Number Gossip
(Enter a number and I'll tell you everything you wanted to know about it but were afraid to ask.)
Unique Properties of 9
- 9 is the smallest odd composite number
- 9 is the maximum number of cubes that are needed to sum to any positive integer
- 9 is the largest perfect power that is a neighbor of another perfect power (9 = 32 is a neighbor of 8 = 2^3)
- 9 is the only number (except one) which is equal to the sum of the digits of its square
- 9 is the only non-trivial square consisting of only odd digits
- 9 is the smallest number of distinct integer-sided squares needed to tile a rectangle
- 9 is the smallest odd number such that no odd Fibonacci number is divisible by it
- a number is divisible by 9 if and only if the sum of its digits is divisible by 9. 9 is the largest number with this divisibility property
- a nine-point circle can be constructed for every triangle, and it passes through 9 significant triangle points: side midpoints, altitude foots, and midpoints between vertices and the orthocenter