Polynomial Counting

Articles about generalizations of positional number systems, explained using the concept of counting on polynomials.

Publication dates correspond to the original WordPress publication dates.

Polynomial Counting 1: A primer

An exploration into generalizations of positional number systems to irrational numbers.

Polynomial Counting 2: Binary and beyond

Continuing to explore irrational counting systems and discovering problems with certain polynomials.

Polynomial Counting 3: The third degree

Interesting results on simple irrational counting systems involving only zero and one.

Polynomial Counting 4: Two 2's

Using irrational fractional counting systems to generate chaotic behavior.

Polynomial Counting 5: Pentamerous multiplication

Arithmetic in non-geometric integral systems and surprisingly regular errors therein.

Counting in 2D, Part 1: Lines, Leaves, and Sand

An introduction to two-dimensional counting using polynomials of two variables.

Counting in 2D, Part 2: Reorienting Polynomials

Geometric properties of certain 2D systems and attempts to classify them.

Polynomial Counting 4, Addendum

Additional notes on irrational -adic expansions, including complex embeddings thereof.