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Relevant bibliographies by topics / Golden circle

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Journal articles

Academic literature on the topic 'Golden circle'

Author: Grafiati

Published: 4 June 2021

Last updated: 15 February 2022

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Journal articles on the topic "Golden circle"

1

Linn, Stacy L., and David K. Neal. "Approximating Pi with the Golden Ratio." Mathematics Teacher 99, no. 7 (2006): 472–77. http://dx.doi.org/10.5951/mt.99.7.0472.

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Around 225 BC, Archimedes wrote the treatise Measurement of a Circle, which contained the first derivation of a formula for the area of a circle and the first formal approximation of the constant we now call π. At that time, it was already known that the ratio of the areas of two circles equals the ratio of the squares of their diameters. This result had appeared in Euclid's Elements (Euclid 1956) as Proposition 12.2.

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2

Nakajima, Yoshiaki, and Hirohiko Ohta. "Effect of Golden Ratio on the Beauty of Double Concentric Circles." Perceptual and Motor Skills 69, no. 3-1 (1989): 767–70. http://dx.doi.org/10.1177/00315125890693-111.

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The effect of golden ratio for the aesthetic preference of double concentric circles was investigated. 124 Japanese college students were asked to choose one concentric circle in each 36 pairs combined among nine kinds of concentric circles. Analysis showed that the beauty of circles was the highest at stimulus No. 4 and two possible interpretations were indicated.

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3

Pierrehumbert, Raymond T. "A golden circle in the sky." Nature 447, no. 7147 (2007): 911. http://dx.doi.org/10.1038/447911b.

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4

Toskovic, Oliver, and Slobodan Markovic. "Aesthetic preference of object position on pictures." Psihologija 36, no. 3 (2003): 313–30. http://dx.doi.org/10.2298/psi0303313t.

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In this study three hypothesis were evaluated. The first claims that the golden section position is an ideal position of an object on a picture and that this position does not depend on picture shape, or on the number of objects on it. According to the second hypothesis, the aesthetically optimal effect is achieved when the focus is on the right side of the picture ( for asymmetrically composed pictures). According to the third hypothesis, there is an influence of previous stimulation on aesthetic experience; that is, because of the monotony, the aesthetic preference of observers will change.

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5

Willoughby, H. E. "The Golden Radius in Balanced Atmospheric Flows." Monthly Weather Review 139, no. 4 (2011): 1164–68. http://dx.doi.org/10.1175/2010mwr3579.1.

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Abstract In gradient-balanced, cyclonic flow around low pressure systems, a golden radius exists where RG, the gradient-wind Rossby number, is φ−1 = 0.618 034, the inverse golden ratio. There, the geostrophic, cyclostrophic, and inertia-circle approximations to the wind all produce equal magnitudes. The ratio of the gradient wind to any of these approximations is φ−1. In anomalous (anticyclonic) flow around a low, the golden radius falls where RG = −φ = −1.618 034, and the magnitude of the ratio of the anomalous wind to any of the two-term approximations is φ. In normal flow, the golden radius

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6

Rand, D. A. "Existence, nonexistence and universal breakdown of dissipative golden invariant tori. I. Golden critical circle maps." Nonlinearity 5, no. 3 (1992): 639–62. http://dx.doi.org/10.1088/0951-7715/5/3/002.

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7

Tengberg, M., D. T. Potts, and H. P. Francfort. "The golden leaves of Ur." Antiquity 82, no. 318 (2008): 925–36. http://dx.doi.org/10.1017/s0003598x00097684.

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AbstractThe famous headdress of Pu-abum at Ur is an object of great beauty. But the authors show that the gold leaves of the headdresses and diadems of her court circle can tell an even richer story. Identifying among them the leaves of the sissoo tree, they show that its symbolic usage celebrated a wide range of properties, from medicine to furniture. These were properties appreciated not only in Mesopotamia but in eastern Iran and the Indus Valley, home to the sissoo tree as well as to neighbouring civilisations.

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8

VALSAMMA, K. M., and K. BABU JOSEPH. "TRAJECTORY SCALING FUNCTION OF POLYNOMIAL CIRCLE MAPS." International Journal of Bifurcation and Chaos 04, no. 02 (1994): 471–75. http://dx.doi.org/10.1142/s0218127494000344.

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The universality of trajectory scaling function (TSF) for the polynomial form of the circle map in the quasiperiodic-to-chaos transition is discussed. It is found that the TSF gets bumpier with increase in the degree of inflection z, for both Golden and Silver Mean cases, and shows multiple scaling with increase in z, reflecting the monotone decrease of α with increasing z. The effect of noise is also studied.

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9

Сафиулина, Yu Safiulina, Шмурнов, and V. Shmurnov. "Golden Section’s Numerical Approximations in Terms of Graphics and Application." Geometry & Graphics 2, no. 2 (2014): 15–20. http://dx.doi.org/10.12737/5585.

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Golden proportion’s graphic plotting methods have been considered. A history related to gradual development of views on Golden section problem as «law of beauty» is traced. Numerical ratios most frequently used in the art for approximations related to division of a line segment in extreme and mean ratio have been provided. An original scheme for «Golden rectangle» construction based on application offered by Leonardo da Vinci for the quadrature of circle problem solution has been proposed.

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10

Hamm, Andreas, and Robert Graham. "Scaling for small random perturbations of golden critical circle maps." Physical Review A 46, no. 10 (1992): 6323–33. http://dx.doi.org/10.1103/physreva.46.6323.

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