To follow up on the most fascinating direct-democracy push in the world: The UK government has rejected a petition to change the soccer-ball illustration on certain road signs, making it so they are no longer geometrically impossible, covered solely with hexagons rather than the necessary mix of hexagons and pentagons. Part of the government argument, which you can read here at the online petition, is:
The purpose of a traffic sign is not to raise public appreciation and awareness of geometry which is better dealt with in other ways. If the correct geometry were put onto a sign, it would only be visible close up and not from the distance at which drivers will see the sign. The detail of the geometry would also not be taken in by most drivers who were merely looking at the sign for direction. The higher level of attention needed to understand the geometry could distract a driver’s view away from the road for longer than necessary which could therefore increase the risk of an incident.
I’m not sure why seeing a drawing of a ball with hexagons and pentagons would require a “higher level of attention” that one with just hexagons.
Matt Parker, the self-styled “stand-up mathematician” who mixes comedy and some surprisingly high-level mathematics, has vowed to continue the drive. If 100,000 British citizens sign the online petition, it has to be discussed in Parliament.
Here’s a good proof of why you can’t cover a soccer ball only with hexagons (or only with pentagons, for that matter). it uses Euler’s formula V−E+F=2 (where V is the number of vertices, E is the number of edges, and F is the number of faces).
No, this has nothing whatsoever to do with New Hampshire, but I love the story too much to leave it out.