Geometry is a branch of mathematical science that studies the measurements and properties of figures on a plane or space.
It is interesting to note that geometry was the science that initially was concerned with measuring extensions (geo = earth; meter = measure), but the Greek geometers were able to evolve their techniques until they were able to find the exact measurements of figures such as the straight line, the line, the curve, as well as a surface limited by lines and its volume. In this way, the expression geometry was developed more and more and establishing relations of which there are two main types: of position (the line A is parallel to the line B) and the metric (the segment BC is three times the segment AB). The way in which ancient geometers demonstrated these relationships is the basis of the method par excellence of modern mathematics: proof.
The main art of the Greek geometers was their ability to create a multitude of theorems that linked a series of principles through innumerable chains of reasons. These theorems were the basis that supported Euclidean geometry.
Thanks to these demonstrations with which axioms, definitions and arguments are presented linked to each other, Euclidean geometry in relation to previous geometers. Euclides based his work on fundamental concepts on which a series of explicitly stated relationships were projected to create new concepts and establish new relationships.
Therefore, Euclidean geometry, like the later ones by Riemann, Lovachevski and Descartes, was based on deduction , working with certain figures (equations and symbols) and allowing this knowledge to be transmitted to other people.
Algorithmic: fusion of algebra and geometry that starts from applying calculus to solving large problems.
Analytical: the figures are studied through a mathematical analysis and a coordinate system .
Descriptive: in this branch of mathematics, the solution of geometric problems is carried out through operations performed on a plane that represents the figures of solids.
Projective: branch of geometry whose study objective is the projections of figures in a given plane.