# Small Universal Cellular Automata in Hyperbolic SpacesWhy Hyperbolic Geometry?

Small Universal Cellular Automata in Hyperbolic Spaces: Why Hyperbolic Geometry? [In this first chapter, I shall introduce the unfamiliar reader to hyperbolic geometry. Section 1.1 is a very short survey about the history of this geometry. This history is a very important step in the general history of sciences. But this would require almost a whole book. Another summary can be found in [34] where much interesting information is given about hyperbolic geometry, in particular from an aesthetic point of view. In Section 1.2, I give a few general indications on this geometry. In Section 1.3, I introduce the Poincaré’s model which is intensively used in the other chapters of the book.] http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png

# Small Universal Cellular Automata in Hyperbolic SpacesWhy Hyperbolic Geometry?

26 pages

/lp/springer-journals/small-universal-cellular-automata-in-hyperbolic-spaces-why-hyperbolic-ZvvdMSq4uP
Publisher
Springer Berlin Heidelberg
ISBN
978-3-642-36662-8
Pages
1 –26
DOI
10.1007/978-3-642-36663-5_1
Publisher site
See Chapter on Publisher Site

### Abstract

[In this first chapter, I shall introduce the unfamiliar reader to hyperbolic geometry. Section 1.1 is a very short survey about the history of this geometry. This history is a very important step in the general history of sciences. But this would require almost a whole book. Another summary can be found in [34] where much interesting information is given about hyperbolic geometry, in particular from an aesthetic point of view. In Section 1.2, I give a few general indications on this geometry. In Section 1.3, I introduce the Poincaré’s model which is intensively used in the other chapters of the book.]

Published: Jan 1, 2013

Keywords: Acute Angle; Euclidean Geometry; Euclidean Plane; Hyperbolic Plane; Hyperbolic Geometry