Non-Euclidean Geometry
All the geometrical figures that do not come under Euclidean Geometry are studied under Non-Euclidean Geometry. This is the branch of geometry that deals with 3-Dimensional figures, curves, planes, prism, etc. This branch of geometry commonly defines spherical geometry and hyperbolic geometry.
Euclidean and Non-Euclidean Geometry Differences
The basic differences between Euclidean and Non-Euclidean Geometry are that Euclidean Geometry deals with flat figures in 2-Dimension and Non-Euclidean Geometry deals with spherical geometry and hyperbolic geometry in 3D.
This difference can be understood with the help of an example of a parallel line.
In Euclidean Geometry there is only one line parallel to another line and passing through a fixed point, whereas in Non-Euclidean Geometry we can have multiple lines in 3-Dimensions which are at a constant distance from a line and passes through a line.
Euclidean Geometry
Euclidean geometry is the study of 2-Dimensional geometrical shapes and figures. Euclidean geometry is based on different axioms and theorems. The word geometry is derived from the Greek words ‘geo’ meaning Earth and ‘metrein’ meaning ‘To measure’. Thus, geometry is the measure of the Earth or various shapes present on the Earth.
Euclidean geometry as the name suggests was first used by the famous Greek mathematician Euclid. He described the geometry of flat objects in his book “Elements” and was the pioneer in this field. He gives various axioms or postulates that are obvious universal truths, (but they can not be proved by usual means). He stated 5 main axioms which are discussed below in the article.
In this article, we have provided the axioms and Postulates given by Euclid, and a detailed overview of Euclid’s Geometry including its definition, examples, theorem, and advantages.
Table of Content
- History of Euclid Geometry | Who was Euclid?
- What is Euclidean Geometry?
- Euclidean Geometry Definition
- History of Euclidean Geometry
- Euclid’s Definitions
- Examples of Euclidean Geometry
- Non-Euclidean Geometry
- Euclidean and Non-Euclidean Geometry Differences
- Theorems Proved by Euclid
- Euclidean Geometry in Engineering
- Properties of Euclidean Geometry
- Elements in Euclidean Geometry
- Euclid’s Axioms
- Euclid’s Postulates
- Euclidean Geometry Examples
- Euclidean Geometry Class 9
- Practice Problems on Euclidean Geometry