Page:The Life of the Spider.djvu/401

The Geometry of the Epeira's Web

to the geometer's speculations. A figure, which was at first but a tentative glimpse, becomes a reality by the fall of a pebble out of the vertical.

The same speculations take up the parabola 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 describes a 'catenary,' a line very simple in shape, but endowed with an algebraic symbol that has to resort to a kind of cabalistic number 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 represented by the following series carried out ad infinitum:

$e=1+{\frac {1}{1}}+{\frac {1}{1.2}}+{\frac {1}{1.2.3}}+{\frac {1}{1.2.3.4}}+{\frac {1}{1.2.3.4.5}}+{\text{etc.}}$

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:

$e=2.7182818{\text{ . . . }}$

With this weird number are we now sta-

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