A collection of interactive mathematical and STEM-related applications built with modern web technologies. This educational suite provides comprehensive tools for exploring arithmetic, geometry, trigonometry, and 3D mathematics as well as Physics and Programming Concepts (TBD)
- 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
- 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
- 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
- Exact Mathematical Values: Fractions and radicals instead of decimals (โ2/2, ฯ/3, etc.)
- Dual Angle Notation: Shows both decimal and ฯ representations (1.57 (ฯ/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
- 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
- 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 ฯ 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
- 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
- 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
- Exact Mathematical Notation: Uses fractions (1/2) and radicals (โ2/2)
- Symbolic Representations: Shows ฯ notation alongside decimal values
- Mathematical Accuracy: Precise calculations without floating-point errors
- Progressive Enhancement: Graceful degradation for all device types
- 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
- Modern web browser (Chrome, Firefox, Safari, Edge)
- No additional software or dependencies required
-
Clone the repository:
git clone https://github.com/goodrichster/graham-projects.git cd graham-projects -
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
-
Open your browser and navigate to:
http://localhost:8080
- 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
- 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
- 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
- Chrome: 80+ โ
- Firefox: 75+ โ
- Safari: 13+ โ
- Edge: 80+ โ
- Mobile Browsers: iOS Safari 13+, Chrome Mobile 80+ โ
graham-projects/
โโโ index.html # Main navigation page
โโโ calculator/ # Arithmetic calculator
โ โโโ index.html
โ โโโ calc.js
โโโ polygon/ # 2D polygon explorer
โ โโโ index.html
โ โโโ poly.js
โโโ unit-circle/ # Trigonometry application
โ โโโ index.html
โ โโโ unit-circle.js
โโโ polyhedron/ # 3D geometry explorer
โ โโโ index.html
โ โโโ polyhedron.js
โโโ physics/ # Physics simulations
โ โโโ index.html
โ โโโ physics.js
โโโ calculus/ # Calculus simulations
โ โโโ index.html
โ โโโ calculus.js
โโโ README.md
- 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
This project is open source and available under the MIT License.
Graham Goodrich
- Educational Mathematics Applications
- Modern Web Development
- Interactive Learning Tools
Contributions are welcome! Please feel free to submit issues, feature requests, or pull requests.
- 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
- 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
STEM-based content for illustrating topics in Mathematics, Science, and Programming.
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