The Dogs in Pursuit Problem
6 days ago
- #calculus
- #mathematics
- #puzzle
- Four dogs start at the corners of a square with side length 1, each running towards the dog immediately anti-clockwise to it.
- All dogs run at the same speed, spiraling towards the center until they collide.
- The problem asks how far each dog travels before collision.
- Bonus: Extend the problem to equilateral triangles and regular pentagons.
- The puzzle is inspired by pursuit problems, which often involve calculus.
- Steven Strogatz, a mathematician, highlights the Infinity Principle in calculus—breaking complex motions into simpler parts.
- Pursuit problems are visually engaging and historically significant in calculus.
- The spiral paths of the dogs resemble mathematical art or optical illusions.
- The article promotes Strogatz's book 'Infinite Powers' and the author's 'Football School' series.