darkknight25/Mathematics_Formulas_Dataset

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