## Applied methods in the theory of nonlinear oscillations by V. M. Starzhinskii

By V. M. Starzhinskii

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18) among other geometrical progressions, and this fact is a reason for the wide spread prevalence of the golden logarithmic spiral in forms and structures of nature. 3. 11). 11), then we get the representation t in the form of the following continued fraction 1 τ = 1+ . 20) τ = 1+ . 1 1+ 1 1+ 1 1+ 1 + ... 20) in mathematics is called a Continued or Chain fraction. Note that the theory of continued fractions is one of the most impor tant topics of modern mathematics. 4. 10). 10), then we will get the following representation for τ: τ = 1 + τ.

However, many mathematicians used the term “Mid dle and Two Ends,” in particular: Abu Kamil (850 930), al Biruni (973 1050), Ger hard of Cremona (12th century), Adelard (12th century), Campanus of Novara (13th century), and Billingsley (1570). In addition to the definitions of the “divi sion in the extreme and mean ratio” and “proportion having a middle and two ends,” other definitions, namely: “divina proportione,” “proportionally divided,” “contin uous proportion,” “medial section,” “the golden number,” and “the golden section” were used.

S. htm (Every attempt was made to contact the author for permission, Mr. 6. 8. 11. 11. 573 Richard Wesley Hamming credit Samuel P. com/photos/fdecomite/ 2985635111 Fiddlehead fern credit James W. 6 a Aloe spiral credit J. com/photos/ philprice/2610013436 Whirlpool Galaxy M51 credit NASA, ESA, S. org The Spiralof Life credit Mr. newsphotoid=1309 Smolny Cathedral in St. jpg St. jpg Golden Section in Contemporary Abstract and Applied Art Polyhedral Universe credit Teja Krasek No. 258 from Cosmic Measures collection credit Astrid Fitzgerald Nine credit Marion Drennen Double Pentagram Pentagons credit John Michell Cosmic Gems credit Teja Krasek Pentagonal Hexagons credit John Michell No.