In very ancient times, a young man, deciding to be witty, asked his teacher what profit could come from studying geometry.

Unhappy idea: the master was the great Greek mathematician **Euclid**, for whom geometry was very serious. And his response to boldness was overwhelming: calling a slave, he handed him some coins and ordered them to be handed over to the pupil who from that moment ceased to be Euclid's pupil.

This boy - it must be said - was not the only one to suffer at Euclid's hands because of geometry. Besides him, many people had a hard time with the great Greek, including Pharaoh himself from Egypt. Ptolemy I's problems arose the day he asked Euclid to adopt an easier method of teaching him geometry and received the laconic reply: "There are no real roads to geometry."

Alexandria, capital of geometry

Long before Euclid, geometry was a common subject in Egypt. Surveyors used it to measure terrain, builders turned to her to design their pyramids, and with her youth became infernal as she learned to handle the constant Pi — a serious headache for students at that time as well. So famous was Egyptian geometry that Greek-named mathematicians such as Tales of Miletus and Pythagoras shook from their land to go to Egypt to see what was new about angles and lines. It was with Euclid, however, that the geometry of Egypt became truly formidable, making Alexandria the great world center of the compass and the square around the third century BC.

It all started with the "Elements," a 13-volume book, in which Euclid brought together everything known about mathematics in his time - arithmetic, plane geometry, proportion theory, and solid geometry. Systematizing the great mass of knowledge that the Egyptians had disorderly acquired over time, the Greek mathematician gave logical order and thoroughly detailed the properties of geometric figures, areas and volumes, and established the concept of geometric place. Then, to complete, he enunciated the famous "Parallel Postulate", which states: "If a line, intersecting two others, forms internal angles on the same side, smaller than two straight lines, these others, extending to infinity, meet -the side where the angles are less than two straight. "

The dissident geometries

For Euclid, geometry was a deductive science that operated from certain basic hypotheses - the "axioms." These were considered obvious and therefore of unnecessary explanation. The "Parallel Postulate", for example, was an axiom - there was no point in discussing it. However, it turns out that in the nineteenth century mathematicians decided to start discussing the axioms. And so many did that it turned out to be a surprising fact: the "Parallel Postulate" - the backbone of the Euclidean system - was enough to make possible the development of new geometric systems. The mathematician Lobatchevsky was the first to declare his independence by creating his own theory. Another geometry master, Riemann, followed suit and created a different system.

These new conceptions, which became known by the name of "non-Euclidean theories", allowed the exact sciences of the twentieth century a series of advances, including the elaboration of Einstein's Theory of Relativity, which proved that these theories, Contrary to what many claimed, they actually had practical applications.

In addition to math, optics and acoustics

The theory of relativity, establishing that the universe is finite, has eliminated the old Euclidean notion of the endless world. And the continuous progress of modern mathematics gradually changed the concepts of the master of Alexandria.

We live in new times, it is good that there are new ideas. But one cannot help but respect the admirable talent of old Euclid, who, while creating his prodigious mathematical system, still found time to study optics and write extensively about it; to study acoustics and brilliantly develop the theme, especially in terms of consonance and dissonance. His writings on this subject may be considered one of the earliest known treatises on Musical Harmony. Moreover, it must be borne in mind that for man to come to the conclusion that the universe has an end, he had to use for two millennia the mathematics created by Euclid - a man who believed in infinity.

*Bibliography*: Encyclopedic Dictionary Knowing - Cultural April