A geometrical puzzle challenges readers to design the shortest road system connecting four towns arranged at the corners of a square. The solution, surprisingly, isn’t immediately obvious – common attempts like looping around all towns or direct X-shaped roads prove inefficient.
The most elegant answer is found not through calculation, but through physics. Placing a model of the puzzle in soapy water reveals the optimal structure as bubbles spontaneously form around the corners, minimizing surface area just as they would minimize road length. The resulting network resembles a star-shaped pattern, where roads radiate from a central point, reducing total asphalt usage.
This method highlights how nature inherently seeks minimal energy states, applying the same principle to both bubbles and road systems. The puzzle’s underlying geometry is familiar: it mirrors the arrangement of tension structures in real-world designs.
The article also spotlights new interactive math centers, MathsWorld London and MathsCity Leeds. These venues feature exhibits like giant bubble machines, elliptical pool tables, and build-your-own arches, making math playful and accessible.
The key takeaway is that minimal structures arise naturally, whether in soap bubbles or road networks. The puzzle is a reminder that simple physical demonstrations can sometimes provide better solutions than complex calculations.
Locations:
- MathsWorld London: 6 Burrell St, London, SE1 0UN
- MathsCity Leeds: Zurich House, 4 Canal Wharf, Leeds, LS11 5PS
