well, without looking it up anywhere.... 3.141592654 (which is 9)...
How many decimal places do you know for the natural number e?
or, if no one wants to answer that one, another mathematical query I've been dying to calculate lately....
What is the ratio of the number of prime numbers {2,3,5,7,11,13,...} to the number of natural numbers {0,1,2,3,4,5,...}?
(for starting help with this question.... consider the following sets of multiples:
for 2 -> {2,4,6,8,...}, the ratio of these to the natural numbers is 1/2...
for 3 -> {3,6,9,12,...}, the ratio of these to the natural numbers is 1/3...
for 5 -> {5,10,15,20,...}, the ratio of these to the natural numbers is 1/5...
so, if you look at these ratios, take the ratio of natural numbers to natural numbers, and subtract the multiples.... 1 - 1/2 - 1/3 - 1/5... but, you need to add back in some of the numbers which are duplicated (6, 12, 18, ... are in both sets, so you need to add them back in to avoid the duplication...
thus you get something like 1 - 1/2 - 1/3 + 1/(2*3) - 1/5 + 1/(2*5) + 1/(3*5) - 1/(2*3*5) [because we've doubled up on removing them] - 1/7 + 1/(2*7) ....
What number does this equal once you get sufficiently far out? Does it actually converge? I don't know these answers, but I'm curious enough that when I have time I'm going to sit down and figure them out...
And yes, I am a math geek...