https://github.com/zelosleone/lean-theorems

A repository for studying and implementing Lean theorems, focusing on mathematical and philosophical concepts.
https://github.com/zelosleone/lean-theorems

euclidean-geometry formal-verification geometry lean lean4 mathematics philosophical-logic philosophical-mathematics real-analysis theorem-proving theorem-provings topology

Last synced: about 1 month ago
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A repository for studying and implementing Lean theorems, focusing on mathematical and philosophical concepts.

• Host: GitHub
• URL: https://github.com/zelosleone/lean-theorems
• Owner: zelosleone
• License: mit
• Created: 2024-11-02T19:52:32.000Z (about 2 months ago)
• Default Branch: main
• Last Pushed: 2024-11-02T20:09:36.000Z (about 2 months ago)
• Last Synced: 2024-11-02T20:27:12.877Z (about 2 months ago)
• Topics: euclidean-geometry, formal-verification, geometry, lean, lean4, mathematics, philosophical-logic, philosophical-mathematics, real-analysis, theorem-proving, theorem-provings, topology
• Language: Lean
• Homepage:
• Size: 0 Bytes
• Stars: 0
• Watchers: 1
• Forks: 0
• Open Issues: 0
• Metadata Files:
  • Readme: README.md
  • License: LICENSE

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README

        
# Lean Theorems

A repository dedicated to my journey learning and implementing theorems in Lean 4. This space serves as both a study log and implementation archive for various mathematical and philosophical theorems.

## Repository Structure

- 📁 **Studying/**

  - 📁 **Philosophical/**

    - `sri_yantra.lean` - Implementation of Sri Yantra geometric properties and theorems using Lean 4

## Current Projects

### Sri Yantra Implementation Details

The Sri Yantra implementation focuses on formalizing sacred geometry using rigorous mathematical proofs in Lean 4. 

#### Core Structures

- `SriYantraTriangle`: Represents the fundamental triangular structures with:

  - Equilateral triangle properties

  - Circumcenter calculations

  - Sacred proportion constraints

  - Angular relationships (2π sum constraint)

- `ShaktiPath`: Models the energy pathways with:

  - Continuous path properties

  - Start and end point definitions

  - Flow direction constraints

  - Energy flow angle calculations (0 ≤ θ ≤ 2π)

#### Key Theorems

1. **Geometric Properties**

- Golden Ratio relationships (φ = (1 + √5)/2)

- Sacred circle ratios (√3 relationship between circumradius and inradius)

- Angular relationships (π/6 relationships between triangles)

2. **Pathway Analysis**

- Intersection point properties (54 critical points)

- Bindu flow characteristics

- Mandala structure (9 centers and 9 radii)

3. **Unified Properties**

The implementation proves a comprehensive theorem (`sri_yantra_complete_properties`) that unifies:

- Golden ratio relationships

- Sacred circle proportions

- Angular symmetries

- Pathway intersections

- Bindu flow properties

- Mandala structural relationships

## Prerequisites

### Core Requirements

- **Lean 4**

  - Installation of Lean 4 compiler

  - Basic understanding of Lean syntax

  - Experience with functional programming concepts

### Library Dependencies

- **Mathlib**

  - Core mathematical libraries

  - Theorem proving foundations

  - Type theory basics

### Mathematical Background

#### Required Knowledge:

- **Euclidean Geometry**

  - Geometric constructions

  - Triangle properties

  - Circle theorems

  - Vector spaces

- **Metric Spaces**

  - Distance functions

  - Convergence concepts

  - Completeness

  - Topology fundamentals

- **Topology**

  - Open and closed sets

  - Continuous functions

  - Connectedness

  - Compactness

- **Real Analysis**

  - Limit theory

  - Continuity

  - Differentiation

  - Integration theory

## Future Plans

### Mathematical Implementations

1. **Philosophical Mathematics**

   - Sacred geometry theorems

   - Number theory relationships

   - Geometric patterns in nature

   - Mathematical symmetry principles

2. **Classical Theorems**

   - Fundamental theorem of algebra

   - Prime number theorems

   - Group theory foundations

   - Topology fundamentals

### Learning Track

1. **Study Notes**

   - Theorem proving techniques

   - Lean 4 best practices

   - Mathematical proof strategies

   - Code organization patterns

2. **Progress Tracking**

   - Implementation milestones

   - Theorem complexity progression

   - Learning achievements

   - Documentation improvements

### Planned Features

- Comprehensive documentation

- Example collections

- Tutorial sections

- Reference implementations