Taxicab Geometry

What is taxicab geometry?

Taxicab geometry is the distance between two points measured along axes at right angles. At a plane with point 1 at (x1, y1) and point 2 at (x2, y2), the total distance is equal to the equation of |x1 - x2| + |y1 - y2|. Taxicab geometry takes a non-euclidean approach to plane figures (two dimensional objects). This type of take on geometry is sometimes referred to as "urban geometry" because the grid lines can be equated to an urban city. In the figure below, each point can be seen as an intersection of two streets.
Taxicab Geometry
Taxicab Geometry
Then, the distance of each grid line to the next intersection can be called a block.

In typical geometry, the shortest distance is a straight line between two points (the green line). In taxicab geometry, the shortest distance can be a straight line if the points lie on the same axis. However, as seen in the figure, the taxicab geometry distances are the red, blue, and yellow paths.

Taxicab Geometry Tasks
Big Ideas About Taxicab Geometry
Teaching taxicab geometry
Teacher Resources