The Golden Ratio and its Effects on the Perceived Visual Appeal of Photos

The golden ratio (GR) has long been proposed to be the most visually appealing geometric proportion (Green, 1995). As a result, many popular sources have claimed that composition guidelines made from the GR such as the phi grid, the golden spiral, and the golden layout can be used to enhance the visual appeal of photographs. However, empirical evidence to substantiate this claim is inadequate. The purpose of this study is to analyze whether three GR composition guidelines, the phi grid, the golden spiral, and the golden layout, can create photo adaptations that are consistently perceived as more visually appealing than their non-golden ratio (NGR) counterparts. A digital survey was created and released on social media, targeting adults ages 18 through 64 with an interest in art. Respondents were presented with 9 pairs of photos, consisting of two photo adaptations, a GR version (made with one of the GR guidelines), and a NGR version. Respondents were instructed to choose the photo which they perceived to be more visually appealing. The results from the survey indicated that there was no inherent preference towards GR photos overall. However, when analyzing the results from each golden ratio guideline, it was found that only the golden layout produced GR photos that were more preferred than their NGR counterparts. Further research must be conducted to fully understand the aesthetic appeal of the golden layout. Until then, creative individuals should be skeptical of recommendations for using the GR to produce visual compositions.

Robust Model Predictive Control with Almost Zero Online Computation

This paper provides a strategy for the problem of robust model predictive control of constrained, discrete-time systems with state and output disturbances. Using the linear matrix inequality (LMI) method, the nested geometric proportion asymptotically stable ellipsoid (GPASE) strategy is designed off-line, and then the designed shrinking ellipsoids strategy assures the system converges on the equivalent with an exponential convergence velocity. The biggest advantage of this method is the online computation is almost reduced to zero, which makes it possible to apply the designed control scheme not only to plants with slowly varying parameters, but also to fast ones. Finally, a simulation example shows the validity of the proposed technique.

The Two Supreme Principles of Plato’s Cosmos—the One and the Indefinite Dyad—the Division of a Straight Line into Extreme and Mean Ratio, and Pingala’s Mātrāmeru

The objective of this paper is to propose a mathematical interpretation of the continuous geometric proportion (Timaeus, 32a) with which Plato accomplishes the goal to unify, harmonically and symmetrically, the Two Opposite Elements of Timaeus Cosmos—Fire and Earth—through the Mean Ratio. As we know, from the algebraic point of view, it is possible to compose a continuous geometric proportion just starting from two different quantities a (Fire) and b (Earth); their sum would be the third term, so that we would obtain the continuous geometric proportion par excellence, which carries out the agreement of opposites most perfectly: (a + b)/a = a/b. This equal proportion, applied to linear geometry, corresponds to what Euclid called the Division into Extreme and Mean Ratio (DEMR) or The Golden Proportion. In fact, according to my mathematical interpretation, in the Timaeus 32b and in the Epinomis 991 a–b, Plato uses Pingala’s Mātrāmeru or The First Analogy of the Double to mould the body of the Cosmos as a whole, to the point of identifying the two supreme principles of the Cosmos—the One (1) and the Indefinite Dyad (Φ and1/Φ)—with the DEMR. In effect, Fire and Earth are joined not by a single Mean Ratio but by two (namely, Air and Water). Moreover, using the Platonic approach to analyse the geometric properties of the shape of the Cosmos as a whole, I think that Timaeus constructed the 12 pentagonal faces of Dodecahedron by means of elementary Golden Triangles (a/b = Φ) and the Mātrāmeru sequence. And, this would prove that my mathematical interpretation of the platonic texts is at least plausible.

