PL
 |
EN
Preferencje help
Polish version English version Język
Widoczny [Schowaj] Abstrakt
Liczba wyników

Znaleziono wyników: 5

Liczba wyników na stronie
first rewind previous Strona / 1 next fast forward last
Wyniki wyszukiwania
help Sortuj według:

help Ogranicz wyniki do:
first rewind previous Strona / 1 next fast forward last
1
Content available Geogebra and problems of tangent circles
Billich M.
Scientific Issues of Jan Długosz University in Częstochowa. Mathematics
|
2017
|
Vol. 22
23--29
EN
There are many mathematical programmes for teaching and learning geometry from middle school to the university level. Dynamic software package Geogebra can help students to explore and understand more concepts in geometry on their own. In this paper we are concentrating in one of the most interesting and less known two-dimensional transformations like inversion with respect to a circle supported by GeoGebra. The use of this transformation through GeoGebra makes possible a number of elegant solutions to classical construction problems in geometry. Contribution of this paper is presentation of some problems which require the construction of the circle tangent to given circles.
2
Content available Computer proofs in plane geometry
Billich M.
Scientific Issues of Jan Długosz University in Częstochowa. Mathematics
|
2011
|
Vol. 16
197--204
EN
Over the past 25 years highly successful methods for geometry theorem proving have been developed. We will use elementary and understandable examples to show the nature of the techniques for verification of geometric constructions made with interactive geometry environment and for proving geometric statements. In addition to some informations about the WinGCLC software with specific language, we look at the system GeoThms that integrates Automatic Theorem Provers, Dynamic Geometry Tools and a database. The abovementioned system provides an environment suitable for new ways of studying and teaching geometry at different levels.
3
Content available Some remarks on mappings that preserve unit distance
Billich M.
Scientific Issues of Jan Długosz University in Częstochowa. Mathematics
|
2009
|
Vol. 14
7-11
EN
In the present paper we investigate some properties on isometric mappings between Euclidean spaces. In addition, non-isometric distance one preserving mappings are also considered.
4
Content available remote Mappings preserving some distances
Billich M.
Scientific Issues of Jan Długosz University in Częstochowa. Mathematics
|
2008
|
Vol. 13
10-14
EN
We deal with mappings which preserve unit (some positive) distance, as well as with mappings contracting (expanding) some distance. In particular, we show that a mapping preserving three positive distances is an isometry.
5
Content available remote Notion of distance for Euclidean plane
Billich M.
Scientific Issues of Jan Długosz University in Częstochowa. Mathematics
|
2007
|
Vol. 12
11-16
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.
first rewind previous Strona / 1 next fast forward last
JavaScript jest wyłączony w Twojej przeglądarce internetowej. Włącz go, a następnie odśwież stronę, aby móc w pełni z niej korzystać.