IRRATIONALS AND IMAGINARY NUMBERS 121

In addition to the foregoing, there have been a surprising
number of suggestions as to how # could be expressed:

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Another remarkable quantity is the number ¢, the approxi-
mate value of which is 2-718281828459, so named after its dis-
coverer, Leonhard Euler. This number has many applica-
tions. It is closely associated with statistical theory and is of
immense importance in the calculus. It is the base to which
natural logarithms are calculated, and is also concerned in
compound interest calculations. This last use helps to give a
clearer picture of the nature of the number ¢ and is therefore
well worth a little attention.

If £1 is loaned at 2 per cent. compound interest per
annum, at the end of the first year the debt will have in-

creased to
£(1+-02)

If, however, the interest were to be reckoned at the end of
every month instead of at the end of every year, it would be
found to increase more rapidly. At the end of the first month,
the total debt would be:

(+3)

   

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TSP L.