scholarly journals DNA Structure and the Golden Ratio Revisited

Symmetry ◽  
2021 ◽  
Vol 13 (10) ◽  
pp. 1949
Author(s):  
Stuart Henry Larsen
Keyword(s):  
Rotational Symmetry ◽  
Irrational Number ◽  
Golden Ratio ◽  
Dna Structure ◽  
Axial Structure ◽  
Life On Earth

B-DNA, the informational molecule for life on earth, appears to contain ratios structured around the irrational number 1.618…, often known as the “golden ratio”. This occurs in the ratio of the length:width of one turn of the helix; the ratio of the spacing of the two helices; and in the axial structure of the molecule which has ten-fold rotational symmetry. That this occurs in the information-carrying molecule for life is unexpected, and suggests the action of some process. What this process might be is unclear, but it is central to any understanding of the formation of DNA, and so life.

scholarly journals Auditory Cue Based on the Golden Ratio Can Improve Gait Patterns in People with Parkinson’s Disease

Sensors ◽  
2021 ◽  
Vol 21 (3) ◽  
pp. 911
Author(s):  
Valeria Belluscio ◽  
Marco Iosa ◽  
Giuseppe Vannozzi ◽  
Stefano Paravati ◽  
Antonella Peppe
Keyword(s):  
Parkinson’S Disease ◽  
Parkinson's Disease ◽  
Muscle Activation ◽  
Irrational Number ◽  
Golden Ratio ◽  
Yahr Stage ◽  
Gait Patterns ◽  
Temporal Parameters ◽  
Auditory Cue ◽  
Spatio Temporal

The harmonic structure of walking relies on an irrational number called the golden ratio (ϕ): in healthy subjects, it coincides with the stride-to-stance ratio, and it is associated with a smooth gait modality. This smoothness is lost in people with Parkinson’s disease (PD), due to deficiencies in the execution of movements. However, external auditory cues seem to facilitate movement, by enabling the timing of muscle activation, and helping in initiating and modulating motor output. Based on a harmonic fractal structure of gait, can the administration of an auditory cue based on individual’s ϕ-rhythm improve, in acute, gait patterns in people with PD? A total of 20 participants (16 males, age 70.9 ± 8.4 years, Hoehn and Yahr stage-II) were assessed through stereophotogrammetry: gait spatio-temporal parameters, and stride-to-stance ratio were computed before, during, and after the ϕ-rhythm administration. Results show improvements in terms of stride length (p = 0.018), walking speed (p = 0.014), and toe clearance (p = 0.013) when comparing gait patterns before and after the stimulus. Furthermore, the stride-to-stance ratio seems to correlate with almost all spatio-temporal parameters, but it shows the main changes in the before–during rhythm comparison. In conclusion, ϕ-rhythm seems an effective cue able to compensate for defective internal rhythm of the basal ganglia in PD.

scholarly journals The Golden Ratio of Gait Harmony: Repetitive Proportions of Repetitive Gait Phases

2013 ◽  
Vol 2013 ◽  
pp. 1-7 ◽  
Author(s):  
Marco Iosa ◽  
Augusto Fusco ◽  
Fabio Marchetti ◽  
Giovanni Morone ◽  
Carlo Caltagirone ◽  
...  
Keyword(s):  
Gait Cycle ◽  
Irrational Number ◽  
Golden Ratio ◽  
Repeated Measure ◽  
Human Gait ◽  
Double Support ◽  
Gait Parameters ◽  
Measure Analysis ◽  
Repeated Measure Analysis ◽  
Support Phase

In nature, many physical and biological systems have structures showing harmonic properties. Some of them were found related to the irrational number known as the golden ratio that has important symmetric and harmonic properties. In this study, the spatiotemporal gait parameters of 25 healthy subjects were analyzed using a stereophotogrammetric system with 25 retroreflective markers located on their skin. The proportions of gait phases were compared with , the value of which is about 1.6180. The ratio between the entire gait cycle and stance phase resulted in 1.620 ± 0.058, that between stance and the swing phase was 1.629 ± 0.173, and that between swing and the double support phase was 1.684 ± 0.357. All these ratios did not differ significantly from each other (, , repeated measure analysis of variance) or from (, resp.,t-tests). The repetitive gait phases of physiological walking were found in turn in repetitive proportions with each other, revealing an intrinsic harmonic structure. Harmony could be the key for facilitating the control of repetitive walking. Harmony is a powerful unifying factor between seemingly disparate fields of nature, including human gait.

scholarly journals Jak pokazać to, czego pokazać nie można? O obrazowaniu liczb niewymiernych

2020 ◽  
Vol 15 (3) ◽  
pp. 17-30
Author(s):  
Jakub Jernajczyk
Keyword(s):  
Irrational Number ◽  
Golden Ratio ◽  
Visual Artists ◽  
Geometrical Method ◽  
Square Roots ◽  
Visual Imagination ◽  
Starting Point ◽  
Mathematical Problems ◽  
Number Π

In this article, I would like to draw attention to the cognitive potential of an image, showing how significant the role of visual imagination in mathematics is. I will focus here mainly on the possibilities of visualizing irrational numbers.Our starting point is the intuitive case of the square root of two, observed in the diagonal of a square. We will also discuss a simple, geometrical method of constructing the square roots of all integers. Next, we move over to the golden ratio, hidden in a regular pentagon. We will use a looped, endless animation to visualize the irrational number φ. Then we will have a closer look at the famous number π and discuss two different attempts to find its visual representation. In the last two sections of the article, we consider the possibility of indicating rational and irrational real numbers and also grasp the whole set of real numbers.All the issues discussed in this article have inspired visual artists to create artworks that can help to understand relatively advanced mathematical problems.

