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
Famous quotes containing the words representing, irrational, numbers, note, golden, ratio and/or 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)
“I had but three chairs in my house; one for solitude, two for friendship; three for society. When visitors came in larger and unexpected numbers there was but the third chair for them all, but they generally economized the room by standing up.”
—Henry David Thoreau (1817–1862)
“In it he proves that all things are true and states how the truths of all contradictions may be reconciled physically, such as for example that white is black and black is white; that one can be and not be at the same time; that there can be hills without valleys; that nothingness is something and that everything, which is, is not. But take note that he proves all these unheard-of paradoxes without any fallacious or sophistical reasoning.”
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