# 🎨 Symergetics: Symbolic Synergetics for Rational Arithmetic

**Daniel Ari Friedman** (2025) · *Zenodo*

[![DOI](https://img.shields.io/badge/DOI-10.5281%2Fzenodo.17114389-blue)](https://doi.org/10.5281/zenodo.17114389)

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## Abstract

> 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.

## Keywords

`Symergetics` · `Synergetics` · `Buckminster Fuller` · `rational arithmetic` · `Quadray coordinates` · `IVM lattice` · `symbolic computation` · `computational geometry`

## Key Contributions

- 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

- 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.

## 🎯 Consulting & Tutoring

**Available for AI Research Consulting and Tutoring.** [Contact Daniel Ari Friedman, PhD](https://danielarifriedman.com/) for collaboration on Active Inference, Bayesian modeling, and computational biology.

## Citation

```bibtex
@article{2025_Symergetics,
  author = {Daniel Ari Friedman},
  title = {{Symergetics: Symbolic Synergetics for Rational Arithmetic}},
  journal = {Zenodo},
  year = {2025},
  doi = {10.5281/zenodo.17114389},
}
```

## File Inventory

- `AGENTS.md` (1,927 bytes)
- `2025_Symergetics.pdf` (5,730,668 bytes)
- `README.md` (1,621 bytes)
- `SKILL.md` (1,733 bytes)