Geometry of Shadows

Geometry of Shadows
Author: Giorgio De Chirico
Publisher: Public Space Books, A
Total Pages: 124
Release: 2019-10
Genre: Art
ISBN: 9780998267548

Gathered from early twentieth-century Italian magazines, manuscripts, correspondence, television recordings, and ephemeral art volumes, Geometry of Shadows is the first comprehensive collection of Giorgio de Chirico's Italian poetry, with award-winning poet Stefania Heim's translations presented alongside the Italian originals.

Shadows of the Circle

Shadows of the Circle
Author: Vagn Lundsgaard Hansen
Publisher: World Scientific
Total Pages: 128
Release: 1998
Genre: Mathematics
ISBN: 9789810234188

The aim of this book is to throw light on various facets of geometry through development of four geometrical themes. The first theme is about the ellipse, the shape of the shadow east by a circle. The next, a natural continuation of the first, is a study of all three types of conic sections, the ellipse, the parabola and the hyperbola. The third theme is about certain properties of geometrical figures related to the problem of finding the largest area that can be enclosed by a curve of given length. This problem is called the isoperimetric problem. In itself, this topic contains motivation for major parts of the curriculum in mathematics at college level and sets the stage for more advanced mathematical subjects such as functions of several variables and the calculus of variations. Here, three types of conic section are discussed briefly. The emergence of non-Euclidean geometries in the beginning of the nineteenth century represents one of the dramatic episodes in the history of mathematics. In the last theme the non-Euclidean geometry in the Poincare disc model of the hyperbolic plane is developed.

Shadows of Reality

Shadows of Reality
Author: Tony Robbin
Publisher: Yale University Press
Total Pages: 151
Release: 2008-10-01
Genre: Art
ISBN: 0300129629

In this insightful book, which is a revisionist math history as well as a revisionist art history, Tony Robbin, well known for his innovative computer visualizations of hyperspace, investigates different models of the fourth dimension and how these are applied in art and physics. Robbin explores the distinction between the slicing, or Flatland, model and the projection, or shadow, model. He compares the history of these two models and their uses and misuses in popular discussions. Robbin breaks new ground with his original argument that Picasso used the projection model to invent cubism, and that Minkowski had four-dimensional projective geometry in mind when he structured special relativity. The discussion is brought to the present with an exposition of the projection model in the most creative ideas about space in contemporary mathematics such as twisters, quasicrystals, and quantum topology. Robbin clarifies these esoteric concepts with understandable drawings and diagrams. Robbin proposes that the powerful role of projective geometry in the development of current mathematical ideas has been long overlooked and that our attachment to the slicing model is essentially a conceptual block that hinders progress in understanding contemporary models of spacetime. He offers a fascinating review of how projective ideas are the source of some of today’s most exciting developments in art, math, physics, and computer visualization.

Shadow Geometry

Shadow Geometry
Author: Daphne Harwood Trivett
Publisher:
Total Pages: 46
Release: 1974
Genre: Juvenile Nonfiction
ISBN: 9780690730562

Introduces the principles of geometry through the use of shadows.

The Visual World of Shadows

The Visual World of Shadows
Author: Roberto Casati
Publisher: MIT Press
Total Pages: 407
Release: 2023-12-26
Genre: Science
ISBN: 0262550849

How the perception of shadows, studied by vision scientists and visual artists, reveals the inner workings of the visual system. In The Visual World of Shadows, Roberto Casati and Patrick Cavanagh examine how the perception of shadows, as studied by vision scientists and visual artists, reveals the inner workings of the visual system. Shadows are at once a massive problem for vision—which must distinguish them from objects or material features of objects—and a resource, signaling the presence, location, shape, and size of objects. Casati and Cavanagh draw up an inventory of information retrievable from shadows, showing their amazing variety. They present an overview of the visual system, distinguishing between measurement and inference. They discuss the shadow mission, the work done by the visual brain to parse, and perhaps discard, the information from shadows; shadow ownership, the association of a shadow with the object that casts it; shadow labeling, the visual system's ability to tell shadows from nonshadows; and the shadow concept, our knowledge about shadows as a category. Casati and Cavanagh then apply the theoretical apparatus they have developed for shadows to other phenomena: illumination, reflection, and transparency. Finally, they examine the art of the shadow, paying tribute to artists' exploration of shadow, analyzing a series of artworks (reproduced in color) from a rich and fascinating art historical corpus.

Conceptual Spaces

Conceptual Spaces
Author: Peter Gardenfors
Publisher: MIT Press
Total Pages: 324
Release: 2004-01-30
Genre: Psychology
ISBN: 9780262572194

Within cognitive science, two approaches currently dominate the problem of modeling representations. The symbolic approach views cognition as computation involving symbolic manipulation. Connectionism, a special case of associationism, models associations using artificial neuron networks. Peter Gärdenfors offers his theory of conceptual representations as a bridge between the symbolic and connectionist approaches. Symbolic representation is particularly weak at modeling concept learning, which is paramount for understanding many cognitive phenomena. Concept learning is closely tied to the notion of similarity, which is also poorly served by the symbolic approach. Gärdenfors's theory of conceptual spaces presents a framework for representing information on the conceptual level. A conceptual space is built up from geometrical structures based on a number of quality dimensions. The main applications of the theory are on the constructive side of cognitive science: as a constructive model the theory can be applied to the development of artificial systems capable of solving cognitive tasks. Gärdenfors also shows how conceptual spaces can serve as an explanatory framework for a number of empirical theories, in particular those concerning concept formation, induction, and semantics. His aim is to present a coherent research program that can be used as a basis for more detailed investigations.