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:
“... today we round out the first century of a professed republic,—with woman figuratively representing freedom—and yet all free, save woman.”
—Phoebe W. Couzins (1845–1913)
“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)
“Our religion vulgarly stands on numbers of believers. Whenever the appeal is made—no matter how indirectly—to numbers, proclamation is then and there made, that religion is not. He that finds God a sweet, enveloping presence, who shall dare to come in?”
—Ralph Waldo Emerson (1803–1882)
“There’s not a note of mine that’s worth the noting.”
—William Shakespeare (1564–1616)
“Love’s secrets, being mysteries, ever pertain to the transcendent and the infinite; and so they are as airy bridges, by which our further shadows pass over into the regions of the golden mists and exhalations; whence all poetical, lovely thoughts are engendered, and drop into us, as though pearls should drop from rainbows.”
—Herman Melville (1819–1891)
“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)
“There is but one pride pardonable; that of being above doing a base or dishonorable action.”
—Samuel Richardson (1689–1761)