Search results for "Golden ratio"
showing 7 items of 7 documents
U.I.R.D.A. – Unbuilt Italian Rationalism Digital Archive
2018
For twenty years, the architecture of Italian rationalism through the digital modelling has been investigated. Very often, the production of a model and the consequent representation of tridimensional views, in many case studies, as outcome of the research on architecture have been considered. Actually, the digital model, intended as a critical tool, has to be conceived as a ‘starting point' for graphic analysis of architecture and not as the outcome. Indeed, it is associated to other graphics, sometimes not ‘deducted' from the model, useful for the understanding/translation of architecture. The construction of the model is not the construction of a simple image, operation, which is often c…
Right-jumps and pattern avoiding permutations
2015
We study the iteration of the process "a particle jumps to the right" in permutations. We prove that the set of permutations obtained in this model after a given number of iterations from the identity is a class of pattern avoiding permutations. We characterize the elements of the basis of this class and we enumerate these "forbidden minimal patterns" by giving their bivariate exponential generating function: we achieve this via a catalytic variable, the number of left-to-right maxima. We show that this generating function is a D-finite function satisfying a nice differential equation of order~2. We give some congruence properties for the coefficients of this generating function, and we sho…
Generalized Fibonacci Dynamical Systems
2009
In this paper we consider generalizations of dynamical systems that are based on the Fibonacci sequence. We first study stability properties of such systems for both the continuous and discrete–time case. Then, by considering the Kronecker operator, a further class of dynamical systems is introduced whose outputs can be used to define possible generalization of the golden section. Appli- cations of such system may range from realization of digital filters, manufacturing of tissue with fractal property, etc. Properties of sequences generated by these systems are partially considered and has to be further addressed.
Twin axial vortices generated by Fibonacci lenses.
2013
Optical vortex beams, generated by Diffractive Optical Elements (DOEs), are capable of creating optical traps and other multifunctional micromanipulators for very specific tasks in the microscopic scale. Using the Fibonacci sequence, we have discovered a new family of DOEs that inherently behave as bifocal vortex lenses, and where the ratio of the two focal distances approaches the golden mean. The disctintive optical properties of these Fibonacci vortex lenses are experimentally demonstrated. We believe that the versatility and potential scalability of these lenses may allow for new applications in micro and nanophotonics.
Didactics of mathematics and architecture: the golden ratio in la Lonja de Valencia
2016
[EN] This paper has a twofold purpose. First, to structure and relate a teaching experience on the tutoring of a graduation work in Mathematics made in the University of Valencia. The main property of the didactic purpose involved in the project is that it deals with the geometric properties of a landmark building of the city of Valencia. Our aim is to analyze the process of formulation, firming up, documentation and elaboration of the work that was followed during this experience. Second, to analyze the methodology used to obtain and valuate the results that come from one of the fundamental parts of this work: the harmonic decomposition of the building named Lonja de la Seda in Valencia
Words with the Maximum Number of Abelian Squares
2015
An abelian square is the concatenation of two words that are anagrams of one another. A word of length n can contain \(\varTheta (n^2)\) distinct factors that are abelian squares. We study infinite words such that the number of abelian square factors of length n grows quadratically with n.
Computational Experiments with the Roots of Fibonacci-like Polynomials as a Window to Mathematics Research
2022
Fibonacci-like polynomials, the roots of which are responsible for a cyclic behavior of orbits of a second-order two-parametric difference equation, are considered. Using Maple and Wolfram Alpha, the location of the largest and the smallest roots responsible for the cycles of period p among the roots responsible for the cycles of periods 2kp (period-doubling) and kp (period-multiplying) has been determined. These purely computational results of experimental mathematics, made possible by the use of modern digital tools, can be used as a motivation for confirmation through not-yet-developed methods of formal mathematics. peerReviewed