Whole numbers that, as a ratio, approximate pi (π)

Let's find a high-accuracy ratio for pi (π) that's easier to remember than 1396262 / 444444 and more accurate than 355 / 113.

Number patterns like 444444 are arguably easy to remember. Since there are infinitely many ratios that are close to pi (π), there could be some large-numbered ratio that is both easy to remember and surprisingly close to reproducing pi (π) -- even more accurate than 355 / 113.

Below, type in a starting numerator, and hit "Go!" It scrolls fast, but if something catches your eye, if you think you see a numerator-denominator set that might be easy to remember, click "Pause". Remember, you can alter the numerator any way you want.