Writing Golden Ratio Base Numbers in Standard Form
211.01φ is not a standard base-φ numeral, since it contains a "11" and a "2", which isn't a "0" or "1", and contains a 1=-1, which isn't a "0" or "1" either.
To "standardize" a numeral, we can use the following substitutions: 011φ = 100φ, 0200φ = 1001φ and 010φ = 101φ. We can apply the substitutions in any order we like, as the result is the same. Below, the substitutions used are on the right, the resulting number on the left.
211.01φ 300.01φ 011φ → 100φ 1101.01φ 0200φ → 1001φ 10001.01φ 011φ → 100φ (again) 10001.101φ 010φ → 101φ 10000.011φ 010φ → 101φ (again) 10000.1φ 011φ → 100φ (again)Any positive number with a non-standard terminating base-φ representation can be uniquely standardized in this manner. If we get to a point where all digits are "0" or "1", except for the first digit being negative, then the number is negative. This can be converted to the negative of a base-φ representation by negating every digit, standardizing the result, and then marking it as negative. For example, use a minus sign, or some other significance to denote negative numbers. If the arithmetic is being performed on a computer, an error message may be returned.
Note that when adding the digits "9" and "1", the result is a single digit "(10)", "A" or similar, as we are not working in decimal.
Read more about this topic: Golden Ratio Base
Famous quotes containing the words writing, golden, ratio, base, numbers, standard and/or form:
“A song is no song unless the circumstance is free and fine. If a singer sing from a sense of duty or from seeing no way to escape, I had rather have none. Those only can sleep who do not care to sleep; and those only write or speak best who do not too much respect the writing or the speaking.”
—Ralph Waldo Emerson (1803–1882)
“If you associate enough with older people who do enjoy their lives, who are not stored away in any golden ghettos, you will gain a sense of continuity and of the possibility for a full life.”
—Margaret Mead (1901–1978)
“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)
“Music is of two kinds: one petty, poor, second-rate, never varying, its base the hundred or so phrasings which all musicians understand, a babbling which is more or less pleasant, the life that most composers live.”
—Honoré De Balzac (1799–1850)
“All ye poets of the age,
All ye witlings of the stage,
Learn your jingles to reform,
Crop your numbers to conform.
Let your little verses flow
Gently, sweetly, row by row;
Let the verse the subject fit,
Little subject, little wit.
Namby-Pamby is your guide,
Albion’s joy, Hibernia’s pride.”
—Henry Carey (1693?–1743)
“I don’t have any problem with a reporter or a news person who says the President is uninformed on this issue or that issue. I don’t think any of us would challenge that. I do have a problem with the singular focus on this, as if that’s the only standard by which we ought to judge a president. What we learned in the last administration was how little having an encyclopedic grasp of all the facts has to do with governing.”
—David R. Gergen (b. 1942)
“I have discovered the most exciting, the most arduous literary form of all, the most difficult to master, the most pregnant in curious possibilities. I mean the advertisement.... It is far easier to write ten passably effective Sonnets, good enough to take in the not too inquiring critic, than one effective advertisement that will take in a few thousand of the uncritical buying public.”
—Aldous Huxley (1894–1963)