Year LVII, Issue 1, 2014<<Archive>>
Еducаtionаl Tеchnologiеs
INTEGRATING SOFTWARE APPLICATIONS – SOME EXEMPLARY PROBLEMS
The present article deals with a problem, the solution of which is related to the integrated use of the basic software applications studied within the high school course of Information Technologies (IT). A large group of components of the school curriculum n...
word processing, integrated activities, integrated document, didactical problems
HEURISTICS BY EXCEL
The paper considers methodology for a large scale mathematical problem solving by Electronic Table. A consecutive analysis is produced for localization and argumentation of the solutions by augmenting the experimentation domain. When the table method is insu...
problem solving, equation, numbers, tables, macros
COMPUTER-GENERATED MATHEMATICS: ELABORATION OF A TOPIC FROM EUCLIDEAN GEOMETRY
In the paper an elaboration of a topic from Euclidean Geometry by the computer program ‘Discoverer’ is shown. A theorem or a group of similar theorems are used as starting points. The paper presents 283 theorems which are discovered by the computer program ‘...
computer-generated mathematics, Euclidean geometry, Discoverer, mathematical olympiad
Еducаtionаl Маttеrs
THEORETICAL-PRACTICAL BASE OF VECTOR-ALGEBRAIC MODELING IN GEOMETRY EDUCATION
The paper consists of two parts – theoretical and applied. In the theoretical part a selection and classification of the basic concepts (objects and relations) and statements (axioms and theorems) of Veil’s geometric system has been made, with the help of...
vector algebra, modeling, education, geometry, heuristics
A GENERALIZATION OF THE PYTHAGORAEN THEOREM IN EXTRACURRICULAR CLASSES OF MATHEMATICS
The paper considers the Pythagorean theorem, its generalization for arbitrary triangle and exemplary applications. It is suitable for outstanding students in th e \(7^{\text {th }}\) and \(8^{\text {th }}\) grade.
Pythagorean theorem, generalization, proof, application
Еducаtionаl Rеsеаrch
SOME INEQUALITIES IN THE TRIANGLE
The paper considers some inequalities in the triangle connecting the semi-perimeter, the circumradius and the inradius.
triangle, semi-perimeter, circumradius, inradius, inequality
SEVERAL HOMOTHETICALLY GENERATED PROPERTIES OF THE FEUERBACH CONFIGURATIONS
The present paper considers generalizations of some known properties from the geometry of the triangle, which are connected with the circum-circles and the in-circles. The generalizations are several properties of a special combination of ce...
triangle, homothety, Feuerbach configuration, Euler curve