I was at the aspie meetup on Monday. Another aspie showed up, and we resumed our previous mathematical discussion with the square root of two. (Yes, we can spend hours discussing the square root of 2. The other diners probably thought we were nuts.) I remarked that 297/210 is 99/70, which is a convergent of the continued fraction expansion and thus a very close approximation to sqrt(2) (it's 1.4142857).
Not having access to Markus Kuhn's page, we then doubled and guessed when to add 1, and got 1189/841, which we verified by multiplying (which we could do in our heads if they were wired together). He then noticed that 841 is 29 squared. 1189=41*29, and 41/29 is another convergent. You can get a convergent from the previous one like this: 99/70=(2*29+41)/(41+29). So A4 has the most accurate aspect ratio (as do A3 and A2), while A0 has more accurate area. phma