Comparison of Calculated and Recorded Electron Energy-Loss Spectra of Aluminium and Carbon

1990 ◽  
Vol 48 (2) ◽  
pp. 64-65
Author(s):  
L. Reimer ◽  
R. Oelgeklaus
Keyword(s):  
Fourier Transform ◽  
Energy Loss ◽  
Electron Energy ◽  
Rotational Symmetry ◽  
Mean Free Path ◽  
Single Scattering ◽  
Specimen Thickness ◽  
Two Dimensional ◽  
Image Position ◽  
Electron Energy Loss

Quantitative electron energy-loss spectroscopy (EELS) needs a correction for the limited collection aperture α and a deconvolution of recorded spectra for eliminating the influence of multiple inelastic scattering. Reversely, it is of interest to calculate the influence of multiple scattering on EELS. The distribution f(w,θ,z) of scattered electrons as a function of energy loss w, scattering angle θ and reduced specimen thickness z=t/Λ (Λ=total mean-free-path) can either be recorded by angular-resolved EELS or calculated by a convolution of a normalized single-scattering function ϕ(w,θ). For rotational symmetry in angle (amorphous or polycrystalline specimens) this can be realised by the following sequence of operations :(1)where the two-dimensional distribution in angle is reduced to a one-dimensional function by a projection P, T is a two-dimensional Fourier transform in angle θ and energy loss w and the exponent -1 indicates a deprojection and inverse Fourier transform, respectively.

Is There Unintelligent Life on Earth?

1980 ◽  
Vol 25 (12) ◽  
pp. 991-992
Author(s):  
J. M. WARREN
Keyword(s):  
Life On Earth

Review of the Current State and Future Development in Standardizing Natural Lighting in Interiors

2018 ◽  
pp. 5-26 ◽  
Author(s):  
Stanislav Darula
Keyword(s):  
Human Life ◽  
Natural Light ◽  
Artificial Lighting ◽  
Computer Tools ◽  
Natural Lighting ◽  
Current State ◽  
Minimum Requirements ◽  
Life On Earth ◽  
Window Design

Three elements mainly wind, water and sun seemed to determine in ancient ages the basic phenomena of life on Earth. Architectural history documented the importance of sun influence on urban and building construction already in layouts of Mesopotamian and Greek houses. Not only sun radiation but especially daylight played a significant role in the creation of indoor environment. Later, in the 20th century, a search of interaction between human life in buildings and natural conditions were studied considering well­being and energy conscious design recently using computer tools in complex research and more detail interdisciplinary solutions. At the same time the restricted daytime availability of natural light was supplemented by more efficient and continually cheaper artificial lighting of interiors. There are two main approaches to standardize the design and evaluation of indoor visual environment. The first is based on the determination of the minimum requirements respecting human health and visibility needs in all activities while the second emphasizes the behaviour and comfort of occupants in buildings considering year­around natural changes of physical quantities like light, temperature, noise and energy consumption. The new current standardization basis for daylight evaluation and window design criteria stimulate the study of methodology principles that historically were based on the overcast type of sky luminance pattern avoiding yearly availability of sky illuminance levels. New trends to base the daylight standardization on yearly or long­term availability of daylight are using the averages or median sky illuminance levels to characterise local climatological conditions. This paper offers the review and discussion about the principles of the natural light standardization with a short introduction to the history and current state, with a trial to focus on the possible development of lighting engineering and its standards in future.

Making the Différance: Between Derrida and Stiegler

Derrida Today ◽  
2020 ◽  
Vol 13 (1) ◽  
pp. 1-16
Author(s):  
Francesco Vitale
Keyword(s):  
Natural Condition ◽  
Ecological Crisis ◽  
Human Being ◽  
Effective Response ◽  
Life On Earth

This paper intends to verify the extent and effectiveness of the transforming appropriation of the Derridean concept of ‘differance’ by Stiegler with respect to the problems that, according to Stiegler, make this creative critical operation necessary; in particular with respect to the most recent question concerning the possibility of thinking about and putting into practice a ‘neganthropological différance’ capable of facing the ecological crisis that today seems to threaten the very existence of life on earth. The paper goes back to Technics and Time 1. to analyze the distinction between ‘vital difference’ and ‘noetic difference’ that constitutes the condition of possibility of the ‘neganthropological différance.’ In this perspective, the distinction proposed by Stiegler seems to re-propose the hierarchically oriented oppositional structure that characterizes metaphysical thought and in particular the opposition between man and animal, attributing to the human being the ability to free himself from the constraints of his biological-natural condition. Finally, the paper attempts to account for the repercussions of this approach on the very possibility of an effective response to the ecological crisis, concluding with a provocation regarding the role that theory can and must play with regard to such an urgent and far-reaching problem.

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