Geometry is the study of figures and solids. It was created by ancient philosophers and mathematicians like Euclid and Plato. Euclidean geometry, based on the axioms of Euclid, is the best-known branch of geometry. Non-Euclidean geometry, on the other hand, is based on different axioms.

## What is geometry? A brief definition of geometry and its main concepts.

Geometry is the branch of mathematics that studies figures and spaces. It is characterized by the precision and rigor of its reasoning, as well as by the beauty of its constructions.

Among the branches of mathematics, geometry is the one that allows us to represent and analyze figures and spaces. In geometry, we study the properties of objects such as points, lines, angles, surfaces and solids. We also learn to construct these objects using precise rules.

Euclidean geometry, which is the most common form of geometry, is based on the axioms of Euclid, a Greek mathematician from the 3rd century BCE. These axioms are propositions that are accepted without proof, such as Euclid's postulate which states that “no more than three points can be aligned”. From these axioms, we develop all of Euclidean geometry.

There are other forms of geometry, such as non-Euclidean geometry, which are based on different axioms. Non-Euclidean geometry is actually the geometry that we use in everyday life, because it corresponds better to reality. For example, in non-Euclidean geometry, no more than three points can be aligned, but it is possible for a point and its mirror image to be aligned.

Geometry is an ancient science that has been studied by many famous mathematicians, such as Euclid, Pythagoras, Thales, Archimedes, Pappus and Descartes. Geometry concepts are also used in other fields, such as architecture, engineering, physics and cosmology.

## The history of geometry: what was it used for by the ancients and how has it evolved over the centuries?

Geometry was invented by the Babylonians over 4000 years ago. At that time, it was used for building construction and land management. Over the centuries, geometry was perfected by the Greeks, Arabs and Europeans. Euclidean geometry, which is the most common form of geometry today, was created by Euclid, a Greek philosopher from the 3rd century BCE. Non-Euclidean geometry, another form of geometry, was developed in the 19th century by the British mathematician Arthur Cayley.

Geometry is used in many disciplines, including architecture, engineering, construction, medicine and cosmology. It is also used in everyday life, for example to find routes, measure distances and calculate areas.

Geometry is a branch of mathematics that studies figures and spaces. It has a long history that has developed over the centuries. Today, it is used in many fields, including architecture, engineering and navigation.