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:
“There are people who are so presumptuous that they know no other way to praise a greatness that they publicly admire than by representing it as a preliminary stage and bridge leading to themselves.”
—Friedrich Nietzsche (1844–1900)
“For a woman to get a rewarding sense of total creation by way of the multiple monotonous chores that are her daily lot would be as irrational as for an assembly line worker to rejoice that he had created an automobile because he tightened a bolt.”
—Edith Mendel Stern (1901–1975)
“The forward Youth that would appear
Must now forsake his Muses dear,
Nor in the Shadows sing
His Numbers languishing.”
—Andrew Marvell (1621–1678)
“In our Mechanics’ Fair, there must be not only bridges, ploughs, carpenter’s planes, and baking troughs, but also some few finer instruments,—rain-gauges, thermometers, and telescopes; and in society, besides farmers, sailors, and weavers, there must be a few persons of purer fire kept specially as gauges and meters of character; persons of a fine, detecting instinct, who note the smallest accumulations of wit and feeling in the bystander.”
—Ralph Waldo Emerson (1803–1882)
“Such is always the pursuit of knowledge. The celestial fruits, the golden apples of the Hesperides, are ever guarded by a hundred-headed dragon which never sleeps, so that it is an Herculean labor to pluck them.”
—Henry David Thoreau (1817–1862)
“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)
“I am sure my bones would not rest in an English grave, or my clay mix with the earth of that country. I believe the thought would drive me mad on my death-bed could I suppose that any of my friends would be base enough to convey my carcass back to her soil. I would not even feed her worms if I could help it.”
—George Gordon Noel Byron (1788–1824)