3.14 is about 0.00159 less than pi, whereas 22/7 is about 0.00126 greater than pi, making pi approximation day closer to pi than pi day.

This is the research I come here for.

Sure, but by undershooting you can simply wait until the time is 1:59:26.53589793 to celebrate.

Every day is pi-approximation day. It’s just a question of how good the approximation.

The day 1131/12/30 yields 3.1416 repeating.

According to my calculations, the most approximate Pi ISO day expressed literally is 311/9/11 = 3.141414... Of course 311/11/9 also works

132/3/14 = 3.142857142857143. Not bad!

A 355 day lunar calendar would allow for 355/113, which is pretty good.