Math Problem Solver Backend

A Flask-based backend system that provides interactive calculators for Trigonometry and Compound Interest problems, integrated with beautiful frontend templates.

Features

🧮 Trigonometry Calculator (Template 1)

• Calculate Sec C + Cot A for any right triangle
• Works with both Pythagorean triplets and non-integer hypotenuses
• Interactive triangle diagram with dynamic dimensions
• Step-by-step solution display
• Fraction-based calculations for precise results
• Automatic hypotenuse calculation using Pythagorean theorem

💰 Compound Interest Calculator (Template 2)

• Find interest rates from principal, amount, and time
• Calculate compound amounts for any time period
• Detailed step-by-step calculations
• Fraction simplification for rate factors
• Professional mathematical layout

Installation

1. Clone or download the project

   cd /home/rajan/Downloads/Backend/project

2. Install dependencies

   pip install -r requirements.txt

3. Run the application

   python app.py

4. Access the application

   • Open your browser and go to: http://localhost:5000
   • Or access directly: http://0.0.0.0:5000

API Endpoints

Trigonometry

• POST /trigonometry
  • Input: {"perpendicular": 7, "base": 24}
  • Output: Complete trigonometry calculations with fractions

Compound Interest

• POST /interest/rate

  • Input: {"principal": 12000, "amount": 20736, "time": 3}
  • Output: Interest rate calculation with steps

• POST /interest/amount

  • Input: {"principal": 12000, "rate": 20, "time": 2}
  • Output: Compound amount calculation

Usage Examples

Trigonometry Problem

1. Go to http://localhost:5000/template1
2. Enter perpendicular and base values
3. Get instant calculation of Sec C + Cot A
4. View step-by-step solution with triangle diagram

Compound Interest Problem

1. Go to http://localhost:5000/template2
2. Enter principal, amount, and time values
3. Specify calculation time period
4. Get complete solution with rate finding and amount calculation

Project Structure

project/
├── app.py                 # Main Flask application
├── requirements.txt       # Python dependencies
├── templates/            # HTML templates
│   ├── index.html        # Main landing page
│   ├── template1.html    # Trigonometry calculator
│   └── template2.html    # Compound interest calculator
├── static/               # Static assets
│   ├── arrow.png         # Arrow image for templates
│   └── interesticon.png  # Interest calculator icon
└── README.md            # This file

Technical Details

Backend Features

• Flask Framework: Lightweight and flexible web framework
• CORS Support: Cross-origin resource sharing enabled
• Fraction Calculations: Precise mathematical calculations using Python's fractions module
• Input Validation: Comprehensive error handling and validation
• RESTful API: Clean API design for frontend integration

Frontend Features

• Responsive Design: Works on desktop and mobile devices
• Interactive Forms: Real-time input validation
• Dynamic Updates: Live calculation updates without page refresh
• Professional Layout: Maintains original template styling
• Error Handling: User-friendly error messages

Mathematical Accuracy

• Pythagorean Triplets: Automatic verification of right triangle properties
• Fraction Arithmetic: Exact calculations without floating-point errors
• Compound Interest: Precise rate calculations using nth root methods
• Step-by-Step Solutions: Detailed mathematical breakdowns

Sample Problems

Trigonometry Example

• Input: Perpendicular = 7, Base = 24
• Output: Sec C + Cot A = 4/3
• Verification: 7, 24, 25 is a Pythagorean triplet

Non-Pythagorean Example:

• Input: Perpendicular = 5, Base = 6
• Output: Sec C + Cot A = 1834/859 ≈ 2.135
• Hypotenuse: √61 ≈ 7.81 (automatically calculated)

Compound Interest Example

• Input: Principal = ₹12,000, Amount = ₹20,736, Time = 3 years
• Output: Rate = 20%, Amount in 2 years = ₹17,280

Development

To extend the system:

1. Add new calculation types: Extend the calculator classes in app.py
2. Create new templates: Add HTML files in the templates/ directory
3. Add new endpoints: Create new routes in the Flask application
4. Enhance frontend: Modify JavaScript functions in the templates

Troubleshooting

Common Issues

1. Port already in use: Change the port in app.py (line: app.run(port=5001))
2. Missing dependencies: Run pip install -r requirements.txt
3. Images not loading: Ensure images are in the static/ directory
4. CORS errors: The application includes CORS support by default

Error Messages

• "Not a valid right triangle": The entered dimensions don't form a Pythagorean triplet
• "Amount must be greater than principal": Invalid compound interest input
• "All values must be positive": Negative or zero values entered

License

This project is created for educational and demonstration purposes.