Towards 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?
ReadGenerators as Symbolic Exploration
A reflection on the extension and unification of figurate numbers within broader mathematical contexts.
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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