THE BEE. 



the surrounding space, and any number of squares may thus be 

 combined so as to cover a surface like a mosaic pavement without 

 leaving any intermediate unoccupied spaces. 



In like manner six equilateral triangles will have a like pro- 

 perty, and in fine, three regular hexagons being similarly united 

 at one of their corners, will in like manner completely occupy the 

 surrounding space. 



Since no other regular geometrical figure possesses this property, 

 it follows that a regular mosaic pavement must necessarily be 

 composed of one or other *>f these figures. 



Fig. 19 represents such a pavement composed of squares ; and 

 fig. 20, one composed of equilateral triangles ; and in fine, 

 fig. 21, one composed of regular hexagons. 



Fig. 19. 



The angles, in fig. 19, are 90 ; those in fig. 20, are 60; and 

 those in fig. 21, 120. No other angles save these, therefore, 

 could be used in any regular pavement of this kind without 

 leaving intersticial uncovered spaces. 



Now it will be at once perceived that the form presented by the 

 surface of a honey- comb is that of an hexagonal pavement. "We 

 shall presently see why the bee has selected this in preference to 

 either of the other possible forms. 

 26 



