### Project 6: Parallels and Connections

Prepare to turn in work that follows the guidelines. I will post on ASULearn answers to select questions I receive via messaging there or in office hours! You may work alone or in a group of at most 3 people, and turn in one project per group.

### Problem 1

Roads to Geometry Exercises 2.3 #1

### Problem 2

Roads to Geometry Exercises 2.7 #2 (all three parts)

### Problem 3

Roads to Geometry Exercises 4.2 #1

### Problem 4

Geometric Viewpoint Problems for Section 1.2 # 15 part a) [prove that this statement proves Playfair's and that Playfair's proves this statement, ie both directions, assuming only Euclid's first 28 propositions as well as Theorem 1.2.1 in the book]

### Problem 5

Explore parallels in a creative way - produce an imaginative work of your own making involving parallels on the sphere (no parallels), the plane (1 parallel), and hyperbolic geometry (infinitely many parallels) For example, this might be a series of photographs or physical models, a poem, a youtube video, a song, written as a newspaper interview, a newsletter bulletin, a powerpoint presentation, a study guide, a classroom worksheet, ... It must be something that you can turn in. Be sure to acknowledge any references where it is due, including pictures.