Reuleaux Triangle in 3D
applied
These three objects have constant width, meaning that when placed between two flat surfaces, they roll smoothly, as if they were balls — even though it doesn’t look like they should be able to.
Introduction
From the article below: Mathematicians Discover New Shapes to Solve Decades-Old Geometry Problem Mathematicians have long wondered how “shapes of constant width” behave in higher dimensions. A surprisingly simple construction has given them an answer.
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
Geometry
Constant Width Curves
Engineering
Reuleaux Triangle