My Journey with Figurate Numbers
How I developed two of my most downloaded libraries that fuse mathematics, art, and music.
Two Years Leading to FigurateNum v3 Visualizations in the Complex Plane
A short personal note on a new way of visualizing figurate numbers in FigurateNum v3, bringing them into the complex plane through generating functions and domain coloring.
Counting a Figurate Property in Cayley–Dickson Algebras
A naive question about Cayley-Dickson algebras, enumerated by a figurate number via type systems, and how that question naturally incorporates itself into other algebraic structures and particularities.
Gamma Functions for Figurate Numbers
I plant a question motivated by generalizing the GCD to varieties and inspired by Euler's interpolation: Does there exist a function attached to each figurate number that extends it to continuous domains, analogous to how the Gamma function extends the factorial?
Generators as Symbolic Exploration
A reflection on the extension and unification of figurate numbers within broader mathematical contexts.