Mathematical philosophy, a study of fate and freedom; lectures for educated laymen, by Cassius J. Keyser.

VARIABLES AND LIMITS 251
things: observe, for example, that K is geometric,-a
specific curve,-and that, like R, L and A are numericalspecific numbers. Consider the indicated inscribed regular polygons-the triangle (or 3-side), hexagon (or 6-side),
do-decagon (or I2-side), 24-side, 48-side, and so on endlessly; note that the nth polygon of the unending row has
FIG. 26.
3 X2-~ sides. You see that n is a variable whose range
is the class of positive integers. Denote by P, the nth
polygon, by Ln the perimeter (length) of P,, by An the
area of (size or magnitude of) Pn, and by dn the length of
the perpendicular from C to a side of P.. The symbols
PJ, Ln, An and d. are variables. Which ones are geometric? Which numerical? They are functions of n.