mathematics Symbol π. The proportionality constant of the circle - of its circumference to its diameter and of its area to one quarter the area of the square within which it is precisely inscribed. A precise valuation for pi, albeit with very slow convergence, is given by
π = 4(1 - ⅓ + ⅕ - 1⁄7 + …)
= 3.141 592 653 589 793 238 462 643 383 279 502 884 197 169 399~with reciprocal
π-1 = 0.318 309 886 183 790 671 537 767 526 745 028 724 068 919 291~The number π is irrational, i.e. it cannot be expressed precisely as the quotient of two integers (and, further, it is transcendental - see number). It can, of course, be approximated to as closely as desired, starting with the rough estimate of 3 through the familiar 22/7 then onward. Some of the historic approximates, with discrepancy from true value, are:
