Homework Sets
Due Wednesday 9/19/18. Homework 1 pdf. Large print version pdf. Solutions pdf.
Due Wednesday 9/26/18. Homework 2 pdf. Large print version pdf. Solutions pdf.
Due Wednesday 10/3/18. Homework 3 pdf. Diagrams pdf. Large print version pdf. Solutions pdf.
Due Wednesday 10/10/18. Homework 4 pdf. Large print version pdf. Solutions pdf.
Midterm review problems pdf. Large print version pdf. Solutions pdf.
Midterm exam pdf. Large print version pdf. Solutions pdf.
Due Wednesday 10/31/18. Homework 5 pdf. Large print version pdf. Solutions pdf.
Due Wednesday 11/7/18. Homework 6 pdf. Large print version pdf. Solutions pdf.
Due Wednesday 11/14/18. Homework 7 pdf. Large print version pdf. Solutions pdf.
Due Friday 12/7/18. Homework 8 pdf. Large print version pdf. Solutions pdf.
Final review problems pdf. Large print version pdf. Solutions pdf.
Instructions for constructing a paper model of the hyperbolic plane:
Print out this page and make several photocopies. Cut out the collar regions and build the surface by successively attaching the inside of one collar to the outside of another and also attaching the collars end to end. (I used small pieces of sticky tape to do this; if you put the tape all on one side you'll be able to draw with a pencil on the other side.) When you have made a reasonably large surface you will find that the edge of the surface is wavy (so that the edge is longer than if the surface was flat). Now put the surface on a table, take a ruler and press one edge of the ruler down on the surface so that the surface touches the table along the edge of the ruler, and draw a line on the surface with a pencil. This line is a hyperbolic line in the hyperbolic plane. If you draw 3 lines forming a hyperbolic triangle you will be able to see that the sum a+b+c of the angles of the triangle is less than pi. In fact pi-(a+b+c) is proportional to the area of the triangle (and in the mathematical study of the hyperbolic plane we choose units so that we have equality here).