Three Dimensional Shift-Like Mappings of Dynamical Degree Golden Ratio

Author(s):  
Kazutoshi Maegawa
2013 ◽  
Vol 83 (5) ◽  
pp. 801-808 ◽  
Author(s):  
Alberto Rossetti ◽  
Marcio De Menezes ◽  
Riccardo Rosati ◽  
Virgilio F. Ferrario ◽  
Chiarella Sforza

ABSTRACT Objective: To demonstrate if one or more golden relationships between different measurements of the human face exist. Materials and Methods: To make our measurements, we used three-dimensional (3D) stereophotogrammetry, which has proved to be the “gold standard” in the field of facial anthropometry. We obtained 3D stereophotogrammetric facial acquisitions of 400 healthy young adult subjects, then had them scored by an Evaluation Jury. Each subject received an esthetic evaluation ranging from 0 to 40. Individuals with a score larger than 28 were considered very attractive (VA), and individuals with a score lower than 12 were considered not attractive (NA). Fifteen subjects per group were chosen by chance, with a final total group of 60 subjects: 15 VA males, 15 NA males, 15 VA females, and 15 NA females. For each subject, a set of facial distances was obtained from the stereophotogrammetric facial reconstruction, and 10 ratios were computed. The effects of sex and attractiveness were tested by analysis of variance. Additionally, Student's t-tests verified if the ratios were statistically different from the golden ratio. Results: For nine ratios, no significant effects of sex or attractiveness were found. Only the eye-mouth distance/height of the mandible ratio was significantly influenced by sex (P  =  .035) and attractiveness (P  =  .032). Seven out of 10 ratios were statistically different from the hypothetical value of 1.618, and only three of them were similar to the golden ratio. Conclusions: Ratios between 3D facial distances were not related to attractiveness. Most of the facial ratios were different from the golden ratio.


2020 ◽  
pp. 133-149
Author(s):  
Santiago Javier Santamaría-Bedón

La biomimética imita los procesos naturales para plantear posibles soluciones a problemas humanos y ha sido aplicado por varias profesiones, convirtiéndose en una práctica recurrente para adoptar nuevas morfologías o principios funcionales. Leonardo de Pisa empleó estos fenómenos y desarrolló una serie matemática llamada sucesión de Fibonacci, dando lugar posteriormente a la proporción áurea. Estos descubrimientos matemáticos se manifiestan en forma concurrente en patrones geométricos de los procesos y estructuras de la naturaleza como en la distribución de hojas en las plantas. El objetivo de este artículo es proponer recursos formales procedentes de la aplicación de la biomimética de manera superficial/reductiva, que adopta la morfología de la planta Sempervivum tectorum L. para futuras soluciones formales y funcionales del ámbito del diseño. Para ello, se aplica la fotogrametría como técnica para capturar información bidimensional mediante fotografías y convertirlas en información tridimensional, obteniendo un modelo idéntico al original. La digitalización del elemento natural cumple con la siguiente metodología: preparación del entorno, toma de datos, alineación de fotografías, creación de nube de puntos densa, creación de malla y la textura. Posteriormente se realiza la construcción de modelos 3D, siguiendo el recorrido helicoidal digitalizado. Esta trayectoria crea un patrón en forma de hélice que se repite en sentido radial, tomando como referencia el eje vertical, de esta manera se crea un vórtice en la corona del sólido. A partir de esta estructura se realiza variaciones morfológicas, respetando la dirección de la hélice matriz. Palabras clave: Morfología, fotogrametría, ángulo de oro, sucesión de Fibonacci, diseño. AbstractBiomimetics mimics natural processes to propose possible solutions to human problems and has been applied by various professions, making it a recurring practice to adopt new morphologies or functional principles. Leonardo of Pisa used these phenomena and developed a mathematical series called the Fibonacci sequence, later giving rise to the golden ratio. These mathematical discoveries are manifested concurrently in geometric patterns of the processes and structures of nature as in the distribution of leaves in plants. The objective of this article was to propose formal resources from the application of biomimetics in a superficial / reductive way, which adopts the morphology of the Sempervivum tectorum L. plant for future formal and functional solutions in the field of design. To this end, photogrammetry was applied as a technique to capture two-dimensional information through photographs and convert them into three-dimensional information, obtaining a model identical to the original. The digitization of the natural element complied with the following methodology: environment preparation, data collection, photo alignment, dense point cloud creation, mesh and texture creation. Subsequently, the construction of 3D models is carried out, following the digitized helical path. This path created a helix-shaped pattern that was repeated radially, taking the vertical axis as a reference, thus creating a vortex in the crown of the solid. Morphological variations were made from this structure, respecting the direction of the parent helix. Keywords: Morphology, digital photogrammetry, golden angle, Fibonacci sequence, design.


