Golden mean base

Golden mean base

The Golden mean (φ) can be used as a number base. In it, all integers have representations of finite length. If you include the rule that you cannot have the digit sequence "11" within a numeral, each integer has a unique numeral. Examples:

Decimal Powers of φ Base φ

1 φ⁰ 1

2 φ¹+φ^-2 10.01

3 φ²+φ^-2 100.01

4 φ²+φ⁰+φ^-2 101.01

5 φ³+φ^-1+φ^-4 1000.1001

6 φ³+φ¹+φ^-4 1010.0001

7 φ⁴+φ^-4 10000.0001

8 φ⁴+φ⁰+φ^-4 10001.0001

9 φ⁴+φ¹+φ^-2+φ^-4 10010.0101

External Links

Using Powers of Phi to represent Integers (Base Phi) (http://www.mcs.surrey.ac.uk/Personal/R.Knott/Fibonacci/phigits.html)

Decimal	Powers of φ	Base φ
1	φ⁰	1
2	φ¹+φ^-2	10.01
3	φ²+φ^-2	100.01
4	φ²+φ⁰+φ^-2	101.01
5	φ³+φ^-1+φ^-4	1000.1001
6	φ³+φ¹+φ^-4	1010.0001
7	φ⁴+φ^-4	10000.0001
8	φ⁴+φ⁰+φ^-4	10001.0001
9	φ⁴+φ¹+φ^-2+φ^-4	10010.0101