Rounding To Simple Fractions
In some contexts it is desirable to round a given number x to a "neat" fraction — that is, the nearest fraction z = m/n whose numerator m and denominator n do not exceed a given maximum. This problem is fairly distinct from that of rounding a value to a fixed number of decimal or binary digits, or to a multiple of a given unit m. This problem is related to Farey sequences, the Stern-Brocot tree, and continued fractions.
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Famous quotes containing the words rounding and/or simple:
“People forget that it is the eye that makes the horizon, and the rounding mind’s eye which makes this or that man a type or representative of humanity with the name of hero or saint.”
—Ralph Waldo Emerson (1803–1882)
“Poetry is the most direct and simple means of expressing oneself in words: the most primitive nations have poetry, but only quite well developed civilizations can produce good prose. So don’t think of poetry as a perverse and unnatural way of distorting ordinary prose statements: prose is a much less natural way of speaking than poetry is. If you listen to small children, and to the amount of chanting and singsong in their speech, you’ll see what I mean.”
—Northrop Frye (1912–1991)