2. Types of Geometry 📚

Within the big world of geometry we can find different types of geometry (Arki, 2017):

• Euclidean Geometry

Euclidean geometry is the most common and traditional type of geometry. It deals with the study of two-dimensional and three-dimensional shapes and their properties. It also includes the study of lines, points, angles, and planes. Euclidean geometry is based on a set of axioms, which are self-evident truths that do not require proof.

• Non-Euclidean Geometry

Non-Euclidean geometry is a type of geometry that contradicts some of the assumptions of Euclidean geometry. It includes hyperbolic geometry and elliptic geometry. Hyperbolic geometry deals with the study of shapes and properties on a surface with a constant negative curvature. Elliptic geometry, on the other hand, deals with shapes and properties on a surface with a constant positive curvature.

• Analytic Geometry

Analytic geometry is a type of geometry that uses algebraic equations and coordinates to study geometric shapes and their properties. It was developed by French mathematician René Descartes in the 17th century. Analytic geometry allows mathematicians to solve geometric problems using algebraic equations, which makes it a useful tool in many fields of science and engineering.

• Projective Geometry

Projective geometry is a type of geometry that studies properties that remain the same when a geometric figure is projected onto a plane. Projective geometry is useful in computer graphics, computer vision, and robotics.

• Differential Geometry

Differential geometry is a type of geometry that deals with the study of curves and surfaces in three-dimensional space. It uses tools from calculus to study the properties of curves and surfaces, such as curvature, tangent vectors, and normal vectors. Differential geometry is used in physics to study the curvature of spacetime in Einstein's theory of general relativity.

In conclusion, the study of geometry has evolved over time, leading to the development of various types of geometry. Each type of geometry has its unique characteristics, properties, and applications. Understanding the different types of geometry is essential for students and professionals in various fields such as engineering, physics, and computer science.