Symergetics: Symbolic Synergetics for Rational Arithmetic

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Citation KeyFriedman2025SymergeticsSymbolicSynergeticsRational020

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Overview

Extracted from the local paper documentation when available.

This paper introduces Symergetics, an open-source Python package designed to address the precision limitations of floating-point arithmetic in geometric calculations by providing exact rational arithmetic methods within the Synergetics framework. It enables accurate geometric pattern discovery and all-integer accounting necessary for exploring Buckminster Fuller's principles.

SymergeticsSynergeticsBuckminster Fullerrational arithmeticQuadray coordinatesIVM latticesymbolic computationcomputational geometry

Use Notes

Concise findings and methods pulled from README/SKILL documentation.

Findings / Concepts

Development of the Symergetics package for exact rational arithmetic in geometric computations.
Implementation of a Quadray coordinate system for precise tetrahedral geometry.
Exact volume calculations for Platonic solids using isotropic vector matrix (IVM) units.
Pattern analysis algorithms for Scheherazade numbers and primorial sequences using exact arithmetic.

Methods / Techniques

Utilization of exact rational arithmetic with automatic simplification to eliminate approximation errors.
Adoption of a Quadray coordinate system to maintain spatial relationships in tetrahedral geometry.
Execution of volume calculations for Platonic solids based on IVM units.
Implementation of pattern discovery algorithms that leverage exact arithmetic for enhanced mathematical insights.

Citation

Plain-text citation for quick reuse.

Friedman, Daniel Ari. 2025. Symergetics: Symbolic Synergetics for Rational Arithmetic. Zenodo.

Primary source Documentation BibTeX