Why the Fastest Path Isn't the Shortest -- The Brachistochrone problem
What if the shortest path… isn't the fastest?
In this video, I explore the Brachistochrone Problem — a fascinating 300-year-old problem in mathematics and physics.
If a ball moves between the same two points under gravity, which path gets it there in the least time?
I built a model with three different paths — a straight path, a deep curve, and the Brachistochrone — and raced them to find out.
The surprising answer is the cycloid: a curve that balances gaining speed quickly with the distance the ball has to travel.
The Brachistochrone is more than just a mathematical puzzle. It introduced a powerful way of thinking about optimization: finding the best possible solution rather than simply choosing the shortest or most obvious one.
This is my submission for the Breakthrough Junior Challenge 2026.
Adisesh Mundra
Grade 9 | Fountainhead School
Category: Physics
Topic: The Brachistochrone Problem
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