Excerpted from A Dictionary of Fabulous Beasts, by Richard Barber and Anne Riches and Numbers, by David Wells.

Number: 0.7404…

pi/sqrt(18)

How closely can identical spheres be packed together?  The obvious way is to arrange one layer on a plane so that each sphere touches 6 others, and then arrange adjacent layers, so that each sphere touches 3 others in each layer (12 in all) and so on.  However, no mathematician has been able to prove this ‘obvious’ fact.

If that were the closest packing, the density would be this number.

‘Many mathematicians believe, and all physicists know, that the density cannot exceed pi/sqrt(18).’ [Rogers]

Beast: Amphisbaena

A two-headed creature, sometimes shown with feathers, but described as a snake by Pliny and by Lucan in his description of the terrors of the African desert in the Pharsalia.  When one head was asleep, the other remained awake, particular while hatching eggs; in this case the head on duty woke up the other one when it was time for it to take over.  Curiously enough, it proves to be a real animal, a limbless lizard which can move both backwards and forwards, and which rears its tail if frightened, pretending that it is a second head.