The axiom system of similarity geometry : the problem of independency of axioms

• Autorzy: Waligóra, B.
• Języki publikacji: EN

Abstrakty

EN

There are the axiomatics of the central geometry of similarities in papers [2], [3] and [4]. The primitive notions of these axiomatics are the set E, the distinguished point O, the operation of the addition of points and the quaternary relation of similarity P. The paper [2] contains an axiom system of 2-dimensional geometry. The paper [3] contains an axiom system of the central geometry of similarities for dimensions > 2. These axiomatics have been studying in order to attain the solution to the problem of independency of the axioms. This paper contains the models of independence for some axioms and the proofs of dependence for another axioms. This paper contains plain form of some axioms too.

Słowa kluczowe

PL

system aksjomatyczny; geometria centralna podobieństw

EN

axiom system; central similarity geometry

• Czasopismo: Prace Naukowe Instytutu Matematyki i Informatyki Politechniki Częstochowskiej
• Rocznik: 2003
• Tom: Vol. 2, nr 1
• Strony: 191--202
• Opis fizyczny: Bibliogr. 4 poz., rys.

Twórcy

autor

Waligóra, B.

• Institute of Mathematics and Computer Science, Czestochowa University of Technology

Bibliografia

• [1] Szmielew W., From affine to Euclidean geometry, An axiomatic approach, PWN-Polish Scientific Publishers, Warszawa 1983.
• [2] Waligóra B., On some system of axioms of central similarity geometry, ZN Geometria XV, Poznań 1986.
• [3] Waligóra B., One some dimension-free central similarity system, ZN Geometria XVII, Poznań 1988.
• [4] Waligóra B., Pewna aksjomatyka geometrii centralnej podobieństw, Doctoral dissertation, UMK, Toruń 1986.

Uwagi

EN

The papers have been presented during the session devoted to application of mathematics (as part of International Conference on Parallel Processing and Applied Mathematics).