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)
“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)
“I’m not even thinking straight any more. Numbers buzz in my head like wasps.”
—Kurt Neumann (1906–1958)
“What is line? It is life. A line must live at each point along its course in such a way that the artist’s presence makes itself felt above that of the model.... With the writer, line takes precedence over form and content. It runs through the words he assembles. It strikes a continuous note unperceived by ear or eye. It is, in a way, the soul’s style, and if the line ceases to have a life of its own, if it only describes an arabesque, the soul is missing and the writing dies.”
—Jean Cocteau (1889–1963)
“Love took up the glass of Time, and turned it in his glowing hands;
Every moment, lightly shaken, ran itself in golden sands.
Love took up the harp of Life, and smote on all the chords with
might;
Smote the chord of Self, that, trembling, passed in music out of sight.”
—Alfred Tennyson (1809–1892)
“Personal rights, universally the same, demand a government framed on the ratio of the census: property demands a government framed on the ratio of owners and of owning.”
—Ralph Waldo Emerson (1803–1882)
“Things base and vile, holding no quantity,
Love can transpose to form and dignity.
Love looks not with the eyes, but with the mind,
And therefore is winged Cupid painted blind.”
—William Shakespeare (1564–1616)