Graham's Mathematical Applications Suite

https://goodrichster.github.io/graham-projects/index.html

A collection of interactive mathematical applications built with modern web technologies. This educational suite provides comprehensive tools for exploring arithmetic, geometry, trigonometry, and 3D mathematics.

🚀 Live Applications

• Calculator - Enhanced arithmetic calculator with modern UI
• Polygon Explorer - Interactive 2D polygon visualization and analysis
• Unit Circle Explorer - Comprehensive trigonometry with exact mathematical values
• Polyhedron Explorer - 3D geometric solids with Euler's formula verification
• Physics Simulations - Interactive AP Physics 1 concepts and visualizations
• Calculus Simulations - Comprehensive AP Calculus AB derivatives, integration, and rational function analysis

📱 Features

🧮 Calculator

• Modern Interface: Clean, responsive design with visual feedback
• Enhanced Functionality: Supports decimal numbers and all basic operations
• Error Handling: Division by zero protection and input validation
• Keyboard Shortcuts: Ctrl/Cmd + mathematical operators
• Real-time Results: Instant calculations with animated feedback

🔷 Polygon Explorer

• Interactive Visualization: Real-time polygon rendering on HTML5 canvas
• Dual Controls: Dropdown selection and slider for sides (3-20)
• Mathematical Analysis: Displays interior angles and polygon properties
• Coordinate Display: Shows exact vertex coordinates in a formatted table
• Keyboard Navigation: Arrow keys for quick adjustments

⚪ Unit Circle Explorer

• Exact Mathematical Values: Fractions and radicals instead of decimals (√2/2, π/3, etc.)
• Dual Angle Notation: Shows both decimal and π representations (1.57 (π/2))
• Interactive Visualization: Real-time unit circle with coordinate display
• Comprehensive Table: All trigonometric values for common angles
• Animation Controls: Smooth rotation with start/stop functionality
• Preset Angles: Quick access to standard trigonometric angles

📐 Polyhedron Explorer

• 3D Visualization: Interactive rendering with rotation controls
• Euler's Formula: Complete verification table showing V - E + F = 2
• Multiple Polyhedra: 9 different solids including Platonic solids
• Real-time Rotation: X/Y axis controls with auto-rotation feature
• Educational Display: Vertex, edge, and face counts with verification

⚛️ Physics Simulations

• Projectile Motion: Interactive trajectory visualization with customizable velocity, angle, and gravity
• Air Resistance Effects: Compare trajectories with and without air drag
• Trajectory Comparison: Overlay multiple projectile paths for analysis
• Real-time Calculations: Displays theoretical values for range, max height, and flight time
• Vector Analysis: Shows velocity components and magnitude during flight
• Forces & Motion: Newton's laws with interactive force diagrams and net force visualization
• Energy Conservation: KE/PE transformations in ramps, pendulums, and springs with energy bar charts
• Momentum & Collisions: Elastic, inelastic, and perfectly inelastic collision analysis
• Simple Harmonic Motion: Spring-mass systems and pendulums with exact period calculations
• Circular Motion: Uniform circular motion with centripetal force and angular velocity analysis
• Educational Formulas: Mathematical equations displayed alongside simulations
• Exact Mathematical Notation: Uses π notation and exact radical representations
• AP Physics 1 Aligned: Covers core concepts from kinematics to energy conservation
• Multiple Simulation Types: Six different physics concepts with interactive controls

📊 Calculus Simulations

• Numerical Integration: Interactive visualization of integration approximation methods
• Riemann Sums: Left and Right Riemann sum calculations with color-coded rectangles
• Midpoint Rule: Enhanced midpoint approximation with visual representation
• Trapezoidal Rule: Accurate trapezoidal integration with geometric visualization
• Method Comparison: Side-by-side comparison of all four numerical integration techniques
• Real-time Calculations: Displays exact numerical values for each approximation method
• Data Table Integration: Uses realistic AP Calculus data points for authentic problem solving
• Responsive Scaling: Automatically adjusts canvas scale to accommodate large data ranges (y-values up to 150)
• Color-coded Visualization: Orange for left Riemann, purple for right Riemann, blue for midpoint, green for trapezoidal
• Rectangle Rendering: Accurate geometric representation with proper baseline calculations
• Rational Function Analysis: Complete analysis of rational functions with asymptote detection
• Vertical Asymptotes: Automatic detection and visualization of vertical asymptotes
• Horizontal Asymptotes: Analysis based on polynomial degree comparison
• Slant Asymptotes: Polynomial long division for oblique asymptote computation
• Hole Detection: Identifies removable discontinuities in rational functions
• Critical Points: Finds and analyzes local extrema and inflection points
• End Behavior Analysis: Mathematical explanation of function behavior at infinity
• Interactive Function Input: Custom rational function entry with real-time analysis
• Step-by-step Solutions: Detailed mathematical explanations for all computations
• Derivative Rules Flashcards: Interactive study cards for all 16 essential derivative formulas
• 3D Card Flip Animation: Smooth card transitions with mathematical typography
• Progress Tracking: Visual progress bar showing cards reviewed with shuffle and reset options
• Comprehensive Rule Set: Covers constant, power, product, quotient, chain, trigonometric, logarithmic, and exponential rules
• AP Calculus AB Aligned: Covers numerical integration, rational function analysis, and derivative memorization from AP curriculum

