eukleidovský

Eukleidovská refers to geometry described by the axioms and postulates laid down by the ancient Greek mathematician Euclid in his work Elements. This is the classical geometry that is typically taught in schools. It is characterized by its reliance on deductive reasoning, starting from a set of basic assumptions that are accepted as true without proof. These assumptions include notions about points, lines, planes, and their relationships.

The most famous of these is Euclid's fifth postulate, often called the parallel postulate. It states that if a straight line falling on two straight lines makes the interior angles on the same side less than two right angles, the two straight lines, if produced indefinitely, meet on that side on which are the angles less than the two right angles. For centuries, mathematicians attempted to prove this postulate from the others, believing it was not as fundamental.

These attempts, however, led to the development of non-Euclidean geometries, which are geometries where the parallel postulate does not hold. In contrast, eukleidovská geometry is consistent and complete within its own framework. It forms the basis of much of our understanding of space and measurement in everyday contexts, such as surveying and architecture. The axiomatic system of eukleidovská geometry has been a cornerstone of mathematical thought for over two millennia, influencing the development of logic and proof.