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 the visualization layer of FigurateNum v3, where figurate numbers enter the complex plane through 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.
AI Assistance
AI tools are used to assist with grammar and occasional discussion of ideas. Final review remains with the author.