🛠 Technical Specifications

Modern Architecture

• Vanilla JavaScript: No external dependencies for optimal performance
• Responsive Design: Works seamlessly on desktop, tablet, and mobile
• Offline Functionality: No CDN dependencies, fully self-contained
• HTML5 Canvas: Hardware-accelerated graphics for smooth animations

Educational Standards

• Exact Mathematical Notation: Uses fractions (1/2) and radicals (√2/2)
• Symbolic Representations: Shows π notation alongside decimal values
• Mathematical Accuracy: Precise calculations without floating-point errors
• Progressive Enhancement: Graceful degradation for all device types

Code Quality

• Modern ES6+: Uses latest JavaScript features and best practices
• Error Handling: Comprehensive validation and user feedback
• Performance Optimized: Efficient rendering and calculation algorithms
• Clean Architecture: Modular design with clear separation of concerns

🚀 Getting Started

Prerequisites

• Modern web browser (Chrome, Firefox, Safari, Edge)
• No additional software or dependencies required

Installation

1. Clone the repository:

   git clone https://github.com/goodrichster/graham-projects.git
   cd graham-projects

2. Start a local web server:

   # Using Python 3
   python3 -m http.server 8080
   
   # Using Node.js
   npx http-server -p 8080
   
   # Using PHP
   php -S localhost:8080

3. Open your browser and navigate to:

   http://localhost:8080
   

Usage

• Navigation: Use the main index page to access all applications
• Keyboard Controls: Each app supports keyboard shortcuts for enhanced usability
• Mobile Support: Touch-friendly interface adapts to all screen sizes
• Offline Use: Applications work without internet connection

📚 Mathematical Concepts

Covered Topics

• Arithmetic: Basic operations with enhanced error handling
• Plane Geometry: Regular polygons and their properties
• Trigonometry: Unit circle, exact values, and function relationships
• Solid Geometry: 3D polyhedra and Euler's formula (V - E + F = 2)
• Physics: Classical mechanics concepts from AP Physics 1 curriculum including circular motion
• Calculus: Numerical integration methods, Riemann sums, rational function analysis, asymptote computation, and derivative rule memorization

Educational Value

• Exact Representations: Teaches symbolic vs. decimal mathematics
• Visual Learning: Interactive graphics reinforce mathematical concepts
• Real-time Feedback: Immediate results help build understanding
• Progressive Complexity: From basic arithmetic to advanced 3D geometry

🎯 Browser Compatibility

• Chrome: 80+ ✅
• Firefox: 75+ ✅
• Safari: 13+ ✅
• Edge: 80+ ✅
• Mobile Browsers: iOS Safari 13+, Chrome Mobile 80+ ✅

🔧 Development

Project Structure

graham-projects/
├── index.html              # Main navigation page
├── calculator/             # Arithmetic calculator
│   ├── index.html
│   └── calc.js
├── polygon/               # 2D polygon explorer
│   ├── index.html
│   └── poly.js
├── unit-circle/          # Trigonometry application
│   ├── index.html
│   └── unit-circle.js
├── polyhedron/           # 3D geometry explorer
│   ├── index.html
│   └── polyhedron.js
├── physics/              # Physics simulations
│   ├── index.html
│   └── physics.js
├── calculus/             # Calculus simulations
│   ├── index.html
│   └── calculus.js
└── README.md

Key Design Principles

• No Build Process: Direct HTML/CSS/JS for simplicity
• Self-Contained: All resources included, no external dependencies
• Responsive First: Mobile-friendly design from the ground up
• Educational Focus: Mathematical accuracy over visual effects

📄 License

This project is open source and available under the MIT License.

👨‍💻 Author

Graham Goodrich

• Educational Mathematics Applications
• Modern Web Development
• Interactive Learning Tools

🤝 Contributing

Contributions are welcome! Please feel free to submit issues, feature requests, or pull requests.

Areas for Enhancement

• Additional polyhedra (prisms, pyramids, irregular solids)
• 3D graphing capabilities
• Statistical analysis tools
• Advanced trigonometric functions
• Additional calculus topics (limits, infinite series, parametric equations)
• Additional physics simulations (waves, electricity, magnetism)
• Symbolic algebra and equation solving
• Probability and statistics modules
• Chemistry simulation modules

📈 Version History

• v3.0.0 - Added comprehensive Calculus Simulations with numerical integration and rational function analysis
• v2.0.0 - Complete suite with all four applications
• v1.1.0 - Added Unit Circle Explorer with exact values
• v1.0.0 - Initial release with Calculator and Polygon Explorer

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Built with modern web technologies for educational excellence 🎓✨