Different Kinds of Geometry

Modern geometry ranges from the study of two-dimensional shapes to the study of gravitational fields.
••• makaule/iStock/Getty Images

Geometry is the study of shapes and sizes in various dimensions. Most of the foundation of geometry was written in Euclid's "Elements," one of the oldest mathematical texts. Geometry has progressed since the ancient times, however. Modern geometry problems involve not only figures on two or three dimensions, but also more complex problems like the study of differentials and gravitational fields.

Euclidean Geometry

Euclidean, or classical, geometry is the most commonly known geometry, and is the geometry taught most often in schools, especially at the lower levels. Euclid described this form of geometry in detail in "Elements," which is considered one of the cornerstones of mathematics. The impact of "Elements" was so big that no other kind of geometry was used for almost 2,000 years.

Non-Euclidean Geometry

Non-Euclidean geometry is essentially an extension of Euclid's principles of geometry to three dimensional objects. Non-Euclidean geometry, also called hyperbolic or elliptic geometry, includes spherical geometry, elliptic geometry and more. This branch of geometry shows how familiar theorems, such as the sum of the angles of a triangle, are very different in a three-dimensional space.

Analytic Geometry

Analytic geometry is the study of geometric figures and constructions using a coordinate system. Lines and curves are represented as set of coordinates, related by a rule of correspondence which usually is a function or a relation. The most used coordinate systems are the Cartesian, polar and parametric systems.

Differential Geometry

Differential geometry studies planes, lines and surfaces in a three-dimensional space using the principles of integral and differential calculus. This branch of geometry focuses on a variety of problems, such as contact surfaces, geodesics (the shortest path between two points on the surface of a sphere), complex manifolds and many more. The application of this branch of geometry ranges from engineering problems to the calculation of gravitational fields.

Related Articles

Facts and Trivia About Trigonometry
The Use of Calculus in Engineering
How to Calculate the Radius of a Square
How to Find Partial Pressures
Algebra 1 Compared to Algebra 2
Types of Trigonometry
How to Find the Vertices of an Ellipse
What Is a Mathematical Expression?
How to Solve a Matrix
How Is Geometry Used in Real Life?
Chemical Bonding Rules
How to Solve a Parabola
How to Find Equations of Tangent Lines
What Are Vertices in Math?
Math Courses in College
What Are the Subsets of a Line in Geometry?
Endpoint Math Formula
How to Name a Line in Geometry
How to Convert Pounds Per Square Foot to PSI
How to Find the Radius of a Curvature

Dont Go!

We Have More Great Sciencing Articles!