Several students are invited to join a group to solve a problem when they log into the Math Forum. Four of them agree to participate. They are given a name for their group and instructions on how to proceed.
The students leave messages in a discussion area to set up a time to work together on the problem. They check in periodically and agree upon a time.
At the agreed upon time, they log into the “Taxicab Geometry” problem site at the Math Forum. They are in a chat area associated with a shared whiteboard. On the whiteboard is a statement of the problem and a diagram (see Figure 1). The problem is to explore geometry on a grid.
The taxicab drivers in Gridville have their own version of geometry to help them find their way around efficiently. The streets in Gridville form a perfect grid, with streets one block away from each other.
The following questions are posed for partial submissions:
- What are the taxicab-lengths of routes A, B and C in the map of Gridville?
- What is the formula for the shortest taxicab-distance along the grid between any point P at (j, k) and any other point Q at (m, n) on the grid ?
- Draw a taxicab-circle of all points that are a distance 4 blocks from a center point.
- What is the taxicab-distance around that taxicab-circle with taxicab radius of 4 blocks?
- What is the formula for the taxicab-circumference of a taxicab-circle of taxicab-radius R?
- What is the area of a taxicab-circle of taxicab-radius R?
- What is the value of taxicab-pi? Remember that taxicab-circumference = 2 x taxicab-pi x taxicab-radius ?
- What is the taxicab-area of a taxicab-circle?