About This Chapter
Non-Euclidean Geometry - Chapter Summary
This chapter provides you with an overview of non-Euclidean geometry, including a review of several different types of geometry that each differ from the standard in their own unique ways. Our instructors demonstrate the differences and uses for each of these non-Euclidean geometry methods. Each of the lessons carefully go over the necessary terminology, definitions, formulas, postulates, and theories that you'll need to know to understand these math concepts. At the end of the chapter, you will be prepared to:
- Describe how non-Euclidean and Euclidean geometry differ
- Analyze the tenets of hyperbolic geometry
- Explain the postulates used in elliptic geometry
1. Differences Between Euclidean & Non-Euclidean Geometry
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.
2. Hyperbolic Geometry: Definition & Postulates
Hyperbolic geometry studies the geometry of hyperbolic, or saddle-shaped surfaces. In this lesson, learn about the history, postulates, and applications of hyperbolic geometry.
3. Elliptic Geometry: Definition & Postulates
Elliptic geometry studies the geometry of spherical surfaces, like the surface of the earth. In this lesson, learn more about elliptic geometry and its postulates and applications.
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Other chapters within the Geometry 101: Intro to Geometry course
- Basics of Geometry
- Logic & Proof in Mathematics
- Intro to Geometric Figures
- Triangle Properties & Construction
- Parallel Lines & Polygons
- Triangle Congruence
- Ratios & Proportions in Geometry
- Similar Polygons
- Quadrilaterals Overview
- Circles Overview
- Overview of Conic Sections
- 3D Geometry
- Analytical Geometry
- Introduction to Trigonometry
- Studying for Geometry 101