Důkladné porozumění elementární matematice
The author presents a solution to a geometric problem concerning two squares inscribed into an equilateral triangle. It deals with finding such a position of the two squares for which the sum of areas is the smallest.
Using examples from elementary mathematics, the article presents some possibilities of using GeoGebra as a tool of active discovery of the mathematical basis of problems. The solving procedures are described by individual steps so that the reader can try them him/herself. The problems were chosen so that different solving strategies can be used in GeoGebra: analytic, synthetic, algebraic.
The author presents a proof that when given triangle , point is a foot of a perpendicular from on , and is the middle of , then if angle equals angle , then angle is a right one.
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 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.