π day is 3/14. But today is super π day: 3/14/15. To celebrate it properly you must do so at 9:26 A.M. or P. M. Years ago, as a student of electrical engineering, I memorized π this far out: 3.14159.
The decimal expansion is non-terminating. But that is not what makes it an irrational number. What makes it irrational is that it cannot be expressed as a fraction the numerator and denominator of which are integers. Compare 1/3. Its decimal expansion is also non-terminating: .3333333 . . . . But it is a rational number because it can be expressed as a fraction the numerator and denominator of which are integers (whole numbers).
An irrational (rational) number is so-called because it cannot (can) be expressed as a ratio of two integers. Thus any puzzlement as to how a number, as opposed to a person, could be rational or irrational calls for therapeutic dissolution, not solution (he said with a sidelong glance in the direction of Wittgenstein).
Yes, there are pseudo-questions. Sometimes we succumb to the bewitchment of our understanding by language. But, pace Wittgestein, it is not the case that all the questions of philosophy are pseudo-questions sired by linguistic bewitchment. I say almost none of them are. So it cannot be the case that philosophy just is the struggle against such bewitchment. (PU #109: Die Philosophie ist ein Kampf gegen die Verhexung unsres Verstandes durch die Mittel unserer Sprache.) What a miserable conception of philosophy! As bad as that of a benighted logical positivist.
Many people don't understand that certain words and phrases are terms of art, technical terms, whose meanings are, or are determined by, their uses in specialized contexts. I once foolishly allowed myself to be suckered into a conversation with an old man. I had occasion to bring up imaginary (complex) numbers in support of some point I was making. He snorted derisively, "How can a number be imaginary?!" The same old fool -- and I was a fool too for talking to him twice -- once balked incredulously at the imago dei. "You mean to tell me that God has an intestinal tract!"
Finally a quick question about infinity. The decimal expansion of π is non-terminating. It thus continues infinitely. The number of digits is infinite. Potentially or actually? I wonder: can the definiteness of π -- its being the ratio of diameter to circumference in a circle -- be taken to show that the number of digits in the decimal expansion is actually infinite?
I'm just asking.
Now go ye forth and celebrate π day in some appropriate and inoffensive way. Eat some pie. Calculate the area of some circle. A = πr2.
Dream about π in the sky. Mock a leftist for wanting π in the future. 'The philosophers have variously interpreted π; the point is to change it!'
UPDATE: Ingvar writes,
Of course the ne plus ultra pi day was 3-14-1592 and whatever happened that day at 6:53 in the morning. So we have one yearly, one every millennium, and one once.