The Cross-Alignment Matrix
Divide 1 by 7 and you get a repeating pattern. Divide 2
The Coherence Decomposition
Walk into a room where everyone is singing the same note. Now
The Three-Tier Conjecture
You can assign a number to every positive integer. Not its size,
The Alignment Limit for All Primes
The digit-partitioning primes are the easy ones. Three of them in base
Digit-Partitioning Primes and the Alignment Formula
Long division is a machine. You feed it a numerator and a
Why the Golden Ratio Selects the Prime Three
There is a machine hiding inside long division. You learned it as
Long Division and Euclid's Lemma
May 2011
Most of us first encountered long division in grade school.
The Effect of Base on Numeric Fields
August 2010
A simple investigation into base and modular patterns
Today I
Geometries Hidden in the Number System
June 2010
Today I would like to share a way of looking
The Golden Ratio
January 2010
The golden ratio, usually written as φ (phi), is one
Arithmetic Foundations
January 2010
Breath
Here is a process most of us never think
Foundational Tables of Multiplication
January 2010
Can numbers reveal additional structure when we change the way