metadata

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


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


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