Pascal's Triangle

Generate Pascal's Triangle online with arbitrary precision BigInt binomial coefficients. Features centered pyramid layout, row sums ($2^n$), and odd number highlighting to reveal the Sierpinski Triangle fractal.

Private • In-browser processing • Zero server uploads

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How to Use Pascal's Triangle

1
Enter Row Count
Type the number of rows of Pascal's Triangle you wish to generate (from 1 to 64).
2
Choose View Option
Toggle Centered layout or enable 'Highlight Odds' to view the Sierpinski fractal.
3
Copy Triangle
Copy the formatted text triangle or inspect individual binomial coefficients.

Key Features

Arbitrary Precision BigInt
Generates rows up to 64 without encountering IEEE 754 floating-point overflow or precision truncation.
Sierpinski Fractal Visualizer
Colorizes or highlights odd numbers (parity modulo 2) to reveal the hidden self-similar Sierpinski Triangle fractal.
Centered Pyramid Formatting
Aligns numbers in an aesthetic geometric triangle for easy readability and printing.
Row Properties & Formulas
Shows row power sums ($2^n$) and combinatoric notations $\binom{n}{k}$.

Common Use Cases

  • Calculating binomial expansion coefficients $(x + y)^n$ in algebra and calculus.
  • Combinatorics and probability theory (determining combinations $\binom{n}{k}$).
  • Studying fractal geometry and modular arithmetic patterns.
  • Teaching elementary and advanced mathematics visually.

Frequently Asked Questions

Pascal's Triangle is a triangular array of binomial coefficients named after Blaise Pascal. Each number is the sum of the two numbers directly above it, with 1s along the edges.

If you color the odd numbers in Pascal's Triangle and leave the even numbers blank, the resulting pattern forms the Sierpinski Triangle fractal.

Yes! Because the generator uses native JavaScript `BigInt`, coefficients exceeding billions and trillions are calculated with 100% exact precision.

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