The Collision Spectrum

The collision transform decomposes the collision invariant into Dirichlet characters. The antisymmetry

The Collision Transform

The collision invariant assigns a signed integer to every coprime class modulo

The Collision Invariant

Long division produces digits. One at a time, from a remainder. The

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,

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