Research non-Euclidean geometry and plan a seminar based on your groups research. Each

Chapter 10, Problem 47

(choose chapter or problem)

Research non-Euclidean geometry and plan a seminar based on your group’s research. Each group member should research one of the following five areas:a. Present an overview of the history of the people who developed non-Euclidean geometry. Who first used the term and why did he never publish his work?b. Present an overview of the connection between Saccheri quadrilaterals and non-Euclidean geometry. Describe the work of Girolamo Saccheri.c. Describe how Albert Einstein applied the ideas of Gauss and Riemann. Discuss the notion of curved space and a fourth dimension.d. Present examples of the work of M. C. Escher that provide ways of visualizing hyperbolic and elliptic geometry.e. Describe how non-Euclidean geometry changed the direction of subsequent research in mathematics. After all research has been completed, the group should plan the order in which each group member will speak. Each person should plan on taking about five minutes for his or her portion of the presentation.