Axioms ◽  
2019 ◽  
Vol 8 (4) ◽  
pp. 136
Author(s):  
Juan Frausto-Solís ◽  
Juan Paulo Sánchez-Hernández ◽  
Fanny G. Maldonado-Nava ◽  
Juan J. González-Barbosa

Protein folding problem (PFP) consists of determining the functional three-dimensional structure of a target protein. PFP is an optimization problem where the objective is to find the structure with the lowest Gibbs free energy. It is significant to solve PFP for use in medical and pharmaceutical applications. Hybrid simulated annealing algorithms (HSA) use a kind of simulated annealing or Monte Carlo method, and they are among the most efficient for PFP. The instances of PFP can be classified as follows: (a) Proteins with a large number of amino acids and (b) peptides with a small number of amino acids. Several HSA have been positively applied for the first case, where I-Tasser has been one of the most successful in the CASP competition. PEP-FOLD3 and golden ratio simulated annealing (GRSA) are also two of these algorithms successfully applied to peptides. This paper presents an enhanced golden simulated annealing (GRSA2) where soft perturbations (collision operators), named “on-wall ineffective collision” and “intermolecular ineffective collision”, are applied to generate new solutions in the metropolis cycle. GRSA2 is tested with a dataset for peptides previously proposed, and a comparison with PEP-FOLD3 and I-Tasser is presented. According to the experimentation, GRSA2 has an equivalent performance to those algorithms.


Leonardo ◽  
2001 ◽  
Vol 34 (3) ◽  
pp. 227-229 ◽  
Author(s):  
Adam Storeygard

The author created a sculpture using a rigorous mathematical procedure informed by aesthetic decisions. The form is based on the relationships found in the golden triangle and its spiral folded into three dimensions. In creating the form, the author discovered a three-dimensional motif (the “golden gnomonoid”) with interesting mathematical properties and sculptural ramifications.


2016 ◽  
Vol 212 (2) ◽  
pp. 245-255 ◽  
Author(s):  
António J. Pereira ◽  
Paulo Aguiar ◽  
Michael Belsley ◽  
Helder Maiato

The understanding of cytoskeleton dynamics has benefited from the capacity to generate fluorescent fiducial marks on cytoskeleton components. Here we show that light-induced imprinting of three-dimensional (3D) fluorescent speckles significantly improves speckle signal and contrast relative to classic (random) fluorescent speckle microscopy. We predict theoretically that speckle imprinting using photobleaching is optimal when the laser energy and fluorophore responsivity are related by the golden ratio. This relation, which we confirm experimentally, translates into a 40% remaining signal after speckle imprinting and provides a rule of thumb in selecting the laser power required to optimally prepare the sample for imaging. This inducible speckle imaging (ISI) technique allows 3D speckle microscopy to be performed in readily available libraries of cell lines or primary tissues expressing fluorescent proteins and does not preclude conventional imaging before speckle imaging. As a proof of concept, we use ISI to measure metaphase spindle microtubule poleward flux in primary cells and explore a scaling relation connecting microtubule flux to metaphase duration.


2013 ◽  
Vol 23 (3) ◽  
pp. 895-922 ◽  
Author(s):  
Kristoffer Glover ◽  
Hardy Hulley ◽  
Goran Peskir

1966 ◽  
Vol 25 ◽  
pp. 227-229 ◽  
Author(s):  
D. Brouwer

The paper presents a summary of the results obtained by C. J. Cohen and E. C. Hubbard, who established by numerical integration that a resonance relation exists between the orbits of Neptune and Pluto. The problem may be explored further by approximating the motion of Pluto by that of a particle with negligible mass in the three-dimensional (circular) restricted problem. The mass of Pluto and the eccentricity of Neptune's orbit are ignored in this approximation. Significant features of the problem appear to be the presence of two critical arguments and the possibility that the orbit may be related to a periodic orbit of the third kind.


Sign in / Sign up

Export Citation Format

Share Document