CHAPTER 1 9MemoryPi (Greek letter m) is defined as the ratio, for any circle, of the
circumference to the diameter (Fig. 19.1). Pican be a source of endless
fascination, and rightly so, because it shows up in a great many places
in mathematics and physics: Maxwell’s equations in electromag-
netism, Einstein’s gravitational field equations in general relativity,
the Schrédinger equation and Heisenberg uncertainly relations in
quantum mechanics, descriptions of vibrating or periodic motion of
all sorts, and so on. It is a deeply significant number in the mathemat-
ical language used to describe the cosmos.
Another aspect of fascination with 7 is that it is an irrational num-
ber—that is, m cannot be represented as a ratio of two integers, and
its decimal representation never ends and does not settle into a per-
manent repeating pattern. Thus, the value of m cannot be computed
exactly; it can only be estimated to greater and greater precision, to an
increasingly large number of decimal places.
Typically m is approximated as 3.14. To ten decimal places it is
3.1415926535. These approximations suffice for all practical pur-
poses. However, esoteric mathematical formulas have been derived
that allow 1 to be computed to an arbitrary number of decimal places,