Mathematical nature's pattern in Zinnia Peruviana

How intriguing is the idea that there is a concurrent mathematical pattern that exists in the stars, the human body, the breeding patterns of domestic rabbits, sea shells and plants? Very tantalizing is the idea that math was not just created to quantify existence, but that existence actually quantifies mathematics. Through exploring the Golden Section and the Fibonacci Series, I have learned that mathematics can extend beyond the survival of the high school student. Mathematical patterns can be observed in a plant’s growth patterns, on its quest to maximize its exposure to light.

Royal Society Open Science, 2016

This citizen science study evaluates the occurrence of Fibonacci structure in the spirals of sunflower ( Helianthus annuus ) seedheads. This phenomenon has competing biomathematical explanations, and our core premise is that observation of both Fibonacci and non-Fibonacci structure is informative for challenging such models. We collected data on 657 sunflowers. In our most reliable data subset, we evaluated 768 clockwise or anticlockwise parastichy numbers of which 565 were Fibonacci numbers, and a further 67 had Fibonacci structure of a predefined type. We also found more complex Fibonacci structures not previously reported in sunflowers. This is the third, and largest, study in the literature, although the first with explicit and independently checkable inclusion and analysis criteria and fully accessible data. This study systematically reports for the first time, to the best of our knowledge, seedheads without Fibonacci structure. Some of these are approximately Fibonacci, and we...

wjeis.org

Mathematics, one of the ancient occupations through the history of humanity, is accepted as a discipline where abstract concepts are predominant and which contains generalities. When evaluated from the point of perception of abstract concepts and working with such concepts, it becomes evident that certain difficulties are experienced during learning and teaching process. One of methods used to overcome such difficulties is to correlate with everyday life and to present samples from real life to the individual. By this means, mathematical concepts can be materialised and lasting learning can be achieved. Even if we are not aware, almost every object or incident around us has a mathematical basis and a relation with mathematics. One of the most express examples to this relation is the Fibonacci numbers, observed in the order of plants, flowers, their leaves even their seed in the nature. This study includes the demonstration the compliance of relation between biology and mathematics, the order of seeds in the sunflower receptacle with the field of mathematics, taking the interdisciplinary study as basis, using Geogebra, one of the information technology tools developed for the field of mathematics and the evaluation of this practice developed by prospective teachers. Herewith it is aimed to emphasise the importance of interdisciplinary studies. In this study, the opinions of prospective biology and mathematics teachers are obtained and consequently it has been found out that they have positive opinion on the establishment of interdisciplinary relation. Furthermore, although it is not nominated as the main research question, it is understood that the information technology tools cannot be used only for materialisation of mathematics but also for establishment interdisciplinary relation.

Leonardo, 2019

There were eras where an educated man could only live up to his standard if he was a poet and a philosopher at the same time, or an experimental or a mathematical researcher. I argue that it is time to return back and look into the areas of physics, mathematics, and botany from different perspective of Fibonacci series.

J Nonlinear Sci, 2008

We present a rigorous mathematical analysis of a discrete dynamical system modeling plant pattern formation. In this model, based on the work of physicists Douady and Couder, fixed points are the spiral or helical lattices often occurring in plants. The frequent occurrence of the Fibonacci sequence in the number of visible spirals is explained by the stability of the fixed points in this system, as well as by the structure of their bifurcation diagram. We provide a detailed study of this diagram.

2014 International Conference on Advanced Computer Science and Information System, 2014

This research proposed a new model to differentiate leaf venation topology patterns using Multiscale Fractal Dimension. Identification of medicinal plants is important considering wide range of biodiversity in Indonesia and significant role of medicinal plants in Indonesia. Plants identification can be performed with shape analysis using plant leaf venation as a feature. Multiscale Fractal Dimension is a shape analysis method that analyze shapes through its complexity. In this research three Indonesian medicinal plants species has their leaf venation topologies modelled with Multiscale Fractal Dimension. The result shows that while the difference is not remarkably clear, there are irregularities that can be made more evident with multiscale analysis. Future works can include Multiscale Fractal Dimension as one technique to identify plants.

Çukurova Üniversitesi Sosyal Bilimler Enstitüsü Dergisi, 2020

In studies presented in the literature, relationships between music and mathematics can sometimes be observed. Leonardo Fibonacci (1170-1250) is well known in mathematics with the Fibonacci Sequence and this sequence used to identify numbers in various music elements, too. In related studies, these numbers have been used to demonstrate the existence of the 'Golden Ratio' using methods and theories borrowed from the components of music. Nevertheless, this relationship has subsequently been seen inaccurate. The studies that previously based some works of Chopin, Mozart, Beethoven, Bach and Bartók on Fibonacci Sequence and Golden Ratio are critically examined in the context of musical and mathematical theories in this study. Qualitative and quantitative research methods were used together in this interdisciplinary research in the field of mathematical sciences and critical musicology. It was examined basically the measure or rhythms (sound duration) within the musical works that allegedly used the Fibonacci Sequence and the Golden Ratio, and it was found these studies yielded values close to the terms of the Fibonacci Sequence and the determined values of the Golden Ratio were 0.618, 1.618, and 0.382. It is determined that mathematical, historical and music theoretical data and findings could not provide enough to support the claims of the related studies. Thus, it was determined that the accuracy of the Fibonacci Sequence and Golden Ratio expressed in the works of the related composers are controversial within the framework of the relevant studies.

International journal of humanities and social sciences, 2016

Tiling is one of the pleasant methods of architectural decoration in all Islamic lands. Tiling has been one of the most important aesthetic manifestation of creator spirit and Iranian artists’ aesthetic, and plant designs used in the seven-color tile are evidence for this claim. Plant designs are beautiful and simple. Despite diversity, they have unity and cohesion. The aim of this paper is to introduce seven-color tiling and plant designs used. In this study, we examined the cedar, Khataei, and pot designs. The, we will respond to this question: 1- what are the features of plant designs? Methodology Library method and content analysis method were used in this study. Library method was used as the main tool to collect data and note taking and video documents were also used in this regard.

osaka-ue.ac.jp

This article examines why many flowers are five-petaled through the use of a five-petal model that draws insight from the location of cell clusters at a shoot apex, rather than from concepts such as the Fibonacci sequence or the Golden ratio which have been referred to in the past. The conclusions drawn are that flowers are most likely to be five-petaled, followed by six-petaled flowers, and that four petals are unstable and almost no flower can be seven-petaled.