Geometry life

 The word geometry has its Greek roots, Geo (earth) and Metria (measurement), which means measurement of the earth. Geometry is a multifaceted branch of mathematics. One could say that the origin of mankind is where geometry comes from, when primitive man in his unconscious way classified objects according to their shape and size. 

It dates back to about three thousand years before Christ (BC), particularly the ancient Egyptians who needed to measure their agricultural fields and in the construction of their great works such as the pyramids and their monuments. These early achievements of geometry were only put into practice, without any kind of reasoning or demonstration. 

All this primitive knowledge was passed on to the Greeks, who were the first to formalise geometry, particularly by considering objects as ideal entities, such as a circle instead of a well's eye and a square instead of a simple wall.

One of the first to see geometry demonstratively through reasoning was Thales of Miletus by the 3rd century BC, Thales' demonstrations become fundamental and are the basis of logic as laws of reasoning. One of his great feats is that he was able to measure the height of the pyramid of Cheops and to predict a solar eclipse. 

Pythagoras and his sect the Pythagoreans have a central role, since his philosophy and its implicit or explicit form has always been within mathematics or physics, being geometry his main study, his most relevant contribution is the "Pythagorean theorem" and the study of right-angled triangles. 

On the other hand, Euclid also participated in the evolution of geometry, he proposed a system in which the veracity of certain propositions is given by being intuitively clear and deduce from them all the other results, his work "THE ELEMENTS" is a model of axiomatic-deductive system, its 5 postulates and the definitions that are developed constitute all the geometry and arithmetic known up to the moment. 

Euclid's elements are of great interest, due to the controversy that originated in the fifth axiom called "The parallels", for centuries this axiom was assumed as undebatable, until the 19th century, when the so-called non-Euclidean geometries were born, which debated this postulate. 

One of the main problems with the fifth postulate is to determine whether or not it is independent of the other four postulates, that is, whether it is considered a postulate or a theorem, so that it can be deduced from the others and therefore be placed among the rest of the results of his work. 

Archimedes and Apollonius also contributed to the study and development of geometry, the former analysed conic sections exhaustively, and introduced into geometry other curves such as the spiral that bears his name, his study of the calculation of the volume of the sphere based on those of the cylinder and the cone, he also elaborated a method to calculate an approximation to the value of Pi (π). For his part Apollonius worked on various constructions of tangency between circles, as well as his conic sections and other curves. 

Interesting video

(235) Introduction to Geometry: Ancient Greece and the Pythagoreans - YouTube