1,720,974 research outputs found
Geometrical Solution for the Trisection Problem
No full textThe trisection problem date back to the Greeks and Arabs and it is related to the algebraic solution of third degree. It concerns construction of an angle equal to one third of a given arbitrary angle, using only two tools: unmarked ruler and compass. The problem is stated impossible to solve for arbitrary angles, as proved by Pierre Wantzel in 1837. In this article, we present some geometric or algebraic methods to solve the problem from the first one due to Greeks until Maria Gaetana Agnesi’s algebraic-geometric effort. Then we propose a geometric approximation’s method based only on straightedge and compass
Faces of Geometry. From Agnesi to Mirzakhani
No full textThe Teatro Comunale was built in Ferrara at the end of the 18th century, at a time when modern theater was gradually leaving the space of the Duke’s Court and Academy to become part of the urban fabric, shifting from representing the elite to turning towards wider communities. The models of court theater and public theater with several levels of boxes coexisted for a long time, until the complete codification of the “teatro all’italiana”, of which the Comunale represents one of the clearest examples. Over time there have been several renovations. However, the plan has never been strongly altered and has come almost intact to this day. This makes the comparison between measured survey and available historical sources particularly significant and interesting.The construction of the Teatro Comunale, which lasted over a decade, started under the papal domination and ended at the time of the Cispadan Republic. Around 1786, at night, the dwellings on the so-called Isola del Cervo were demolished, to start the construction of a first project by Giuseppe Campana. However, the built theater follows the design by Cosimo Morelli, which includes several oval curves for the shape of other spaces such as the courtyard for carriages and the hall. His design also recalls the neighboring oval church of San Carlo designed by Aleotti. From the written sources we can see that the question over the shape that the curve of the Theatre cavea should have followed has been intensely debated. The measured survey of the Ferrara Theatre and the analysis of the actual geometrical layout has been carried out in parallel with the studies of these papers. The Biblioteca Ariostea archives contain documents in which the relationship between geometry and functionality is discussed by designers and experts nominated by the City who financed the construction. The Ferrara Theatre was built in the same period as the Milano Teatro alla Scala, so we may assume that this debate extended beyond the borders of the city.The volume reports on interdisciplinary discussions and interactions between theoretical research and practical studies on geometric structures and their applications in architecture, the arts, design, education, engineering, and mathematics. These related fields of research can enrich each other and renew their mutual interest in these topics through networks of shared inspiration, and can ultimately enhance the quality of geometry and graphics education. Particular attention is dedicated to the contributions that women have made to the scientific community and especially mathematics. The book introduces engineers, architects and designers interested in computer applications, graphics and geometry to the latest advances in the field, with a particular focus on science, the arts and mathematics education
Faces of Geometry II Edition
No full textthe volume on interdisciplinary discussion and interaction between theoretical research and practical studies on geometric structures and their applications in architecture, the art , design, education, engineering, and mathematics. these related fields of research can enrich each other and renew their mutual interest in these topics through networks of shared inspiration, and can ultimately enhance the quality of geometry and graphics education. particular attention is dedicated to the contributions that women have made to the scientific community and especially mathematics. the book introduces engineers, architects and designer interested in computer application , graphics and geometry to the latest advances in the field, with a particular focus on science, the arts and mathematics education
Grete Hermann and effective methods in geometry
No full textSometimes in the history of science we can find scientists who were not acknowledged at their time and only later the scientific community has recognized the importance of their work. Among them there is Grete Hermann, who worked in mathematics, philosophy, and physics during the early to mid twentieth century. To mathematicians she is known as the first Ph.D. student of Emmy Noether in Göttingen and a pioneer of modern computer algebra, but she also discovered a flaw in John von Neumann's proof of the impossibility of hidden variables theory in quantum mechanics and she did further interesting work on the foundations of quantum mechanics. Her collaboration with Emmy Noether and the philosopher Leonard Nelson in Göttingen, her involvement with Heisenberg's group in Leipzig, some aspects of her work in philosophy and education, her activities in socialist groups and in the anti-Nazi underground movement make of Grete Hermann a very interesting intellectual of last century. In this note we will illustrate Hermann’s work and discuss one of her mathematical results, which has had many improvements and now is much cited
Roses in Architecture: One Symbol, Different Objects
No full textLet's look carefully at some objects of Architecture and we'll find that in them we frequently can identify the same geometric shape. It is a particular flat geometric shape that can be presented in various ways, always maintaining regularity and dynamism: the rose window or rosette.
We will stop our attention on two architectures: the Piazza del Campidoglio in Rome and the skyscraper nicknamed «The Gherkin» in London. History, times and architects are very different and yet, looking at them from particular observation points, we come to find in them a rose window of the same type and shape.
Our work aims to intrigue the observations that are made, but also to suggest to a teacher to take the opportunity, following the succession of ideas, to talk to a student in geometric terms of rosettes, of geometric shapes that compose them, but also of analyze its symbolic and aesthetic meaning in the observed architectures
Geometrical and Fashion, the Case of Iris van Herpen
No full textFashion design, in the construction of a piece of clothing, from sketch to modeling, is very close to geometry. Digital design software offers numerous applications. Some designers went beyond, using technology and innovation in a process, that sees in generative modeling software the key of new forms of design that use geometry as a creative tool, that is combined with 3D printing and innovative materials. One of the greatest exponents of this new way of doing fashion is Iris van Herpen
Computational Process and Code-Form Definition in Design
No full textIn design process, drawing has always preceded the construction phase. The act of drawing, based on basic geometric elements such as lines, curves, surfaces and solid, allows to organize one’s ideas, manage resources and predict results
Organic Reference in Design. The Shape between Invention and Imitation
No full textDigital tools and new technology are changing all aspects of today life, up to architecture and design concepts.
They allow a new approach to the nature as a model, which is a concept that drives the theory of Architecture trough centuries. Then the affirmation of digital technologies is radically changing the application of organic models, which does not concern the shape any more, but just the morphing process.
The aim of these notes is to stress significance, reasons and evolution of this reference that confirms the strong relationship between the theoretical heritage of architecture and its today developments, due to the application of digital technology to design, fabrication and construction. The making process find its theoretical validation in shape grammars and in traditional concepts of module, tessellation and and pattern, which rules the design of decoration, surfaces and ordered conformations. Digital application of old basic design’s confirms the value of this heritage as constant of architecture theory
For Representation, a New Reality: Hybrid Immersive Models
No full textIn alignment with the relevant disciplinary tools and methods, we analyse the innovative potential of cubical perspective combining the uniqueness of handmade sketches with their digital navigation. The investigated model (called hybrid for the above mentioned reason) offers the scholar a twofold opportunity: on the one hand, the possibility to exploit the intuitive imme-diacy of the creative idea which is made objective by the graphical signs, and, on the other hand the possibility of manipulating the communication and configuration features of immersive techniques. Over the last few years, the authors have delved into the scientific fundamentals of cubical perspec-tive and verified the peculiarities of the solutions through experimental ap-plications pertaining to the context of architectural drawing. The case stud-ies presented were pedagogically tested and were aimed at promoting the knowledge of the presuppositions that inform the work of good formal struc-ture and conformation designers
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