Search results for "Projective geometry"

Kleinste Kleinsche Flaschen mit Rand

1979

Charakterisierung (A, B)-regul�rer faserungen durch schliessungss�tze

1977

On stable geometries

1994

Within the concept of projective lattice geometry we are considering the class of stable geometries which have also been introduced in [14]. The investigation of their basic properties will result in fundamental structure theorems which especially give a lattice-geometric characterization of free left modules of rank ≥6 over proper right Bezout rings of stable rank 2. This yields a proper generalization of previous results of ours.

On the topology of surfaces with the generalised simple lift property.

2020

In this paper, we study the geometry of surfaces with the generalised simple lift property. This work generalises previous results by Bernstein and Tinaglia, and it is motivated by the fact that leaves of a minimal lamination obtained as a limit of a sequence of properly embedded minimal disks satisfy the generalised simple lift property.

On Barbilian spaces in projective lattice geometries

1992

We introduce the notion of a Barbilian space of a projective lattice geometry in order to investigate the relationship between lattice-geometric properties and the properties of point-hyperplane structures associated with. We obtain a characterization of those projective lattice geometries, the Barbilian space of which is a Veldkamp space.

Le Curve di Apollonio. Innovazione nei processi risolutivi, il caso della parabola.

2012

This study is connected with the research directed on the solving problem of a graphic representation of geometric objects using the informatics language, particularly the graphic software CAD. The solution of these problems requires a reliable command of stereometry and descriptive geometry and it can extend remarkably the level of external geometric competences. The implementation of the means of ICT has brought a higher effectiveness of graphing mapping processes. The modification of informatics means with the goal to simplify applications of descriptive and projective geometry is also of a great didactical importance. In particular, we focus attention on the treatment of the locus "cone…

Pieri and Projective Geometry

2021

Projective geometry can be described as the geometry of the straightedge, in comparison with Euclid’s geometry of straightedge and compass.

Projective Architecture

2009

Sbacchi indaga su quale sia stata la reale influenza della nozione di "proiezione" nell'ambito della progettazione architettonica a partire da Guarini. Per fare ciò vengono presi in considerazione i concetti di luce e ombra così come quelli di linea astratta, piano, sezione, geometria proiettiva e prospettiva. Michele Sbacchi investigates the real influence of the notion of projection on architectural design before and during the age of Guarini. He takes into consideration concepts such as light and shadow, abstract line, plane, section, projective geometry and perspective. To do this he looks at the ideas of Gregorius Saint Vincent, Alberti, Guarini, Desargues and de l’Orme, among others.

On the Reception of Grassmann’s Work in Germany during the 1870’s

1996

It has often been remarked that Grassmann’s mathematics was not widely appreciated during his lifetime. Although awareness of the dimensions of his achievements began to spread in the early 1870’s, even in Germany relatively few mathematicians appear to have been well acquainted with either the original 1844 edition of Grassmann’s Ausdehnungslehre or the mathematically more accessible edition of 1862. The main reasons for this weak and rather delayed reception have been described often enough---Grassmann’s isolated working environment and his nearly impenetrable language---but there are a number of related aspects that still deserve closer consideration.1

Digital and Interactive Learning and Teaching Methods in Descriptive Geometry

2013

Abstract During the course of “Fundamentals and applications of Science of Representation - Geometric drawing” (held at the Faculty of Engineering at the University of Palermo) we successfully tested the adoption of informatics tools to enhance the comprehension and the critical analysis of complex figures in the geometrical space. The peculiarity in the teaching methodology was the adoption of interactive software products (Cabri Geometre and GeoGebra concerning dynamic and geometrical constructions; the well-known Rhinoceros plug-in, Grasshopper, about generating algorithms; Linceo regarding implementing the graphic display of complex solids in augmented reality). According to our experie…