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)
“It is not to be forgotten that what we call rational grounds for our beliefs are often extremely irrational attempts to justify our instincts.”
—Thomas Henry Huxley (1825–95)
“One murder makes a villain, millions a hero. Numbers sanctify, my good fellow.”
—Charlie Chaplin (1889–1977)
“And songs climb out of the flames of the near campfires,
Pale, pastel things exquisite in their frailness
With a note or two to indicate it isn’t lost,
On them at least. The songs decorate our notion of the world
And mark its limits, like a frieze of soap-bubbles.”
—John Ashbery (b. 1927)
“In marble halls as white as milk,
Lined with a skin as soft as silk,
Within a fountain crystal-clear,
A golden apple doth appear.
No doors there are to this stronghold,
Yet thieves break in and steal the gold.”
—Mother Goose (fl. 17th–18th century. In marble walls as white as milk (Riddle: An Egg)
“Official dignity tends to increase in inverse ratio to the importance of the country in which the office is held.”
—Aldous Huxley (1894–1963)
“No love is entirely without worth, even when the frivolous calls to the frivolous and the base to the base.”
—Iris Murdoch (b. 1919)