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:
“There are people who are so presumptuous that they know no other way to praise a greatness that they publicly admire than by representing it as a preliminary stage and bridge leading to themselves.”
—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)
“The only phenomenon with which writing has always been concomitant is the creation of cities and empires, that is the integration of large numbers of individuals into a political system, and their grading into castes or classes.... It seems to have favored the exploitation of human beings rather than their enlightenment.”
—Claude Lévi-Strauss (b. 1908)
“Return our hymn,
like echo fling
a sweet song,
answering note for note.”
—Hilda Doolittle (1886–1961)
“I had a little nut-tree, nothing would it bear
But a golden nutmeg and a silver pear;”
—Mother Goose (fl. 17th–18th century. I had a little nut-tree, nothing would it bear (l. 1–2)
“Official dignity tends to increase in inverse ratio to the importance of the country in which the office is held.”
—Aldous Huxley (1894–1963)
“Who is here so base that would be a bondman? If any, speak, for him have I offended. Who is here so rude that would not be a Roman? If any, speak, for him have I offended. Who is here so vile that will not love his country? If any, speak, for him have I offended.”
—William Shakespeare (1564–1616)