Golden Ratio Base - Representing Irrational Numbers of Note As Golden Ratio Base Numbers

Representing Irrational Numbers of Note As Golden Ratio Base Numbers

The base-φ representations of some interesting numbers:

  • π ≈ 100.0100 1010 1001 0001 0101 0100 0001 0100 ...φ (sequence A102243 in OEIS)
  • e ≈ 100.0000 1000 0100 1000 0000 0100 ...φ (sequence A105165 in OEIS)
  • √2 ≈ 1.0100 0001 0100 1010 0100 0000 0101 0000 0000 0101 ...φ
  • φ = (1+√5)/2 = 10φ
  • √5 = 10.1φ

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