The Foundation of the City 
similar, and regular, without useless spaces. 
Of the three figures, the hexagon is the most 
proper for convenience and strength. Bees, 
as if they knew this, make their cells regular 
hexagons.* 
“ Again, it has been demonstrated that, by 
making the bottoms of the cells to consist 
of three planes meeting in a point, there is 
a saving of material and labour in no way 
inconsiderable. The bees, as if acquainted 
with these principles of solid geometry, 
1 Réaumur suggested the following problem to the 
celebrated mathematician Koenig: “Of all possible 
hexagonal cells with pyramidal base composed of three 
equal and similar rhombs, to find the one whose construc- 
tion would need the least material?” Koenig’s answer was, 
the cell that had for its base three rhombs whose large 
angle was 109° 26”, and the small 70° 34”. Another 
savant, Maraldi, had measured as exactly as possible the 
angles of the rhombs constructed by the bees, and dis- 
covered the larger to be 109° 28”, and the other 70° 32”. 
Between the two solutions there was a difference there- 
fore of only 2”. It is probable that the error, if error 
there be, should be attributed to Maraldi rather than to 
the bees; for it is impossible for any instrument to 
measure the angles of the cells, which are not very clearly 
defined, with infallible precision. 
The problem suggested to Koenig was put to another 
mathematician, Cramer, whose solution came even closer 
to that of the bees, viz. 109° 28}” for the large angle 
and 70° 314” for the small. 
157 
