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 Sound of battle fell upon my ear & heart all day yesterday—even after dark the cannon’s insatiate roar continued ...”
—Elizabeth Blair Lee (1818–?)
“The visual is sorely undervalued in modern scholarship. Art history has attained only a fraction of the conceptual sophistication of literary criticism.... Drunk with self-love, criticism has hugely overestimated the centrality of language to western culture. It has failed to see the electrifying sign language of images.”
—Camille Paglia (b. 1947)