The Life of the Bee 



geometry, follow them most accurately. 

 It is a curious mathematical problem at 

 what precise angle the three planes which 

 compose the bottom of a cell ought to 

 meet, in order to make the greatest pos- 

 sible savmg, or the least expense of mate- 

 rial and labour.^ This is one of the 



^ Reaumur 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 con- 

 struction 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 discovered the larger to be 109° 28", 

 and the other 70° 32". Between the two solutions 

 there was a difference, therefore, of only z" . 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 

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