Untitled
Untitled Untitled
keywords abstract plane geometry, axiomatic system, axiom, undefined term, interpretation, model An axiomatic system is an organized logical structure consisting of undefined terms, axioms, defined terms, a system of inference rules and theorems. A model for an axiomatic system is an interpretation of this system, consisting of the attribution of particular meanings to the undefined terms, in order that the axioms, read in the light of this interpretation, become true propositions. In this work we will present plane geometries, from abstract to neutral or absolute geometries. We will make a brief reference to Euclidean and hyperbolic plane geometries, whose axiomatic systems are categorical. Finally, we will present the real cartesian plane and Poincaré half plane as models for the Euclidean and hyperbolic geometries, respectively.
keywords abstract plane geometry, axiomatic system, axiom, undefined term, interpretation, model An axiomatic system is an organized logical structure consisting of undefined terms, axioms, defined terms, a system of inference rules and theorems. A model for an axiomatic system is an interpretation of this system, consisting of the attribution of particular meanings to the undefined terms, in order that the axioms, read in the light of this interpretation, become true propositions. In this work we will present plane geometries, from abstract to neutral or absolute geometries. We will make a brief reference to Euclidean and hyperbolic plane geometries, whose axiomatic systems are categorical. Finally, we will present the real cartesian plane and Poincaré half plane as models for the Euclidean and hyperbolic geometries, respectively.
- Page 6 and 7: palavras-chave resumo geometria pla
- Page 8: keywords abstract plane geometry, a
- Page 11: keywords abstract plane geometry, a
- Page 16 and 17: ¡ ¡ ¡
- Page 18 and 19: ¡ ¡ ¡
- Page 20 and 21: ¥
- Page 22 and 23: ¥
- Page 24 and 25: ¥
- Page 26 and 27: ¥
- Page 28 and 29: ¥
- Page 30 and 31: ¥
- Page 32 and 33: ¡ ¡ ¡
- Page 34 and 35: ¥
- Page 36 and 37: ¥
- Page 38 and 39: ¥
- Page 40 and 41: ¥
- Page 42 and 43: ¥
- Page 44 and 45: ¥
- Page 46 and 47: ¥
- Page 48 and 49: ¥
- Page 50 and 51: ¥
- Page 52 and 53: ¥
- Page 54 and 55: ¥
- Page 56 and 57: ¥
- Page 58 and 59: ¥
- Page 60 and 61: ¥
keywords<br />
abstract<br />
plane geometry, axiomatic system, axiom, undefined term, interpretation,<br />
model<br />
An axiomatic system is an organized logical structure consisting of undefined<br />
terms, axioms, defined terms, a system of inference rules and theorems. A<br />
model for an axiomatic system is an interpretation of this system, consisting of<br />
the attribution of particular meanings to the undefined terms, in order that the<br />
axioms, read in the light of this interpretation, become true propositions.<br />
In this work we will present plane geometries, from abstract to neutral or<br />
absolute geometries. We will make a brief reference to Euclidean and<br />
hyperbolic plane geometries, whose axiomatic systems are categorical. Finally,<br />
we will present the real cartesian plane and Poincaré half plane as models for<br />
the Euclidean and hyperbolic geometries, respectively.