One piece of π trivia (catch the pun?): if you can't remember enough digits, just multiply by 355 and divide by 113. Ancient Chinese mathematicians figured out that ratio, which is accurate to six significant digits.
But π is not the only transcendental number, and perhaps it's not even the most important one. The number e is everywhere in mathematics that pertain to differential equations — which, if you ask any physicist, run the universe. e begins with 2.71828, so I suppose we can schedule e Day on February 7, 2018 at 2:08 am.
There are many other transcendental numbers, as well as a few that mathematicians haven't yet established whether they are truly transcendental or not. My favorite is i i, or i raised to the i power. You may remember that i is first presented in high school as the square root of minus one. It's much more than that. You might dismiss i as an "imaginary" number, and it is — sort of. There used to be a joke in electrical engineering school that if you think i is purely imaginary, come inside an electricity generating plant with me and I'll change your mind in a hurry. But from the perspective of a mathematician, i is fair game for manipulation. It turns out that i^i has many possible values, one of which begins with .2078795. So, hold out February 7, 2087 for that one!