ⓘ 1089 (number)
1089 is the integer after 1088 and before 1090. It is a square number, a nonagonal number, a 32gonal number, a 364gonal number, and a centered octagonal number. 1089 is the first reversedivisible number. The next is 2178, and they are the only fourdigit numbers that divide their reverse.
1. In magic
1089 is widely used in magic tricks because it can be "produced" from any two threedigit numbers. This allows it to be used as the basis for a Magicians Choice. For instance, one variation of the book test starts by having the spectator choose any two suitable numbers and then apply some basic math to produce a single fourdigit number. That number is always 1089. The spectator is then asked to turn to page 108 of a book and read the 9th word, which the magician has memorized. To the audience it looks like the number is random, but through manipulation, the result is always the same. It is this property that led University of Oxford mathematician David Acheson to title his 2010 book 1089 and all that: a journey into mathematics.
In base 10, the following steps always yield 1089:
 Add to this result the number produced by reversing its digits.
 Reverse the digits, and subtract the smaller from the larger one.
 Take any threedigit number where the first and last digits differ by 1 or more.
For example, if the spectator chooses 237 or 732:
732 − 237 = 495 + 594 = 10891.1. In magic Explanation
The spectators 3digit number can be written as 100 × A + 10 × B + 1 × C, and its reversal as 100 × C + 10 × B + 1 × A, where 1 ≤ A ≤ 9, 0 ≤ B ≤ 9 and 1 ≤ C ≤ 9. Their difference is 99 × A − C. Note that if A − C is 0, the difference is 0, and we do not get a 3digit number for the next step. If A − C is 1, the difference is 99. Using a leading 0 gives us a 3digit number for the next step.
99 × A − C can also be written as 99 × + 180 = 1089.
1.2. In magic Other properties
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 × 1089 = 1089 ↔ 9 × 1089 = 9801 2 × 1089 = 2178 ↔ 8 × 1089 = 8712 3 × 1089 = 3267 ↔ 7 × 1089 = 7623 4 × 1089 = 4356 ↔ 6 × 1089 = 6534 5 × 1089 = 5445 ↔ 5 × 1089 = 5445Also note the patterns within each column:
1 × 1089 = 1089 2 × 1089 = 2178 3 × 1089 = 3267 4 × 1089 = 4356 5 × 1089 = 5445 6 × 1089 = 6534 7 × 1089 = 7623 8 × 1089 = 8712 9 × 1089 = 9801Numbers formed analogously in other bases, e.g. octal 1067 or hexadecimal 10EF, also have these properties.

E (mathematical constant) 

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