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:
“Brave people may be persuaded to an action by representing it as being more dangerous than it really is.”
—Friedrich Nietzsche (1844–1900)
“How did reason enter the world? As is fitting, in an irrational way, accidentally. We will have to guess at it, like a riddle.”
—Friedrich Nietzsche (1844–1900)
“Think of the earth as a living organism that is being attacked by billions of bacteria whose numbers double every forty years. Either the host dies, or the virus dies, or both die.”
—Gore Vidal (b. 1925)
“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)
“Absolutely speaking, Do unto others as you would that they should do unto you is by no means a golden rule, but the best of current silver. An honest man would have but little occasion for it. It is golden not to have any rule at all in such a case.”
—Henry David Thoreau (1817–1862)
“A magazine or a newspaper is a shop. Each is an experiment and represents a new focus, a new ratio between commerce and intellect.”
—John Jay Chapman (1862–1933)
“Do not gain basely; base gain is equal to ruin.”
—Hesiod (c. 8th century B.C.)