| --- |
| license: mit |
| language: |
| - en |
| tags: |
| - math |
| - formula |
| pretty_name: sunny thakur |
| size_categories: |
| - n<1K |
| --- |
| Mathematics Formulas Dataset |
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| 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. |
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| # Dataset Overview |
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| Total Formulas: 183 |
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| Categories: 12 |
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| Format: JSON Lines (.jsonl) |
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| Size: ~45KB |
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| Last Updated: October 2023 |
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| # Categories Included |
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| Algebra |
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| Basic identities |
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| Polynomial expansions |
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| Quadratic formula |
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| Exponential/logarithmic laws |
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| Trigonometry |
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| Fundamental identities |
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| Angle formulas |
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| Transformation formulas |
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| Trigonometric laws |
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| Calculus |
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| Derivatives |
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| Integrals |
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| Special limits |
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| Fundamental theorems |
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| Geometry |
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| Area/volume formulas |
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| Coordinate geometry |
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| Euler's formula |
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| Vector operations |
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| Probability & Statistics |
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| Basic probability rules |
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| Counting principles |
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| Distribution formulas |
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| Statistical measures |
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| Complex Numbers |
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| Algebraic operations |
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| Polar form conversions |
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| Exponential representation |
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| Roots of unity |
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| Vectors |
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| Vector operations |
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| Dot/cross products |
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| Magnitude calculations |
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| Geometric applications |
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| Sequences & Series |
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| Arithmetic/geometric sequences |
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| Summation formulas |
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| Financial applications |
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| Logarithms |
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| Logarithmic identities |
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| Change of base |
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| Special cases |
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| Exponents |
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| Exponent rules |
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| Fractional exponents |
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| Special cases |
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| Radicals |
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| Radical operations |
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| Simplification rules |
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| Exponent conversions |
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| Logic |
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| Logical equivalences |
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| De Morgan's laws |
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| Truth tables |
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| JSONL Format Specification |
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| 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 |
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| type: Formula subcategory |
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| formula(s): The mathematical expression(s) |
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| variables: List of variables with descriptions (when applicable) |
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| example: Worked examples (when provided) |
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| note: Additional explanations |
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| tags: Search keywords |
| ``` |
| Usage Examples |
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| Python Integration |
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| ```Python |
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| import json |
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| with open('trigonometry.jsonl') as f: |
| for line in f: |
| formula = json.loads(line) |
| print(f"{formula['type']}: {formula['formulas'][0]}") |
| ``` |
| JavaScript Integration |
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| ```javascript |
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| const fs = require('fs'); |
| const readline = require('readline'); |
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| const rl = readline.createInterface({ |
| input: fs.createReadStream('algebra.jsonl'), |
| crlfDelay: Infinity |
| }); |
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| rl.on('line', (line) => { |
| const formula = JSON.parse(line); |
| console.log(formula.formulas[0]); |
| }); |
| ```` |
| # Applications |
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| Educational Software: Power formula cheat sheets and auto-solving features |
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| Flashcard Apps: Create spaced-repetition study decks |
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| AI Training: Enhance math-solving language models |
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| Reference Apps: Build comprehensive math handbooks |
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| Tutoring Systems: Support step-by-step problem solving |
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| # Contribution Guidelines |
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| Fork the repository |
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| Add new formulas in the appropriate category file |
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| Maintain consistent JSONL format |
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| Include proper Unicode mathematical notation |
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| # License |
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| This dataset is released under MIT License, allowing free use in both academic and commercial applications with attribution. |
| Acknowledgements |
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| Compiled by mathematics educators and formatted for machine readability. |
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| owner :Sunny thakur |
