1. History of Geometry 📝

Before starting to talk in depth about geometry and its uses or types, it is very necessary to know what exactly it is, or what said area consists of.

The word "geometry" comes from the Greek "γεωμετρία" (geometry), which in turn is made up of two words: "γη" (gē), which means "land" or "firm ground", and "μετρέω" (metreō) , which means "to measure". (Concepto, 2017)

We conclude that geometry is the measurement, analysis, and study of the characteristics and relationships of earthly figures. It is devoted to the study of the characteristics of the space around particular objects as well as their shape and spatial relationships. 

In addition to being the foundation of many other disciplines (including technical drawing and architecture itself), geometry is a basic area of mathematics (such as physics, mechanics, astronomy, etc.). It has also given rise to a variety of artefacts, including the compass, pantograph, and global positioning system (GPS). (Concepto, 2017)

That is why this area of ​​mathematics has become so important, because over the years it has been essential for the evolution of human reasoning.

What about its origins? - Let’s talk about history

Geometry has its origins practically in the earliest human civilisations. The ancient Babylonians were the inventors of the wheel and therefore of the geometry of circumferences. As such, they were probably the first to recognise the infinite potential of geometric study, which they soon applied to astronomy. So did the ancient Egyptians, who cultivated it sufficiently to apply it to their majestic architectural works, since geometry and arithmetic were then eminently practical sciences (Concepto, 2017)

Of particular importance was the mathematician and geometrician Euclid (325 - 265 BC), recognised as the "father of geometry", who proposed the first geometrical system of proof of results in his celebrated work The Elements, composed around 300 BC in Alexandria. It is there that the differences between the plane (two-dimensional) and space (three-dimensional) are stated for the first time (Concepto, 2017).

Other important contributions to geometry at the time were made by Archimedes (287 - 212 BC) and Apollonius of Perge (262 - 190 BC). In later centuries, however, the development of mathematics moved to the East (India, specifically, and the Muslim world), where geometry developed alongside algebra and trigonometry, linking them with astrology and astronomy.

Thus, interest in the discipline returned to the West only in the European Renaissance, when many new names were added to its study, giving rise to projective geometry and above all to Cartesian geometry or analytical geometry, the fruit of the work of the French philosopher René Descartes (1596-1650), the bearer of a new method of geometric investigation that revolutionised and modernised this field of knowledge.

From then on, modern geometry was born, thanks to great scholars such as the German Carl Friedrich Gauss (1777-1855), the Russian Nikolai Lobachevski (1792-1856), the Hungarian János Bolyai (1802-1860), among many others, who managed to move away from the classical axioms of Euclid and found a new field of the discipline: non-Euclidean geometry.