Taxi Cab Geometry

Non-Euclidian Counting Problem

What is the shortest distance?

• What is the shortest distance from A to B? Let each edge of a square be 1 inch.

What is the shortest distance?

• What is the shortest distance from A to B if you have to stay on the grid lines?

• Verify by having 2 drawings. Explain how you know there isn’t a shorter distance.

How many shortest paths are there?

Problem Solving Skills

• Study a simpler problem and look for patterns.

1x systems

• For the 1x blocks, find the length of a shortest path and how many shortest paths there are. Note any patterns.

2x systems

• For the 2x blocks, find the length of a shortest path and how many shortest paths there are. Note any patterns.

3x systems

• For the 3x blocks, find the length of a shortest path and how many shortest paths there are. Note any patterns.

How many shortest paths are there?