Comprehensive Enhancement of Triangles Documentation with MathWorld Integration #8
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…finitions - Fix all markdown linting issues (blank lines, proper formatting) - Express fundamental properties as mathematical formulas with descriptions - Use Greek letters (α, β, γ) for angles instead of Latin letters - Add comprehensive transversals section with Ceva's and Menelaus' theorems - Include biographical information and external links for mathematical theorems - Create Fundamental Definitions section with key geometric terms: - Concurrent lines, collinear points, vertex, perpendicular, bisect - Improve mathematical notation and LaTeX formatting throughout - Add exterior angles sum property (360°) - Enhance educational value with clear explanations and proper structure
…d improve copilot instructions - Add MathWorld links to all major triangle concepts and theorems - Include links for triangle types (equilateral, isosceles, scalene, acute, right, obtuse) - Add links for fundamental properties (triangle inequality, exterior angles) - Link geometric definitions (concurrent lines, collinear points, vertex, perpendicular, bisector) - Include transversal and cevian concept links (median, altitude, angle bisector) - Add links for special points (circumcenter, incenter, centroid, orthocenter) - Link major theorems (Pythagorean, Heron's formula, Thales, Law of Sines/Cosines) - Include circle properties (circumcircle, incircle, excircles, circumradius, inradius) - Add triangulation application link - Fix MD049 linting issues by removing improper emphasis formatting - Update copilot instructions to require fetch_webpage verification for all MathWorld links - Ensure all links are verified and contextually appropriate for educational reference
- Add version = "0.1.0" to Project.toml following Julia package conventions - Add inventory_version = "0.1.0" to HTML configuration in docs/make.jl - Eliminates warnings about missing version information during documentation builds - Enables proper cross-referencing capabilities for documentation inventory system - Follows Julia ecosystem best practices for package versioning
- Add comprehensive perimeter and semi-perimeter definitions with MathWorld links - Enhance Heron's formula section with detailed explanation and context - Improve trigonometric area formula with clear variable explanations - Add comprehensive coordinate geometry area formula - Expand right triangle section with detailed cathetes/hypotenuse definitions - Add extensive Pythagorean triples content including: - Primitive vs non-primitive triples explanation - Complete generation formula with mathematical derivation - Multiple worked examples - Add comprehensive Geometric Mean Theorem section with: - Alternative theorem names and context - Complete mathematical formulations for all relationships - Detailed explanation of why it's called 'geometric mean' - Links to supporting mathematical concepts - Reorganize special right triangles for improved clarity - Add detailed explanations for educational context throughout - Maintain consistent MathWorld linking for all mathematical concepts
- Reorganize Advanced Right Triangle Theorems section for better flow - Update Thales' Theorem link to use Wikipedia instead of MathWorld for better content - Add detailed derivations for special right triangles: - Complete 45°-45°-90° triangle derivation with Pythagorean theorem explanation - Comprehensive 30°-60°-90° triangle derivation from equilateral triangle construction - Include altitude calculations and geometric reasoning - Add area formula for isosceles right triangle - Improve mathematical explanations with step-by-step geometric constructions - Enhance educational value with clear derivation paths for all special triangle properties - Maintain consistent formatting and mathematical notation throughout
- Add biographical links for Giovanni Ceva and Menelaus of Alexandria - Update concurrent lines link to Wikipedia for better content coverage - Enhance Applications section with more specific and useful links: - Add triangular meshes link for computer graphics applications - Add vector decomposition link for physics applications - Add projectile motion link showing practical triangle applications - Update index.md with current progress status and completion notes - Polish overall documentation quality and cross-references
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This PR represents a comprehensive overhaul of the triangles documentation, transforming it into a professional educational resource with extensive cross-references and mathematical rigor.
Technical Improvements
-Resolve Documenter.jl Warnings: Added proper versioning (v0.1.0) to eliminate inventory warnings
-Link Verification Workflow: Established fetch_webpage verification for all external references
-Markdown Compliance: Fixed MD049 linting issues for professional documentation standards
Documentation Enhancements
-30+ Verified MathWorld Links: Comprehensive educational references for all major concepts
-Detailed Mathematical Content: Enhanced with derivations, examples, and step-by-step explanations
-Historical Context: Added biographical information for key mathematicians
-Practical Applications: Expanded applications section with specific use cases
Educational Value
Transformed basic triangle reference into comprehensive learning resource suitable for self-study and mathematical education.
Quality Assurance
-All external links verified functional
-Markdown linting compliance
-Consistent mathematical notation
-Documentation builds without warnings