Náplní článku je konstrukce společných tečen dvou kuželoseček, Nejprve zavedeme tři pojmy - kolineaci, Pascalovu závitnici a tečnu kuželosečky, poté užitím jejich vlastností provedeme konstrukci společných tečen dvou elips. Nakonec aplikujeme myšlenky užité pro dvě elipsy na zbývající možná zadání dvou kuželoseček.
The paper analyzes school approaches to solving plane geometry problems and the requirements students should meet in solving them. Further, it presents a new utility, the GeoTest system, that provides users with an on-line environment for solving such problems and also with an instant automatic evaluation of the solutions of given tasks.
The article concerns the following problem: Given square with the side of 1. Find points so that the sum is the smallest possible. Four solutions are given which are examples of the connection between several mathematical disciplines (geometry, algebra and calculus). The article concludes with a note on the history of the presented problem (leading to P. Fermat and others).
The paper presents demonstrations of activity-oriented mathematics teaching methods focused on using construction sets of geometric solids Polydron in the teaching of mathematics. The text contains mathematical tasks and methodic notes to the use of Polydron building sets in the teaching of mathematics.