Note:  Problems this semester will be posted by 3:00pm on Mondays. 
 

Take a cylinder of paper of diameter 1 (for example, the carboard tube in the middle of a roll of paper towel) and cut it at a 45° angle.  Now take the paper cylinder, cut it vertically and unroll it so it lays flat.  See the figure on the left.  What is the function that describes the shape of the top of the paper?