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)
“Out of the darkness where Philomela sat,
Her fairy numbers issued. What then ailed me?
My ears are called capacious but they failed me,
Her classics registered a little flat!
I rose, and venomously spat.”
—John Crowe Ransom (1888–1974)
“And songs climb out of the flames of the near campfires,
Pale, pastel things exquisite in their frailness
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And mark its limits, like a frieze of soap-bubbles.”
—John Ashbery (b. 1927)
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Must give—for what? for lead, hazard for lead?
This casket threatens. Men that hazard all
Do it in hope of fair advantages;
A golden mind stoops not to shows of dross.”
—William Shakespeare (1564–1616)
“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.)