Since 9 is one less than our number base, testing for divisibility by nine is as simple as adding all the digits together, until you get a one-digit number. If it is nine, the original number is divisible by 9. For instance, 48735 is divisible by nine since the sum of its digits is 27, and the sum of 27's digits is 9.
Since 9 contains the prime 3 twice, a regular 9-sided polygon can't be constructed with a compass and straightedge.
9 and 8 are the only perfect powers differing by 1.