The goal of the article is to show the origin and development of proofs. Different approaches to a geometrical problem with triangle are demonstrated. The beginning of solution of the problem is not only in logic, but also in intuition and imagination.
The article focuses on the approaches to the teaching of the same subject matter, namely the theorems for congruent triangles. The approaches mainly differ in the pupils' participation on the creation of new knowledge and are ordered on the scale instructional teaching - constructivist teaching. Three of the approaches have been tested in real classrooms and the trials are described in the article.
Addition of curves yields an interesting possibility for geometric experiments at basic and secondary schools. Addition of curves and surfaces is a tool used in architecture. The article presents some problems with solutions which can be used at the primary and secondary schools and which allow for pupils' experimenting and making hypotheses.
In the first part, we assume well known characteristics of ellipse which are given by triangle construction using main circles. We extend them on some lesser known features like Apollonius's theorem of associated radii of the ellipse. In the second part, we assume triangle construction of ellipse given by associated radii.
V tomto článku se budeme zabývat vyšetřováním množin bodů pomocí programu GeoGebra, který je v současnosti asi nejrozšířenějším matematickým softwarem používaným při výuce v Česku a v dalších mnoha zemích. Článek obsahuje dva problémy, které mají demonstrovat dva důležité aspekty GeoGebry a obecně programů DGS (Dynamic Geometry Systems). Prvním aspektem je stále těsnější propojení DGS s funkcemi, které byly až do nedávna typické pouze pro třídu programů CAS (Computer Algebra Systems). Jedním z výsledků...