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
Read more about this topic: Golden Ratio Base
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—Friedrich Nietzsche (1844–1900)
“The irrational may be attractive in the abstract, but not in cab drives, dinner guests, or elderly relatives.”
—Mason Cooley (b. 1927)
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—Bible: Hebrew Numbers 35:33.
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With a note or two to indicate it isn’t lost,
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“Do not gain basely; base gain is equal to ruin.”
—Hesiod (c. 8th century B.C.)