The Collision Periodic Table
In 1869, Mendeleev arranged the known elements into a grid. Each element
The Collision Spectrum
The previous paper decomposed the collision invariant into its natural frequencies: Dirichlet
The Collision Transform
The collision invariant assigns a signed integer to every coprime class modulo
The Collision Invariant
The digit function $\delta(r) = \lfloor br/p \rfloor$ sorts remainders into
The Three-Tier Theorem
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
Some primes enforce a kind of total order on the fractions they
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