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This space serves as both a study log and implementation archive for various mathematical and philosophical theorems.\n\n## Repository Structure\n\n- 📁 **Studying/**\n  - 📁 **Philosophical/**\n    - `sri_yantra.lean` - Implementation of Sri Yantra geometric properties and theorems using Lean 4\n\n## Current Projects\n\n### Sri Yantra Implementation Details\n\nThe Sri Yantra implementation focuses on formalizing sacred geometry using rigorous mathematical proofs in Lean 4. \n\n#### Core Structures\n- `SriYantraTriangle`: Represents the fundamental triangular structures with:\n  - Equilateral triangle properties\n  - Circumcenter calculations\n  - Sacred proportion constraints\n  - Angular relationships (2π sum constraint)\n\n- `ShaktiPath`: Models the energy pathways with:\n  - Continuous path properties\n  - Start and end point definitions\n  - Flow direction constraints\n  - Energy flow angle calculations (0 ≤ θ ≤ 2π)\n\n#### Key Theorems\n\n1. **Geometric Properties**\n- Golden Ratio relationships (φ = (1 + √5)/2)\n- Sacred circle ratios (√3 relationship between circumradius and inradius)\n- Angular relationships (π/6 relationships between triangles)\n\n2. **Pathway Analysis**\n- Intersection point properties (54 critical points)\n- Bindu flow characteristics\n- Mandala structure (9 centers and 9 radii)\n\n3. **Unified Properties**\nThe implementation proves a comprehensive theorem (`sri_yantra_complete_properties`) that unifies:\n- Golden ratio relationships\n- Sacred circle proportions\n- Angular symmetries\n- Pathway intersections\n- Bindu flow properties\n- Mandala structural relationships\n\n## Prerequisites\n\n### Core Requirements\n- **Lean 4**\n  - Installation of Lean 4 compiler\n  - Basic understanding of Lean syntax\n  - Experience with functional programming concepts\n\n### Library Dependencies\n- **Mathlib**\n  - Core mathematical libraries\n  - Theorem proving foundations\n  - Type theory basics\n\n### Mathematical Background\n#### Required Knowledge:\n- **Euclidean Geometry**\n  - Geometric constructions\n  - Triangle properties\n  - Circle theorems\n  - Vector spaces\n\n- **Metric Spaces**\n  - Distance functions\n  - Convergence concepts\n  - Completeness\n  - Topology fundamentals\n\n- **Topology**\n  - Open and closed sets\n  - Continuous functions\n  - Connectedness\n  - Compactness\n\n- **Real Analysis**\n  - Limit theory\n  - Continuity\n  - Differentiation\n  - Integration theory\n\n## Future Plans\n\n### Mathematical Implementations\n1. **Philosophical Mathematics**\n   - Sacred geometry theorems\n   - Number theory relationships\n   - Geometric patterns in nature\n   - Mathematical symmetry principles\n\n2. **Classical Theorems**\n   - Fundamental theorem of algebra\n   - Prime number theorems\n   - Group theory foundations\n   - Topology fundamentals\n\n### Learning Track\n1. **Study Notes**\n   - Theorem proving techniques\n   - Lean 4 best practices\n   - Mathematical proof strategies\n   - Code organization patterns\n\n2. **Progress Tracking**\n   - Implementation milestones\n   - Theorem complexity progression\n   - Learning achievements\n   - Documentation improvements\n\n### Planned Features\n- Comprehensive documentation\n- Example collections\n- Tutorial sections\n- Reference implementations\n","project_url":"https://awesome.ecosyste.ms/api/v1/projects/github.com%2Fzelosleone%2Flean-theorems","html_url":"https://awesome.ecosyste.ms/projects/github.com%2Fzelosleone%2Flean-theorems","lists_url":"https://awesome.ecosyste.ms/api/v1/projects/github.com%2Fzelosleone%2Flean-theorems/lists"}