Notion of distance for Euclidean plane

• Autorzy: Billich M.
• Języki publikacji: EN

Abstrakty

EN

One motivation for developing axiomatic systems is to determine precisely which precisely which properties of certain objects can be deduced nom which other properties. The purpose is to choose a certain fundamental set of properties from which the other properties of the object can be deduced. Some of axioms of Euclidean plane based on the notion ef distance are considered. The notions of linear and planar sets are introduced in terms of distance. Thus Euclidean plane is regarded as a distance space with a metric satisfying the corresponding properties.

Słowa kluczowe

EN

geometry; system axioms; Euclidean plane; Euclidean geometry

PL

geometria; aksjomaty systemu; płaszczyzna euklidesowa; geometria euklidesowa

• Wydawca: Wydawnictwo Uniwersytetu Humanistyczno-Przyrodniczego im. Jana Długosza w Częstochowie
• Czasopismo: Scientific Issues of Jan Długosz University in Częstochowa. Mathematics
• Rocznik: 2007
• Tom: Vol. 12
• Strony: 11--16
• Opis fizyczny: Bibliogr. 4 poz.

Twórcy

autor

Billich M.

• Pedagogical Faculty Catholic University in Ružomberok: Place A. Hlinka 56, (J34 01 Ružomberok, Slovak Republic

Bibliografia

• [1] W. Benz. Real Geometries. BI Wissenschaftsverlag, Mannheim-Leipzig-Wien- Zurich, 1994.
• [2] A. A. Ivanov. Metričeskaja aksiomatika Euklidova prostranstva. Zapiski naučnych serninarov POMI, Vol. 279, 89-110, 2001.
• [3] M. Ó Searcóid. Metric Spaces. Springer, London, 2006.
• [4] T. Šalát. Metrické priestory, Alfa, Bratislava, 1981.