机灵小蜜蜂The Ingenious Honey Bees

4° The Ingenious Honey Bees. Man has long shown interest in the seeming geometrical sagacity of the honey bees. The first known man to report on this mathematical acumen was the eminent Greek geometer Pappus, who flourished in Alexandria some sixteen hundred years ago. In Book V of his famous Mathematical Collection we find the following passage concerning the extremum properties of the cells of the bees' honeycombs:

Presumably because they know themselves to be entrusted with the task of bringing from the gods to the accomplished portion of mankind a share of ambrosia in this form, they do not think it proper to pour it carelessly on ground or wood, or any other ugly or irregular material; but first collecting the sweets of the most beautiful flowers which grow upon the earth, they make from them for the reception of the honey, the vessels which we call honeycombs (with cells) all equal and similar, and contiguous to one another, and hexagonal in form. And that they have contrived this by virtue of a certain geometrical forethought, we may infer in this way. They would necessarily think that the figures must be such as to be contiguous to one another, that is to say, to have their sides in common in order that no foreign matter could enter into the interstices between them and so defile the purity of the produce. Now there are three rectilinear figures which are capable of fulfilling this condition, I mean regular figures which are equilateral and equiangular, for bees would have none of figures which are not uniform.... There being then three figures capable by themselves of exactly filling up the space about the same point, the bees by reason of their instinctive wisdom chose for their construction the figure which has most angles, because they conceived it would hold more honey than either of the other two.