An audacious heist at the Louvre saw thieves make off with priceless crown jewels in broad daylight – here is how a decades-old geometry problem can help museums boost their security.

It took just eight minutes. In those 480 seconds, thieves trundled their way upwards on a mechanical platform to reach a first floor balcony of the Louvre museum in Paris before cutting their way through a window in broad daylight. Once inside, they broke into two glass display cases and then escaped with eight priceless Napoleonic-era crown jewels. It was a "daring heist" that has shaken France to its core.

Seven suspects have now been arrested over the theft. One of the lingering questions that has dogged the robbery investigation, however, is why the thieves were not spotted sooner.

At a hearing in front of the French Senate in the immediate aftermath of the robbery, Laurence des Cars, the director of the world famous museum, admitted that the museum had "failed to protect" the crown jewels. She admitted that the only camera covering the balcony the thieves used was facing the wrong way and a preliminary report revealed one in three rooms in the Denon wing where the thieves struck had no security cameras. More generally Des Cars acknowledged that cuts in surveillance and security staff had left the museum vulnerable and insisted that the Louvre's security system must be reinforced to "look everywhere".

Alarms at the museum apparently sounded as they should, according to the French culture ministry. Yet it is the third high profile theft from French museums in two months, which have left the ministry implementing new security plans across France.

While there's no doubt that modern museum security is a complex and expensive affair, there is also an intriguing 50-year-old mathematical problem that deals with this very issue.

It asks, what’s the minimum number of guards – or equivalently 360-degree CCTV cameras – needed in order to keep a whole museum under observation? It is known as the museum problem, or the art gallery problem. The solution is an elegant one.

We'll assume that all the walls of our imaginary museum are straight lines so that the floorplan is what mathematicians call a polygon, a shape with hard edges and corners. The cameras must be at fixed positions, but they can see in all directions. To ensure the whole museum is covered, we should be able to draw a straight line from any point in the floor plan to at least one of the cameras.

Take the hexagon-shaped gallery on the left of the diagram below. No matter where you place the camera, you'll be able to see floor and walls of the entire space. When every position can be seen from every other in this way, we call the gallery shape a convex polygon. The L-shaped........

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