Java Number Cruncher: The Java Programmer's Guide to Numerical Computing By Ronald Mak
Table of Contents
Part IV. The Joys of Computation
Chapter 13. Computing p
It is truly amazing that a number so easily described?athe ratio of a circle's circumference to its diameter?acould have occupied the minds of so many eminent mathematicians over the centuries. The number p is both irrational and transcendental , [1] and people have been attempting to devise formulas and algorithms that compute estimates of its value or that can generate as many of its exact digits as possible.
[1] An irrational number is one that cannot be expressed as the ratio of two integers. A transcendental number is one that cannot be the root of a polynomial equation with integer coefficients. Another transcendental number is e, the base of natural logarithms.
In this chapter, we'll look at some of these attempts. The BigFunctions class we wrote in Chapter 12 will enable us to test some of the formulas and algorithms.
