scholarly journals Real Projective Plane Mapping for Detection of Orthogonal Vanishing Points

2013 ◽  
Author(s):  
Markéta Dubská ◽  
Adam Herout
Keyword(s):  
Projective Plane ◽  
Real Projective Plane ◽  
Vanishing Points

Gilles Deleuze's Luminous Philosophy

2020 ◽  
Author(s):  
Hanjo Berressem
Keyword(s):  
Projective Plane ◽  
Visual Arts ◽  
Whole Body ◽  
Literary Studies ◽  
Chronological Order ◽  
Real Projective Plane ◽  
Cinema Studies ◽  
The Real

Providing a comprehensive reading of Deleuzian philosophy, Gilles Deleuze’s Luminous Philosophy argues that this philosophy’s most consistent conceptual spine and figure of thought is its inherent luminism. When Deleuze notes in Cinema 1 that ‘the plane of immanence is entirely made up of light’, he ties this philosophical luminism directly to the notion of the complementarity of the photon in its aspects of both particle and wave. Engaging, in chronological order, the whole body and range of Deleuze’s and Deleuze and Guattari’s writing, the book traces the ‘line of light’ that runs through Deleuze’s work, and it considers the implications of Deleuze’s luminism for the fields of literary studies, historical studies, the visual arts and cinema studies. It contours Deleuze’s luminism both against recent studies that promote a ‘dark Deleuze’ and against the prevalent view that Deleuzian philosophy is a philosophy of difference. Instead, it argues, it is a philosophy of the complementarity of difference and diversity, considered as two reciprocally determining fields that are, in Deleuze’s view, formally distinct but ontologically one. The book, which is the companion volume toFélix Guattari’s Schizoanalytic Ecology, argues that the ‘real projective plane’ is the ‘surface of thought’ of Deleuze’s philosophical luminism.

MODELS OF THE REAL PROJECTIVE PLANE

1989 ◽  
Vol 21 (3) ◽  
pp. 294-295
Author(s):  
E. Rees
Keyword(s):  
Projective Plane ◽  
Real Projective Plane ◽  
The Real

scholarly journals On the number of triangles in simple arrangements of pseudolines in the real projective plane

1986 ◽  
Vol 60 ◽  
pp. 243-251 ◽  
Author(s):  
Jean-Pierre Roudneff
Keyword(s):  
Projective Plane ◽  
Real Projective Plane ◽  
The Real

THE REAL PROJECTIVE PLANE

1972 ◽  
pp. 131-159
Author(s):  
R.J. Mihalek
Keyword(s):  
Projective Plane ◽  
Real Projective Plane ◽  
The Real

The Real Projective Plane

1993 ◽  
Author(s):  
H. S. M. Coxeter ◽  
George Beck
Keyword(s):  
Projective Plane ◽  
Real Projective Plane ◽  
The Real

scholarly journals Homography in ℝℙ

2016 ◽  
Vol 24 (4) ◽  
pp. 239-251 ◽  
Author(s):  
Roland Coghetto
Keyword(s):  
Projective Space ◽  
Projective Plane ◽  
Projective Spaces ◽  
Invertible Matrix ◽  
Real Projective Plane ◽  
The Real ◽  
Mizar Mathematical Library ◽  
Plücker Relation

Summary The real projective plane has been formalized in Isabelle/HOL by Timothy Makarios [13] and in Coq by Nicolas Magaud, Julien Narboux and Pascal Schreck [12]. Some definitions on the real projective spaces were introduced early in the Mizar Mathematical Library by Wojciech Leonczuk [9], Krzysztof Prazmowski [10] and by Wojciech Skaba [18]. In this article, we check with the Mizar system [4], some properties on the determinants and the Grassmann-Plücker relation in rank 3 [2], [1], [7], [16], [17]. Then we show that the projective space induced (in the sense defined in [9]) by ℝ3 is a projective plane (in the sense defined in [10]). Finally, in the real projective plane, we define the homography induced by a 3-by-3 invertible matrix and we show that the images of 3 collinear points are themselves collinear.

The Real Projective Plane

1956 ◽  
Vol 40 (332) ◽  
pp. 153
Author(s):  
D. Pedoe ◽  
H. S. M. Coxeter
Keyword(s):  
Projective Plane ◽  
Real Projective Plane ◽  
The Real

scholarly journals Topological Realizations of Line Arrangements

2017 ◽  
Vol 2019 (8) ◽  
pp. 2295-2331
Author(s):  
Daniel Ruberman ◽  
Laura Starkston
Keyword(s):  
Finite Field ◽  
Projective Plane ◽  
Contact Structure ◽  
Complex Projective Plane ◽  
Real Projective Plane ◽  
Incidence Relation ◽  
Combinatorial Configuration ◽  
Important Variation ◽  
Graph Manifolds ◽  
Complex Projective

Abstract A venerable problem in combinatorics and geometry asks whether a given incidence relation may be realized by a configuration of points and lines. The classic version of this would ask for lines in a projective plane over a field. An important variation allows for pseudolines: embedded circles (isotopic to $\mathbb R\rm{P}^1$) in the real projective plane. In this article we investigate whether a configuration is realized by a collection of 2-spheres embedded, in symplectic, smooth, and topological categories, in the complex projective plane. We find obstructions to the existence of topologically locally flat spheres realizing a configuration, and show for instance that the combinatorial configuration corresponding to the projective plane over any finite field is not realized. Such obstructions are used to show that a particular contact structure on certain graph manifolds is not (strongly) symplectically fillable. We also show that a configuration of real pseudolines can be complexified to give a configuration of smooth, indeed symplectically embedded, 2-spheres.

A CHARACTERIZATION OF THE REAL PROJECTIVE PLANE

2010 ◽  
Vol 21 (12) ◽  
pp. 1605-1617
Author(s):  
JOËL ROUYER
Keyword(s):  
Projective Plane ◽  
Riemannian Geometry ◽  
Smooth Surface ◽  
Real Projective Plane ◽  
Closed Curves ◽  
Farthest Points ◽  
The Real ◽  
Large Sets

It is proved in this article, that in the framework of Riemannian geometry, the existence of large sets of antipodes (i.e. farthest points) for diametral points of a smooth surface has very strong consequences on the topology and the metric of this surface. Roughly speaking, if the sets of antipodes of diametral points are closed curves, then the surface is nothing but the real projective plane.

scholarly journals Straight line arrangements in the real projective plane

1998 ◽  
Vol 20 (2) ◽  
pp. 155-161 ◽  
Author(s):  
D. Forge ◽  
J. L. Ramírez Alfonsín
Keyword(s):  
Projective Plane ◽  
Real Projective Plane ◽  
The Real ◽  
Line Arrangements ◽  
Straight Line
Sign in / Sign up

Export Citation Format

Share Document