README.md

---
license: mit
language:
- en
tags:
- math
- formula
pretty_name: sunny thakur
size_categories:
- n<1K
---
Mathematics Formulas Dataset



A comprehensive collection of 183 essential mathematical formulas across 12 categories, formatted in JSONL for easy integration with educational software, study apps, and AI systems.

# Dataset Overview

    Total Formulas: 183

    Categories: 12

    Format: JSON Lines (.jsonl)

    Size: ~45KB

    Last Updated: October 2023

# Categories Included

    Algebra 

        Basic identities

        Polynomial expansions

        Quadratic formula

        Exponential/logarithmic laws

    Trigonometry 

        Fundamental identities

        Angle formulas

        Transformation formulas

        Trigonometric laws

    Calculus 

        Derivatives

        Integrals

        Special limits

        Fundamental theorems

    Geometry 

        Area/volume formulas

        Coordinate geometry

        Euler's formula

        Vector operations

    Probability & Statistics 

        Basic probability rules

        Counting principles

        Distribution formulas

        Statistical measures

    Complex Numbers 

        Algebraic operations

        Polar form conversions

        Exponential representation

        Roots of unity

    Vectors 

        Vector operations

        Dot/cross products

        Magnitude calculations

        Geometric applications

    Sequences & Series 

        Arithmetic/geometric sequences

        Summation formulas

        Financial applications

    Logarithms 

        Logarithmic identities

        Change of base

        Special cases

    Exponents 

        Exponent rules

        Fractional exponents

        Special cases

    Radicals 

        Radical operations

        Simplification rules

        Exponent conversions

    Logic 

        Logical equivalences

        De Morgan's laws

        Truth tables



JSONL Format Specification

Each line contains a complete JSON object with the following common fields:
```
json

{
  "category": "Trigonometry",
  "type": "Double Angle",
  "formulas": [
    "sin2θ = 2sinθcosθ",
    "cos2θ = cos²θ - sin²θ"
  ],
  "note": "Three equivalent forms for cosine",
  "tags": ["angles", "identities"]
}
```
Standard Fields:
```
    category: Primary subject area

    type: Formula subcategory

    formula(s): The mathematical expression(s)

    variables: List of variables with descriptions (when applicable)

    example: Worked examples (when provided)

    note: Additional explanations

    tags: Search keywords
```
Usage Examples

Python Integration

```Python

import json

with open('trigonometry.jsonl') as f:
    for line in f:
        formula = json.loads(line)
        print(f"{formula['type']}: {formula['formulas'][0]}")
```
JavaScript Integration

```javascript

const fs = require('fs');
const readline = require('readline');

const rl = readline.createInterface({
  input: fs.createReadStream('algebra.jsonl'),
  crlfDelay: Infinity
});

rl.on('line', (line) => {
  const formula = JSON.parse(line);
  console.log(formula.formulas[0]);
});
````
# Applications

    Educational Software: Power formula cheat sheets and auto-solving features

    Flashcard Apps: Create spaced-repetition study decks

    AI Training: Enhance math-solving language models

    Reference Apps: Build comprehensive math handbooks

    Tutoring Systems: Support step-by-step problem solving

# Contribution Guidelines

    Fork the repository

    Add new formulas in the appropriate category file

    Maintain consistent JSONL format

    Include proper Unicode mathematical notation

    

# License

This dataset is released under MIT License, allowing free use in both academic and commercial applications with attribution.
Acknowledgements

Compiled by mathematics educators and formatted for machine readability. 

owner :Sunny thakur