The biologic significance of the divine proportion and Fibonacci series

1982 ◽  
Vol 81 (5) ◽  
pp. 351-370 ◽  
Author(s):  
Robert M. Ricketts
1982 ◽  
Vol 9 (4) ◽  
pp. 401-422 ◽  
Author(s):  
Robert M. Ricketts

1982 ◽  
Vol 82 (2) ◽  
pp. 166-167 ◽  
Author(s):  
Peter M. Sinclair
Keyword(s):  

Author(s):  
A Rakesh Kumar ◽  
Sanjeevikumar Padmanaban ◽  
Partha Sarathi Subudhi ◽  
Frede Blaabjerg ◽  
C Dhanamjayulu

2012 ◽  
Vol 96 (536) ◽  
pp. 213-220
Author(s):  
Harlan J. Brothers

Pascal's triangle is well known for its numerous connections to probability theory [1], combinatorics, Euclidean geometry, fractal geometry, and many number sequences including the Fibonacci series [2,3,4]. It also has a deep connection to the base of natural logarithms, e [5]. This link to e can be used as a springboard for generating a family of related triangles that together create a rich combinatoric object.2. From Pascal to LeibnizIn Brothers [5], the author shows that the growth of Pascal's triangle is related to the limit definition of e.Specifically, we define the sequence sn; as follows [6]:


2021 ◽  
Vol Publish Ahead of Print ◽  
Author(s):  
Sergio Sambataro ◽  
Marco Cicciù ◽  
Riccardo Nocini ◽  
Salvatore Crimi ◽  
Alberto Bianchi ◽  
...  

2016 ◽  
Vol 2016 ◽  
pp. 1-12 ◽  
Author(s):  
Santiago Tello-Mijares ◽  
Francisco Flores

The identification of pollen in an automated way will accelerate different tasks and applications of palynology to aid in, among others, climate change studies, medical allergies calendar, and forensic science. The aim of this paper is to develop a system that automatically captures a hundred microscopic images of pollen and classifies them into the 12 different species from Lagunera Region, Mexico. Many times, the pollen is overlapping on the microscopic images, which increases the difficulty for its automated identification and classification. This paper focuses on a method to segment the overlapping pollen. First, the proposed method segments the overlapping pollen. Second, the method separates the pollen based on the mean shift process (100% segmentation) and erosion by H-minima based on the Fibonacci series. Thus, pollen is characterized by its shape, color, and texture for training and evaluating the performance of three classification techniques: random tree forest, multilayer perceptron, and Bayes net. Using the newly developed system, we obtained segmentation results of 100% and classification on top of 96.2% and 96.1% in recall and precision using multilayer perceptron in twofold cross validation.


2018 ◽  
Vol 14 (1) ◽  
pp. 188-199 ◽  
Author(s):  
Gyan Bahadur Thapa ◽  
Rena Thapa

The Golden Ratio, mathematics and aesthetics are intricately related among each other. In this paper, we exhibit the presence of mathematics in aesthetic impression that appears in nature, classic art, architecture, logo design and much more. The divine proportion can be found in music, poetry and other forms of art, however our focus here is only in the visual ones. The Golden ratio is considered sacred due to its relationship to nature and even the construction of the universe and the human body. It has been used for centuries in the construction of architectural masterpieces by the great artists, who, being able to see its beauty used it in their designs and compositions. We explain how the applications of the Golden ratio in architectures, paintings and geometrical shapes create the mystery of beauty. Further we present the existence of the divine proportion in human body and natural flora and fauna. There are a diverse number of directions, paths and tangents to which the study of this beautiful concept could take us. Besides mathematicians and artists, we expect that this paper will be interesting for general readers as well.  Journal of the Institute of Engineering, 2018, 14(1): 188-199


2008 ◽  
pp. 127-127
Author(s):  
Rafael Alberti
Keyword(s):  

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