TaxiCab Problem
applied
Explore this classic problem in combinatorics.
Introduction
Given that a taxicab driver can only drive up and right, how many possible routes can they take? Suppose they tossed a coin to decide whether to go up or right. How can we use probability to model this scenario? Try it, do you think the expectation matches the theory? Know Python? Code it. There are two options in this scenario, up and right. What if you rolled a dice to decide the direction where the probabilities are biased?
Guiding Questions
- What mathematical models apply to this situation?
- What data do you need to collect and how will you analyze it?
- What assumptions are you making in your mathematical model?
- How can you validate your mathematical conclusions?
- What are the limitations of your approach?
Key Mathematical Concepts
Distance Metrics
Geometric Proofs
Non-Euclidean Geometry
Taxicab Geometry