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:
“... today we round out the first century of a professed republic,—with woman figuratively representing freedom—and yet all free, save woman.”
—Phoebe W. Couzins (1845–1913)
“The irrational may be attractive in the abstract, but not in cab drives, dinner guests, or elderly relatives.”
—Mason Cooley (b. 1927)
“Publishers are notoriously slothful about numbers, unless they’re attached to dollar signs—unlike journalists, quarterbacks, and felony criminal defendents who tend to be keenly aware of numbers at all times.”
—Hunter S. Thompson (b. 1939)
“Alexander Woollcott broadcasts the story of the wife who returned a dog to the Seeing Eye with this note attached: “I am sending the dog back. My husband used to depend on me. Now he is independent, and I never know where he is.””
—For the State of New Jersey, U.S. public relief program (1935-1943)
“A perfect beauty of a sunflower! a perfect excellent lovely
sunflower existence! a sweet natural eye to the new hip moon, woke up alive and excited grasping in the sunset shadow sunrise golden monthly breeze!”
—Allen Ginsberg (b. 1926)
“Personal rights, universally the same, demand a government framed on the ratio of the census: property demands a government framed on the ratio of owners and of owning.”
—Ralph Waldo Emerson (1803–1882)
“Report of fashions in proud Italy,
Whose manners still our tardy-apish nation
Limps after in base imitation.”
—William Shakespeare (1564–1616)