# Pascal’s Triangle

2016-03-26, post № 111

**mathematics**, **programming**, **Pygame**, **Python**, #crown, #generate, #sequence

Pascal’s triangle is an interesting mathematical sequence. It is often written as a triangle, starting with , then . To generate the next row, you add the two numbers above to form another one. So the next row in the sequence is then , and so on (sequence A007318 in OEIS).

One interesting property of Pascal’s triangle is the generation of binomials.

To calculate , you can look at the 𝟦-th row (listed above and when starting to count at 𝟢) and determine

This program generates Pascal’s sequence in a rather unusual shape, looking a bit like a crown.

To get more information about Pascal’s triangle, check out this Wikipedia entry.

## Controls

- ‘F1’ advances the sequence,
- ‘Space’ takes a screenshot.

Source code: pascals-triangle.py

Extra assets: pascals-triangle-3-fontsize-30.png, pascals-triangle_fail.py, pascals-triangle_pascal.py, pascals-triangle_latex.snippet.html

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## Footnotes

- ▲ In
`pascals-triangle_pascal.py`

there is a typo: ‘sedonds’ should say ‘seconds’.