Generators as Symbolic Exploration
A reflection on the extension and unification of figurate numbers within broader mathematical contexts.
ReadTowards 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?
ReadDo Group Actions Define Regular Polytopes and Polytypes in Type Systems?
I introduce an analogy between transitive group actions on flags of polytopes and type systems. This speculative concept aims to offer a naive way of understanding and classifying types through symmetry.
ReadCategory of Modules and Type-Level Programming with Figurate Numbers
I invite you to explore the intersection of figurate numbers and module theory, where type-level programming unlocks new possibilities for math and live coding music.
ReadMy Journey with Figurate Numbers
How I developed two of my most downloaded libraries that fuse mathematics, art, and music.
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