# Non-Euclidean Geometries

Taught by MrA
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Meets NCTM Standards:
Lesson Summary:

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.

Lesson Description:

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.