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[Classical Geometries] Is this a model of geometry? Verify by showing that they follow the three incidence axioms: (I1) Given any two discrete points there exists a unique line containing them (I2) Given any line there exists at least two distinct points lying on it (I3) There exists three non-collinear points We will use Hilbert’s axiom system that is constructed with the three primitive terms point, line and plane (lie on).

[Classical Geometries] Is this a model of geometry? Verify by showing that they follow the three incidence axioms: (I1) Given any two discrete points there exists a unique line containing them (I2) Given any line there exists at least two distinct points lying on it (I3) There exists three non-collinear points We will use Hilbert’s axiom system that is constructed with the three primitive terms point, line and plane (lie on).

Computer Networking: A Top-Down Approach (7th Edition)
Computer Networking: A Top-Down Approach (7th Edition)
7th Edition
ISBN:9780133594140
Author:James Kurose, Keith Ross
Publisher:James Kurose, Keith Ross
Chapter1: Computer Networks And The Internet
Section: Chapter Questions
Problem R1RQ: What is the difference between a host and an end system? List several different types of end...
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[Classical Geometries] Is this a model of geometry? Verify by showing that they follow the three incidence axioms:

(I1) Given any two discrete points there exists a unique line containing them
(I2) Given any line there exists at least two distinct points lying on it
(I3) There exists three non-collinear points

We will use Hilbert’s axiom system that is constructed with the three primitive terms point, line and plane (lie on).

3. H • point: Point on the upper sheet of the hyperboloid. H² = {(x, y, z) = R³|z² = x² + y² + 1, z>0} ● line: great hyperbola 2 on H². lie on: A point p (x, y, z) = 1. Discuss if it is a model of geometry, by verifying the 3 axioms one by one. = (x, y, z) = H² lies on a great hyperbola 1 if
Transcribed Image Text:3. H • point: Point on the upper sheet of the hyperboloid. H² = {(x, y, z) = R³|z² = x² + y² + 1, z>0} ● line: great hyperbola 2 on H². lie on: A point p (x, y, z) = 1. Discuss if it is a model of geometry, by verifying the 3 axioms one by one. = (x, y, z) = H² lies on a great hyperbola 1 if
2A great hyperbola is the intersection of H2 with any plane through the origin of R³.
Transcribed Image Text:2A great hyperbola is the intersection of H2 with any plane through the origin of R³.
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