Suitable Fit

In 1966, Austrian mathematician Leo Moser asked a pleasingly practical question: If a corridor is 1 meter wide, what’s the largest sofa one could squeeze around a corner?  That was 46 years ago, and it’s still an open question. In 1968 Britain’s John Michael Hammersley showed that a sofa shaped somewhat like a telephone receiver could make the turn even if its area were more than 2 square meters (above). In 1992 Joseph Gerver improved this a bit further, but the world’s tenants await a definitive solution. Similar problems concern moving ladders and pianos. Perhaps what we need are wider corridors.

Benham’s Top

Cut out this disc, pierce it with a pencil, and spin it like a top. The colors that appear are not entirely understood; it’s thought that they arise due to the different rates of stimulation of color receptors in the retina. The effect was discovered by the French monk Benedict Prévost in 1826, and then rediscovered 12 times, most famously by the toy maker Charles E. Benham, who marketed an “artificial spectrum top” In 1894. Nature remarked on it that November: “If the direction of rotation is reversed, the order of these tints is also reversed. The cause of these appearances does not appear to have been exactly worked out.”

maths note