sections
a collection of Golden Ratio section instances based on the root 5 proportion
Slides
construction sequence from geogebra
Png
√5 sections
a collection of Golden Ratio section instances based on the root 5 proportion
√2 sections
a collection of Golden Ratio section instances based on the root 2 proportion
Series
- Fibonacci Series
- Lucas Numbers
- Binet's Forumal
Natural Systems
Patterns in the Natural World
- Phi emerges as the ordering principle in so many aspects of living things
History
The story of our conscious awareness of Phi
Since antiquity, Phi has captivated great thinkers
Euclid
Euclid's Elements
- the standard of logic for two thousand years
lines
- A LINE is a proportion that is derived from the relationship of two points
circles
- A CIRCLE is a perpendicular relationship between two points
Study
Important People and References
Forum Geometricorum
Site with curated papers on Geometry
Dr. Norman J. Wildberger
Insight into Mathematics
Rational Trigonometry
Luca Pacioli
author of De Divina Proportione
Ernst Haekel
explorer of the microscopic
Hans Kayser
proportions and harmonics
Johannes Kepler
gifted observer
Roger V. Jean
phyllotaxis and plant morphogenesis
Connect
message - join - support
get and stay connected with phi ARCHITECT
Send a Message
Let us know who you are
We are
- happy to answer questions
- eager to hear feedback
- interested in collaboration
We look forward to hearing from you
Thank You
We will be in touch soon!
Join our Email List
receive regular updates on projects
- Regular postings on research and insights
Subscribe on YouTube
follow the phi ARCHITECT channel for current updates on all projects
posting regular research and education videos
Collaborate on GitHub
Public Repositories for sharing code
All the development code for GEOMETOR is here. As well as out content platform - PHOTON
Support on Patreon
become a part of the community
Connect on LinkedIn
business social network
About
More on the people and mechanisms behind this project
- collaboration
- education
- discovery