Non-Euclidean Geometries
In this lesson, we learn about non-traditional geometries, also known as non-Euclidean geometries. Euclid's five postulates are explained, with special attention given to the controversial fifth postulate (the parallel postulate). We learn about the two types of non-Euclidean geometry: elliptic and hyperbolic geometry. Triangles in these geometries have angles that can be greater or less than 180 degrees, depending on the geometry. We also learn about other non-Euclidean geometries, including absolute, affine, projective, spherical, and taxicab geometries. These non-Euclidean geometries have applications in many observable places, such as our curved universe and the earth.
An explanation of Euclid's five postulates -- and an especially in-depth explanation of Euclid's 5th postulate (the parallel postulate). An explanation of how Elliptic and Hyperbolic geometries work, and a list of non-Euclidean geometries with a brief overview of some of them.
- Lesson Slides - Slides that are written on from the lesson.
- What is Non-Euclidean Geometry?
- What other types of geometry are there?
- What is elliptic geometry?
- What is hyperbolic geometry?
- What is the parallel postulate?
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Staff Review
If you have ever heard that there was such a thing as Geometry that was different from everything you have learned before, and you wanted to know more about it, this is the lesson for you. A great explanation of what it means to have a Non-Euclidean geometry, and what those types of geometries look like. The lesson even starts from an explanation of where these geometries started and includes a list of more geometries for you to study yourself. A truly mind-blowing experience if you are new to this idea. -
robyn2187
In the video, latitude lines and longitude ines on a globe are referred to as not parallel because they intersect at the poles. This is true for longitude lines only. Latitude lines are not straight and are actually "lesser circles" that are equidistance from each other therefore they do not intersect. So it is true that none of the lines are parallel, but for two different reasons.
