Differences Between Euclidean & Non-Euclidean Geometry

An error occurred trying to load this video.

Try refreshing the page, or contact customer support.

Coming up next: What are 2D Shapes? - Definition & Examples

You're on a roll. Keep up the good work!

Take Quiz Watch Next Lesson
Your next lesson will play in 10 seconds
  • 0:04 Who Was Euclid?
  • 0:47 Euclidean Geometry
  • 1:29 Euclidean vs. Non-Euclidean
  • 2:02 Types of Non-Euclidean…
  • 3:27 Lesson Summary
Save Save Save

Want to watch this again later?

Log in or sign up to add this lesson to a Custom Course.

Log in or Sign up

Speed Speed

Recommended Lessons and Courses for You

Lesson Transcript
Instructor: Betsy Chesnutt

Betsy teaches college physics, biology, and engineering and has a Ph.D. in Biomedical Engineering

Euclidean geometry is the study of the geometry of flat surfaces, while non-Euclidean geometries deal with curved surfaces. Here, we'll learn about the differences between these mathematical systems and the different types of non-Euclidean geometry.

Who Was Euclid?

Sometime in the 4th century BCE, a boy was born in Alexandria who would grow up to become one of the most famous mathematicians and thinkers who ever lived. His name was Euclid, which, in Greek, means 'renowned and glorious'.'

Euclid was a famous mathematician in his own time, and he only became more famous and influential in the thousands of years that followed. He wrote a book called The Elements in which he laid out the basic principles of geometry that we still know and use today. His book was the primary textbook used to teach mathematics in the Western world from the time it was written until the beginning of the twentieth century. Even today, much of what is taught in a typical geometry course comes from Euclid.

Euclidian Geometry

This is called Euclidean geometry and it is the study of the geometry of flat surfaces. In Euclidean geometry, the interior angles of a triangle always add together to make 180 degrees, but as we will see, that is not true in the non-Euclidean geometries.

One of the most important of Euclid's postulates in The Elements was the parallel postulate. In simple terms, the parallel postulate says that if you have a line and a point, there is only one other line that you can draw though the point that will be parallel to the original line. This is definitely true on a flat, two-dimensional surface, but it turns out to not be true in some other situations, including when the surface is curved.

Euclidean vs. Non-Euclidean

While Euclidean geometry seeks to understand the geometry of flat, two-dimensional spaces, non-Euclidean geometry studies curved, rather than flat, surfaces. Although Euclidean geometry is useful in many fields, in some cases, non-Euclidean geometry may be more useful. For example, suppose you want to measure the shortest distance between points on the Earth. The surface of the Earth is curved, not flat (a fact that Euclid was not aware of). Of course, techniques from non-Euclidean geometry would be much more useful in this case since the Earth is a sphere.

To unlock this lesson you must be a Study.com Member.
Create your account

Register to view this lesson

Are you a student or a teacher?

Unlock Your Education

See for yourself why 30 million people use Study.com

Become a Study.com member and start learning now.
Become a Member  Back
What teachers are saying about Study.com
Try it risk-free for 30 days

Earning College Credit

Did you know… We have over 200 college courses that prepare you to earn credit by exam that is accepted by over 1,500 colleges and universities. You can test out of the first two years of college and save thousands off your degree. Anyone can earn credit-by-exam regardless of age or education level.

To learn more, visit our Earning Credit Page

Transferring credit to the school of your choice

Not sure what college you want to attend yet? Study.com has thousands of articles about every imaginable degree, area of study and career path that can help you find the school that's right for you.

Create an account to start this course today
Try it risk-free for 30 days!
Create an account