The Geometry of the Epeira's Web 



to the geometer's speculations. A figure, 

 which was at first but a tentative glimpse, be- 

 comes a reality by the fall of a pebble out of 

 the vertical. 



The same speculations take up the para- 

 bola once more, imagine it rolling on an 

 indefinite straight line and ask what course 

 does the focus of this curve follow. The 

 answer comes : the focus of the parabola de- 

 scribes a 'catenary,' a line very simple in 

 shape, but endowed with an algebraic symbol 

 that has to resort to a kind of cabalistic num- 

 ber at variance with any sort of numeration, 

 so much so that the unit refuses to express it, 

 however much we subdivide the unit. It is 

 called the number e. Its value is repre- 

 sented by the following series carried out ad 

 infinitum : 



r=1+ I + r3 + r^3 + l. 2.3.4 + 1.2.3.4.5 +etC- 



If the reader had the patience to work out 

 the few initial terms of this series, which has 

 no limit, because the series of natural numerals 

 itself has none, he would find: 



£=2.7182818 . . . 

 With this weird number are we now sta- 



397 



