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
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“Brave people may be persuaded to an action by representing it as being more dangerous than it really is.”
—Friedrich Nietzsche (1844–1900)
“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)
“The forward Youth that would appear
Must now forsake his Muses dear,
Nor in the Shadows sing
His Numbers languishing.”
—Andrew Marvell (1621–1678)
“The note of the white-throated sparrow, a very inspiriting but almost wiry sound, was first heard in the morning, and with this all the woods rang. This was the prevailing bird in the northern part of Maine. The forest generally was alive with them at this season, and they were proportionally numerous and musical about Bangor. They evidently breed in that State.”
—Henry David Thoreau (1817–1862)
“I wandered lonely as a cloud
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When all at once I saw a crowd,
A host, of golden daffodils;”
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—John Jay Chapman (1862–1933)
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—Miguel De Cervantes (1547–1616)