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:
“He who has learned what is commonly considered the whole art of painting, that is, the art of representing any natural object faithfully, has as yet only learned the language by which his thoughts are to be expressed.”
—John Ruskin (1819–1900)
“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)
“I’m not even thinking straight any more. Numbers buzz in my head like wasps.”
—Kurt Neumann (1906–1958)
“For sounds in winter nights, and often in winter days, I heard the forlorn but melodious note of a hooting owl indefinitely far; such a sound as the frozen earth would yield if struck with a suitable plectrum, the very lingua vernacula of Walden Wood, and quite familiar to me at last, though I never saw the bird while it was making it.”
—Henry David Thoreau (1817–1862)
“Eyes that last I saw in tears
Through division
Here in death’s dream kingdom
The golden vision reappears
I see the eyes but not the tears
This is my affliction”
—T.S. (Thomas Stearns)
“Official dignity tends to increase in inverse ratio to the importance of the country in which the office is held.”
—Aldous Huxley (1894–1963)
“Time, force, and death
Do to this body what extremes you can,
But the strong base and building of my love
Is as the very centre of the earth,
Drawing all things to it.”
—William Shakespeare (1564–1616)