Exploration 3 (Taxicab Geometry)
Department of Mathematics and Computer Studies
York College (CUNY)
Jamaica, New York
Distance below refers to distance using the taxicab metric. Assume that angles are measured as in the Euclidean plane. The lines in this plane have linear equations.
1. Suppose that one is given the points A = (0, 0), B = (2, 4), C = (4, 6) and D = (-2, 4).
a. Find the taxicab distance between every pair of these points.
b. Draw a taxicab circle of radius 2 centered at B.
c. Which of the points A, C, D (if any) lies on or inside the taxicab circle of radius 2 centered at B?
d. Draw the graph (in the analytical geometry sense) of points which are equidistant from D and C.
2. Draw those points which are equidistant from (-2, -2) and (-4, -4).
3. Find the coordinates of 7 points that lie on the taxicab circle of radius 2 centered at (0, 0).
4. Draw the graph of the points in the taxicab plane the sum of whose distances from (-2, 0) and (2, 0) is 8. What name is commonly given to a "curve" of this kind in the Euclidean plane?