The earliest known examples of geometry date back to the Indus Valley Civilization, which developed perfectly organized cities using geometrical principles. The Egyptians and the Mesopotamians also used geometrical techniques to build pyramids and aesthetically pleasing artworks. In the fourth millennium BC, Greeks had learned how to use geometry to solve problems in astronomy, physics and other areas. Geometry was an integral part of their knowledge and, in many ways, reached a completeness and perfection that no other branch had attained before it.

A Greek mathematician named Euclid, living around 300 BC, is often credited with being the first person to introduce the study of geometry and his encyclopedic book The Elements remains the primary textbook for teaching mathematics today.

He was able to create a number of new types of figures, curves, surfaces and solids and, in addition, changed the methodology of geometry from trial-and-error to logical deduction. He also recognized that geometry studies “eternal forms” or abstractions of which physical objects are only approximations, and he formulated the idea of the axiomatic method.

Ancient Greece had a rich and varied culture and many important thinkers contributed to the development of geometry. Some of these people are still remembered, such as Archimedes of Syracuse, who worked on calculating the volume of irregular objects. Others, such as Liu Hui from the kingdom of Cao Wei (179 AD-202 BCE), are less well known but were very influential in the field.

Among the most important Greek geometries was the study of the golden ratio and the problem of dividing an angle into two equal halves, or decans, which was later solved by the mathematician Pythagoras. He also introduced the concept of parallel lines, which was the basis for the modern theory of non-Euclidean geometry.

The simplest and oldest type of geometry is plane geometry, which is the study of shapes with only two dimensions. This type of geometry is the foundation for many branches of mathematics such as engineering, astronomy, and chemistry.

Other more advanced types of geometry include solid geometry, which is the study of rigid three-dimensional shapes such as a cube, and topology, which is the study of geometric edges and surfaces rather than specific shapes. This type of geometry is the foundation for other branches of mathematics such as mathematical physics, and it has helped shape our understanding of the universe.

One of the most important branches of geometry is analytical geometry, which develops methods of analyzing the properties of geometric objects. This branch of mathematics focuses on the relationship between a shape and its surrounding space and is the foundation for many other disciplines, including physics and computer science.