# Taxonomy

## Tags & Categories

• filter all pages by taxonomies

# Send a Message

## Let us know who you are

We are

• eager to hear feedback
• interested in collaboration

We look forward to hearing from you

# Thank You

We will be in touch soon!

• Regular postings on research and insights

## 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

# Connect

## message - join - support

get and stay connected with phi ARCHITECT

## More on the people and mechanisms behind this project

• collaboration
• education
• discovery

# Articles

## concepts, philosophy, documentation

A collection of articles

# 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

# 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

# Logical Systems

## arithmetic, geometry, algebra

• Phi emerges at the outset when exploring the simplest of logical relationships

# The Golden Ratio

## perfection in balance and growth

• divine proportion
• golden ratio
• extreme and mean ratio

# History

## The story of our conscious awareness of Phi

Since antiquity, Phi has captivated great thinkers

# √2 sections

a collection of Golden Ratio section instances based on the root 2 proportion

# 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.

# √5 sections

a collection of Golden Ratio section instances based on the root 5 proportion

# √3 sections

a collection of Golden Ratio section instances based on the root 5 proportion

# base constructions

3 primary Golden Ratio section instances based on the root 5, root 3 and root2 proportions

# Identities

## Algebraic Expressions related to PHI

A study of the algebraic attributes and identities of the Divine Proportion

# Extreme and Mean Ratio

## The Golden Ratio is also a Golden Mean

$\large \frac{a}{b} = \frac{b}{a+b}$

# 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.

# 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.

# GEOMETOR

## exploring the architecture of all that is

• introduction
• mission
• call to action

# Morphology

## forms from the natural world

• crystals
• plants
• animals
• colonies / collections

# 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

# Studies and Animations

## hand drawings, geogebra models, browser-based animations

all constructive geometry is motion in time

# Dr. Norman J. Wildberger

## Insight into Mathematics

Rational Trigonometry

# Unique External

## 6 unique constructions of the golden ratio

Demonstrates 6 ways to construct golden ratio points external to a unit segment

# 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.

# Euclid

## Elements and other studies

parsing original texts for study in photon

# Fundamentals

## concepts in constructive geometry

The geometric studies of Fred Seelig