Course:Study Guide - Final - Bart-Fall07

Part I: Essay type questions

The exam is 1 hour and 50 minutes long.
I will ask some or all of the following questions:

• Compare and contrast Euclidean and hyperbolic geometry.
  

What can you say about the following topics in each of these geometries: a) geodesics, b) polygons (which ones exist, which ones don’t), c) sum of the angles in a triangle, d) sum of the angles in a quadrilateral, e) isometries, f) area, g) Escher’s use of each of the geometries. (Be thorough!)

• Explain everything you know about fractals.
  

a) What is self-similarity? b) Where do we find fractals? c) Explain how to create the Sierpinski triangle or the Koch Snowflake (no need to do both).Draw an example. d) How did Escher use fractals in his art? Name some of his prints based on fractals.

• Explain as much as you can about dimensions.
  

a) Give some examples of 0-, 1-, 2-, 3-dimensional objects. b) Explain how we would create a 4-dimensional cube. Explain how to create a square from a line segment, and how to create a cube from a square (increasing the dimension by 1) and how this process allows us to draw a picture of a 4-dimensional cube. Draw a picture of this 4-dimensional cube.

Part II: Problems based on explorations and homework

• I will take some questions from the homework.
• I will take some questions from the explorations. Go to our main class website to see a list of all the explorations we have covered in class.