Help please. Grade 10. Topic: Basic concepts, axioms of stereometry and the simplest consequences of them.
It is known that at least two planes can be drawn through a given line and point. 1) What is the relative position of the line and point? 2) How many planes can be drawn through these lines and points?
Answers
Euclidean geometry is a mathematical system attributed to Alexandrian Greek mathematician Euclid, which he described in his textbook on geometry: the Elements. Euclid's method consists in assuming a small set of intuitively appealing axioms, and deducing many other propositions (theorems) from these. Although many of Euclid's results had been stated by earlier mathematicians,[1] Euclid was the first to show how these propositions could fit into a comprehensive deductive and logical system.[2] The Elements begins with plane geometry, still taught in secondary school (high school) as the first axiomatic system and the first examples of formal proof. It goes on to the solid geometry of three dimensions. Much of the Elements states results of what are now called algebra and number theory, explained in geometrical language.[1]