Write a group paper about taxicab geometry.  In your paper, you should explain what Taxicab geometry is and what you have learned about it.  You can look at some of the questions below, or any other questions that seem interesting to you.
 

Some possible questions:

• Can you give a formula for taxicab distance? Is taxicab distance always less or more than Euclidean distance?  Can you prove your answer?
• What do taxicab circles look like?  How can they be used?  What is the taxicab value of pi?
• What do taxicab ellipses look like?  How can they be used?  (Recall, an ellipse with foci A and B is {P| d(A,P) + d(B,P) = c}, the set of all of the points that can be drawn using a string of length c attached to points A and B.)
• What happens if we look instead at a set {P|d(A,P) - d(B,P) = c} in Euclidean or taxicab geometry?  What happens in the case where c = 0?
• How do you find the distance from a point to a line in taxicab geometry?  Can you give a careful procedure that always works?  How does this differ from euclidean geometry?  If I have a point A and a line L,  what is {P|d(A,P) = d(P,L)} in euclidean or taxicab geometry?
• Can you use Geometer's Sketchpad to model any of these shapes in taxicab geomery?
• Are there any theorems of Euclidean geometry that aren’t true in taxicab geometry?