 Non-Euclidean Geometry: A Historical InterludeJürgen Richter-Gebert ()
Chapter 24 in Perspectives on Projective Geometry, 2011, pp 465-481 from Springer Abstract: Abstract Imagine you are a two-dimensional being living in the interior of a real nondegenerate fundamental conic of a Cayley-Klein geometry. All your measurements (distances and angles) are done with respect to this Cayley-Klein geometry, and you have no knowledge of the fact that your world is embedded in some larger space (the projective plane in which the Cayley-Klein geometry is defined). One day your dog, your ruler, and you decide to take a long, long walk always following the same direction. How would that feel? In a sense it would not feel very exciting, and this is indeed an exciting thing. The three of you simply go on without anything remarkable happening. A person from the outside observing you will see you all getting smaller and smaller as you approach the boundary of the fundamental object. With your legs shrinking, your step size (observed from the outside) is getting smaller and smaller, too. Keywords: Implicit Assumption; Euclidean Geometry; Straight Line Segment; Hyperbolic Plane; Hyperbolic Geometry (search for similar items in EconPapers) There are no downloads for this item, see the EconPapers FAQ for hints about obtaining it. Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-642-17286-1_24 Ordering information: This item can be ordered from DOI: 10.1007/978-3-642-17286-1_24 Access Statistics for this chapter More chapters in Springer Books from Springer |
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