1089 is the number after 1088 and before 1090. It is 33 squared, a nonagonal number and a centered octagonal number.
It has some interesting mathematical properties.
The number 1089 is the result of the following experiment:
- Take any three-digit integer in which the first digit is at least two more than the last.
- Reverse the digits, and subtract the result from the original number.
- Add to this result the number produced by reversing its digits.
For example:
732 - 237 = 495
495 + 594 = 1089
Multiplying the number 1089 by the integers from 1 to 9 produces a pattern: multipliers adding up to 10 give products that are the digit reversals of each other.
1 x 1089 = 1089
2 x 1089 = 2178
3 x 1089 = 3267
4 x 1089 = 4356
5 x 1089 = 5445
6 x 1089 = 6534
7 x 1089 = 7623
8 x 1089 = 8712
9 x 1089 = 9801
Numbers formed analogously in other bases, e.g. octal 1067 or hexadecimal 10EF, also have these properties.
Last updated: 07-16-2005 21:33:56