THE APPLICATION OF GEOMETRIC PROPORTION AND COMPOSITION THEORY TO THE BNI 46 JAKARTA BUILDING BY SILABAN

Abstract- In terms of history, proportion, composition and geometry have been applied as design elements since long ago, way before the era of modern architecture. The existence of these three elements enables numerous variations and produces freedom of expression. Unfortunately, in current design processes, these visual principles are often overlooked. In fact, they play a role as one of the indicators of aesthetics of a building, as well as exerting influence on human perception in capturing and perceiving a given space. The purpose of this research is to study the application of proportion and composition principles to one of the creations of the Indonesian modern architect Frederich Silaban. The BNI 46 Building design by Silaban acts as the research object, displaying a façade which is crammed with modern thoughts, different on each side but remaining harmonious and visually attractive. The theory of proportion, composition, geometry and structuring principles provide the basis for analyzing the existing object. This research uses the descriptive analytical method with the qualitative approach to data collection of the research object. The next step is the vertical and horizontal analysis of the building enclosure in relation to the implementation of geometric proportion and composition principles in the building. This research is expected to be beneficial in terms of enriching the knowledge and study of geometric proportion and proportion in architecture, adding to the consideration of implementing visual principles for professionals, as well as adding to the archive/portfolio concerning Silaban as one of Indonesia’s pioneering modern architects. Keywords: proportion, composition, Geometry, Silaban

Comparing the efficacy of visual inspection with acetic acid and lugol’s iodine as a screening tool for detecting cervical lesions in asymptomatic women of reproductive age group with colposcopy and biopsy in a tertiary care hospital

Background: A quarter of global burden of carcinoma cervix is experienced in India, where about 1, 26,000 new cases and 71,000 deaths attribute to cervical cancer are estimated to occur each year. Cervical cancer constitutes 15-55% of all female cancer and value of age standardized incidence ranges from 17.2 to 55 per 1 lakh women in different region in India with 5-year survival rate of less than 40% as most are detected at advanced stage. The objective of present study was to identify the incidence of cervical lesions in sexually active asymptomatic women.Methods: This prospective study conducted in a tertiary care hospital for 1 year. This study comprises study subject of 734 women who were attending general and gynecology OPD. All 734 patients were subjected to visual inspection and magnification (VIA/VILI), colposcopy and biopsy was done in the positive patients.Results: Of 734 cases studied, colposcopy was positive in 97 (13.1%). Among 97 cases who were colposcopy positive, VIA/VILI was positive in 90 cases. Colposcopy guided biopsy was positive in 97 cases. The sensitivity of VIA/VILI in detecting preinvasive lesions was 91.84% and specificity was 100% when compared with colposcopy which has sensitivity 98.98% and specificity 100%.Conclusions: There is an enormous increase in the incidence of cancer cervix in geometric proportion. This can be controlled only with the introduction of mass screening programme by magnavision in a coordinated way in low resource settings.

Automatic Offline Formulation of Robust Model Predictive Control Based on Linear Matrix Inequalities Method

Two automatic robust model predictive control strategies are presented for uncertain polytopic linear plants with input and output constraints. A sequence of nested geometric proportion asymptotically stable ellipsoids and controllers is constructed offline first. Then the feedback controllers are automatically selected with the receding horizon online in the first strategy. Finally, a modified automatic offline robust MPC approach is constructed to improve the closed system's performance. The new proposed strategies not only reduce the conservatism but also decrease the online computation. Numerical examples are given to illustrate their effectiveness.

Model Test and Numerical Simulation for Support Time of Tunnel in Loess

The work presented in this paper focuses on support time for tunnel, which has much effect on stability of tunnel. Based on loess tunnel of Zhengzhou-Xi’an high-speed passenger rail line in China, large scale model test with geometric proportion 1: 20 was applied to study on different support time. Supplemental numerical analysis was carried out to investigate the effect of release ratio of stress which cannot be covered by model test. It is revealed that it is asynchronous change for deformation, strain and stress of surround rock. If the supporting constructs prematurely, internal force of support would be excessive greatly and if the supporting constructs too late, it will bring excessive slack pressure which leads to the plastic zone unfavorable, even tunnel collapse. The reasonable support time can improve self-bearing capability of surrounding rock and reduce the cost. The limited displacements about 17.8 cm for crown and 12.9 for horizontal convergence are gained. The research results can act as reference for similar materials tunnel and underground engineering construction.

The Geometry of Zoser's Step Pyramid at Saqqara

The Step Pyramid of Zoser at Saqqara is examined from the point of view of constructive geometry and mensuration. The evidence is that it is based on geometric proportion, though this may simply be the outcome of peg-and-chord technology employed in setting out the monument. The procedure that the architect may have followed in setting out the monument is Ad Quadratum in its most elemental form.