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Chapter 10: Problem 57
Describe how to find the measure of an angle of a regular pentagon.
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In Exercises 15-20, find the measure of the complement and the supplement of each angle. \(52^{\circ}\)
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.
A scale model of a car is constructed so that its length, width, and height are each \(\frac{1}{10}\) the length, width, and height of the actual car. By how many times does the volume of the car exceed its scale model?
In the diagram for Exercises \(17-19\), suppose that you are not told that \(\triangle A B C\) and \(\triangle A D E\) are similar. Instead, you are given that \(\overleftrightarrow{E D}\) and \(\overleftrightarrow{C B}\) are parallel. Under these conditions, explain why the triangles must be similar.
In the musical Company, composer Stephen Sondheim describes the marriage between two of the play's characters as "parallel lines who meet." What is the composer saying about this relationship?
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