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)
“What culture lacks is the taste for anonymous, innumerable germination. Culture is smitten with counting and measuring; it feels out of place and uncomfortable with the innumerable; its efforts tend, on the contrary, to limit the numbers in all domains; it tries to count on its fingers.”
—Jean Dubuffet (1901–1985)
“My note to you I certainly did not expect to see in print; yet I have not been much shocked by the newspaper comments upon it. Those comments constitute a fair specimen of what has occurred to me through life. I have endured a great deal of ridicule without much malice; and have received a great deal of kindness, not quite free from ridicule. I am used to it.”
—Abraham Lincoln (1809–1865)
“A perfect beauty of a sunflower! a perfect excellent lovely
sunflower existence! a sweet natural eye to the new hip moon, woke up alive and excited grasping in the sunset shadow sunrise golden monthly breeze!”
—Allen Ginsberg (b. 1926)
“People are lucky and unlucky not according to what they get absolutely, but according to the ratio between what they get and what they have been led to expect.”
—Samuel Butler (1835–1902)
“Then must you speak
Of one the lov’d not wisely but too well;
Of one not easily jealous, but, being wrought,
Perplex’d in the extreme; of one whose hand,
Like the base Indian, threw a pearl away
Richer than all his tribe;”
—William Shakespeare (1564–1616)