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)
“It is clear that all verbal structures with meaning are verbal imitations of that elusive psychological and physiological process known as thought, a process stumbling through emotional entanglements, sudden irrational convictions, involuntary gleams of insight, rationalized prejudices, and blocks of panic and inertia, finally to reach a completely incommunicable intuition.”
—Northrop Frye (b. 1912)
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“What says the Clock in the Great Clock Tower?
And all alone comes riding there
The King that could make his people stare,
Because he had feathers instead of hair.
A slow low note and an iron bell.”
—William Butler Yeats (1865–1939)
“As I have known them passionate and fine,
The gold for which they leave the golden line
Of lyric is a golden light divine,
Never the gold of darkness from a mine.”
—Robert Frost (1874–1963)
“A magazine or a newspaper is a shop. Each is an experiment and represents a new focus, a new ratio between commerce and intellect.”
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“They must to keep their certainty accuse
All that are different of a base intent;
Pull down established honour; hawk for news
Whatever their loose phantasy invent
And murmur it with bated breath....”
—William Butler Yeats (1865–1939)