Continued Fraction
It can be expressed as the continued fraction (sequence A040002 in OEIS). The sequence of best rational approximations is:
Convergents of the continued fraction are colored; their numerators are 2, 9, 38, 161, ... (sequence A001077 in OEIS), and their denominators are 1, 4, 17, 72, ... (sequence A001076 in OEIS). The other (non-colored) terms are semiconvergents.
Read more about this topic: Square Root Of 5
Famous quotes containing the words continued and/or fraction:
“The cause of Sense, is the External Body, or Object, which presseth the organ proper to each Sense, either immediately, as in the Taste and Touch; or mediately, as in Seeing, Hearing, and Smelling: which pressure, by the mediation of Nerves, and other strings, and membranes of the body, continued inwards to the Brain, and Heart, causeth there a resistance, or counter- pressure, or endeavor of the heart, to deliver it self: which endeavor because Outward, seemeth to be some matter without.”
—Thomas Hobbes (1579–1688)
“The mother as a social servant instead of a home servant will not lack in true mother duty.... From her work, loved and honored though it is, she will return to her home life, the child life, with an eager, ceaseless pleasure, cleansed of all the fret and fraction and weariness that so mar it now.”
—Charlotte Perkins Gilman (1860–1935)