From Triangles to Pentagons

Year: 2025 Authors: Richard Nau; Sharol Nau

Core claim

A spiral of triangles generates Padovan-numbered pentagons with a limiting “Plastic” shape and area formula, while a Goldbach partition supports a second pentagon-based mosaic series.

Topics

pentagon construction, Padovan sequence, Goldbach partition, tiling and tessellation

Domains

recursive sequences, geometric limits, area formulas, mosaic art, tessellation design, generative patterning

Methods

geometric construction, inductive proof, shape normalization, visual comparison

Media

equilateral triangles, isosceles right triangles, mosaic painting, grid-based tiling

Source status

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