Tethered Goats
applied
A classic problem with many interpretations - Explore the mathematical principles and create your own unique investigation.
Introduction
Stuart tethered his goat to one end of a 20-foot length of rope and attached the other end of the rope to a hook fixed to the side of his shed. When he came back, the goat had eaten all the grass within its reach. What was the area eaten? Could the goat have eaten more grass if the rope had been attached to a different point on the shed? Experiment with different lengths of rope and shapes of sheds. Where should the hook be positioned each time to allow the goat to eat the maximum amount of grass? This was an SL Exam question some years ago. An image and measurements is missing - create your own scenario.
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
Optimization
Geometry
Area
Calculus